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Class/Data Structure .ipynb

###Markdown Fundamental Data Structure :The fundamental data structure in python includes - **Primitive type** ( ***Integer, Float, String***, and ***Boolean***) and - **Non-Primitive type** ( ***Array, List, Tuples, Dictionary, Set***, and ***File***) In this tutorial, we are going to discudd about List, Tuples, Set and Dictionary. ListList is built in data structure in python. It is - Mutable i.e., we can change or edite the size of the list by appending, inserting and deleting the elements.- List can hold heterogeneous objects (e.g., integer, string, boolean)Lets try to understand the List: - To initiate a blank List. ###Code l = [] ###Output _____no_output_____ ###Markdown - To find the type of the object. ###Code type(l) ###Output _____no_output_____ ###Markdown - To create a list from scratch. ###Code L = [1,2,3,4,5,6,342,34] L ###Output _____no_output_____ ###Markdown - Indexing of list. ###Code L[0],L[1],L[5] ###Output _____no_output_____ ###Markdown - Revers indexing is also possible. ###Code L[-1],L[-2],L[-3] ###Output _____no_output_____ ###Markdown - To find the length of list. ###Code len(L) ###Output _____no_output_____ ###Markdown - To add the element from last. ###Code L.append(12) L ###Output _____no_output_____ ###Markdown - To find the sum of the elements (if they are of same types like int. double etc) ###Code sum(L) ###Output _____no_output_____ ###Markdown - To find maximum and minimum of the list ###Code max(L), min(L) ###Output _____no_output_____ ###Markdown - To create a list of heterogeneous element types. ###Code L = [1,2.0,3,4,5,"Apple",True, False] ###Output _____no_output_____ ###Markdown - To find the type of elements of a list. ###Code type(L[1]),type(L[5]) ###Output _____no_output_____ ###Markdown - To create a list of list. ###Code L = [[1,2,3],[3,4,5],[5,7,9]] ###Output _____no_output_____ ###Markdown - To find list inside a list. ###Code L[0] L[0][1] ###Output _____no_output_____ ###Markdown - To add two list. It is not as ususal addition. The elements are accumulated. ###Code L1 = [1,2,3] ; L2 = [2,4,6] L1+L2, set(L1+L2) ###Output _____no_output_____ ###Markdown - To add element from end of the list ###Code L = [1,4,2,3,5,6,7] L.append(100) L ###Output _____no_output_____ ###Markdown - To insert element (100) at specific index (1) ###Code L = [1,4,2,3,5,6,7] L.insert(1,100) L ###Output _____no_output_____ ###Markdown - To remove specific element form list. It will remove the first occurance. ###Code L = [1,4,2,3,5,6,7,4] L.remove(4) L ###Output _____no_output_____ ###Markdown - To remove the element from specific index ###Code x=[43,23,12,56,78,89,90] x.pop(-4) x L = [1,4,2,3,5,6,7] L.pop(-1) L ###Output _____no_output_____ ###Markdown - To sort the list ###Code L = [1,10,2,30,5,60,7] L.sort() L ###Output _____no_output_____ ###Markdown To reverse the list ###Code L = [1,4,2,3,5,6,7] L.reverse() L ###Output _____no_output_____ ###Markdown - List comprehension ###Code L = [x for x in range(100)] print(L) L = [x for x in range(100) if x%2==0] print(L) import random as rn rn.randint(0,100) import random as rn R = [rn.randint(0,50) for k in range(200)] print(R) import collections #High Performance Counting C = collections.Counter(R) print(C) R = [rn.choice(['A','T','G','C']) for i in range(200)] print(R) DNA = ''.join(R) DNA DNA.count('A'), DNA.count('AT'), DNA.count('ATG') ###Output _____no_output_____ ###Markdown Mini Assignment:Create a DNA string of 10,000 characters and count the following: A,T,G,C,all combination of two charaters, all combinations of three characters. TuplesTuples are non-mutable, which means we can ot add or remove elements once tuple is defind. - To define a tuples from scratch ###Code t = (2,3,4,5) ###Output _____no_output_____ ###Markdown - Find type ###Code type(t) ###Output _____no_output_____ ###Markdown - Indexing ###Code t[1] L = [(1,2),(2,3),(3,4)] L[0][0] ###Output _____no_output_____ ###Markdown - Create a list of tuples ###Code L = [(1,2),("a","b"),(True, False)] L ###Output _____no_output_____ ###Markdown DictionaryDictionary organizes the data with key-value pair. Dictionary can be nested with other data types. - To initiate a dictionary ###Code D = dict() DD = {} ###Output _____no_output_____ ###Markdown - Create a dictionary from scratch ###Code D = {"fruit":'apple', "vegetable" : 'carrot', "rice": 2.0, 'milk': 10,} ###Output _____no_output_____ ###Markdown - What are keys? ###Code D.keys() ###Output _____no_output_____ ###Markdown - What are values? ###Code D.values() ###Output _____no_output_____ ###Markdown - Indexing ###Code D['fruit'], D["rice"] ###Output _____no_output_____ ###Markdown - Iteration over key and values ###Code for key,value in D.items(): print(key,value) ###Output fruit apple vegetable carrot rice 2.0 milk 10 ###Markdown - To update a dictionary ###Code D.update({"salt": 2.0}) D ###Output _____no_output_____ ###Markdown - To create a list form a Dictionary. Only keys are collected. ###Code list(D) ###Output _____no_output_____ ###Markdown - To create a list of keys only ###Code list(D.keys()) ###Output _____no_output_____ ###Markdown - To create a list of values ###Code list(D.values()) ###Output _____no_output_____ ###Markdown - To create Dictionary of with list, tuples and dictionary ###Code DD = {"names":("John","Harry", "Brat"),\ "roll no": [1,2,3],\ "plan":{"first":[12,34,56],"second":[1,3,5]}} DD import numpy as np X = np.arange(0,np.pi,0.1) print(X) import numpy as np X = np.arange(0,np.pi,0.1) M = {"sin": [np.sin(x) for x in X],\ "cos": [np.cos(x) for x in X],\ "plo":[(x*x+x+1) for x in X],\ "trig": [np.cos(x) + np.sin(x) for x in X]} print(M) import pandas as pd DF = pd.DataFrame(M) DF %matplotlib inline DF.plot() ###Output _____no_output_____

lab2/Part1_MNIST.ipynb

###Markdown Run in Google Colab Copyright Information ###Code # Copyright 2022 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # Modified by Martin Keller-Ressel 2022. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code HUI NAHUI # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 19.4MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=c5e28807a40d465d00e86c5936c4201c3e50a22984dced2e5d3f6887366bf8ce Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' #'''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0837 - accuracy: 0.9766 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0746 - accuracy: 0.9791 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0673 - accuracy: 0.9813 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0608 - accuracy: 0.9835 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0522 - accuracy: 0.9852 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0782 - accuracy: 0.9771 Test accuracy: 0.9771000146865845 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, (3,3), activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(24, (3,3), activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output #'''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 24) 5208 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 24) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 600) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 76928 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 83,666 Trainable params: 83,666 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(tf.keras.optimizers.Adam(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0386 - accuracy: 0.9883 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0217 - accuracy: 0.9934 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0126 - accuracy: 0.9961 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0104 - accuracy: 0.9970 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0079 - accuracy: 0.9975 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) # TODO print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0782 - accuracy: 0.9771 Test accuracy: 0.9771000146865845 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) # TODO print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 33 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_weights) # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 # %tensorflow_version 2.x import tensorflow as tf # !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation='relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - ETA: 8:12 - loss: 2.4209 - accuracy: 0.03 - ETA: 29s - loss: 1.8236 - accuracy: 0.4748 - ETA: 17s - loss: 1.4829 - accuracy: 0.610 - ETA: 11s - loss: 1.2191 - accuracy: 0.682 - ETA: 8s - loss: 1.0395 - accuracy: 0.729 - ETA: 7s - loss: 0.9206 - accuracy: 0.76 - ETA: 6s - loss: 0.8452 - accuracy: 0.78 - ETA: 5s - loss: 0.7855 - accuracy: 0.79 - ETA: 4s - loss: 0.7295 - accuracy: 0.81 - ETA: 4s - loss: 0.6951 - accuracy: 0.81 - ETA: 3s - loss: 0.6655 - accuracy: 0.82 - ETA: 3s - loss: 0.6377 - accuracy: 0.83 - ETA: 3s - loss: 0.6139 - accuracy: 0.83 - ETA: 3s - loss: 0.5915 - accuracy: 0.84 - ETA: 2s - loss: 0.5727 - accuracy: 0.84 - ETA: 2s - loss: 0.5568 - accuracy: 0.85 - ETA: 2s - loss: 0.5444 - accuracy: 0.85 - ETA: 2s - loss: 0.5328 - accuracy: 0.85 - ETA: 2s - loss: 0.5210 - accuracy: 0.85 - ETA: 2s - loss: 0.5112 - accuracy: 0.86 - ETA: 2s - loss: 0.5024 - accuracy: 0.86 - ETA: 1s - loss: 0.4918 - accuracy: 0.86 - ETA: 1s - loss: 0.4839 - accuracy: 0.86 - ETA: 1s - loss: 0.4741 - accuracy: 0.87 - ETA: 1s - loss: 0.4677 - accuracy: 0.87 - ETA: 1s - loss: 0.4619 - accuracy: 0.87 - ETA: 1s - loss: 0.4550 - accuracy: 0.87 - ETA: 1s - loss: 0.4497 - accuracy: 0.87 - ETA: 1s - loss: 0.4442 - accuracy: 0.87 - ETA: 1s - loss: 0.4382 - accuracy: 0.88 - ETA: 1s - loss: 0.4339 - accuracy: 0.88 - ETA: 1s - loss: 0.4281 - accuracy: 0.88 - ETA: 0s - loss: 0.4226 - accuracy: 0.88 - ETA: 0s - loss: 0.4184 - accuracy: 0.88 - ETA: 0s - loss: 0.4136 - accuracy: 0.88 - ETA: 0s - loss: 0.4103 - accuracy: 0.88 - ETA: 0s - loss: 0.4054 - accuracy: 0.88 - ETA: 0s - loss: 0.4025 - accuracy: 0.88 - ETA: 0s - loss: 0.3994 - accuracy: 0.88 - ETA: 0s - loss: 0.3960 - accuracy: 0.89 - 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accuracy: 0.94 - ETA: 1s - loss: 0.2124 - accuracy: 0.93 - ETA: 1s - loss: 0.2121 - accuracy: 0.93 - ETA: 1s - loss: 0.2111 - accuracy: 0.93 - ETA: 1s - loss: 0.2088 - accuracy: 0.94 - ETA: 1s - loss: 0.2088 - accuracy: 0.94 - ETA: 1s - loss: 0.2074 - accuracy: 0.94 - ETA: 1s - loss: 0.2067 - accuracy: 0.94 - ETA: 1s - loss: 0.2066 - accuracy: 0.94 - ETA: 1s - loss: 0.2060 - accuracy: 0.94 - ETA: 1s - loss: 0.2064 - accuracy: 0.94 - ETA: 1s - loss: 0.2068 - accuracy: 0.94 - ETA: 1s - loss: 0.2063 - accuracy: 0.94 - ETA: 1s - loss: 0.2057 - accuracy: 0.94 - ETA: 0s - loss: 0.2047 - accuracy: 0.94 - ETA: 0s - loss: 0.2052 - accuracy: 0.94 - ETA: 0s - loss: 0.2040 - accuracy: 0.94 - ETA: 0s - loss: 0.2025 - accuracy: 0.94 - ETA: 0s - loss: 0.2023 - accuracy: 0.94 - ETA: 0s - loss: 0.2028 - accuracy: 0.94 - ETA: 0s - loss: 0.2024 - accuracy: 0.94 - ETA: 0s - loss: 0.2024 - accuracy: 0.94 - ETA: 0s - loss: 0.2019 - accuracy: 0.94 - ETA: 0s - loss: 0.2013 - accuracy: 0.94 - ETA: 0s - loss: 0.2010 - accuracy: 0.94 - ETA: 0s - loss: 0.2005 - accuracy: 0.94 - ETA: 0s - loss: 0.1997 - accuracy: 0.94 - ETA: 0s - loss: 0.1994 - accuracy: 0.94 - ETA: 0s - loss: 0.1992 - accuracy: 0.94 - ETA: 0s - loss: 0.1983 - accuracy: 0.94 - ETA: 0s - loss: 0.1973 - accuracy: 0.94 - ETA: 0s - loss: 0.1965 - accuracy: 0.94 - ETA: 0s - loss: 0.1959 - accuracy: 0.94 - 2s 40us/sample - loss: 0.1958 - accuracy: 0.9436 Epoch 3/5 60000/60000 [==============================] - ETA: 2s - loss: 0.2652 - accuracy: 0.90 - ETA: 2s - loss: 0.1619 - accuracy: 0.95 - ETA: 2s - loss: 0.1486 - accuracy: 0.96 - ETA: 2s - loss: 0.1544 - accuracy: 0.95 - ETA: 2s - loss: 0.1584 - accuracy: 0.95 - ETA: 2s - loss: 0.1618 - accuracy: 0.95 - ETA: 2s - loss: 0.1625 - accuracy: 0.95 - ETA: 2s - loss: 0.1610 - accuracy: 0.95 - ETA: 1s - loss: 0.1566 - accuracy: 0.95 - ETA: 1s - loss: 0.1541 - accuracy: 0.95 - ETA: 1s - loss: 0.1561 - accuracy: 0.95 - ETA: 1s - loss: 0.1544 - accuracy: 0.95 - ETA: 1s - loss: 0.1547 - accuracy: 0.95 - ETA: 1s - loss: 0.1525 - accuracy: 0.95 - ETA: 1s - loss: 0.1513 - accuracy: 0.95 - ETA: 1s - loss: 0.1525 - accuracy: 0.95 - ETA: 1s - loss: 0.1509 - accuracy: 0.95 - ETA: 1s - loss: 0.1498 - accuracy: 0.95 - ETA: 1s - loss: 0.1516 - accuracy: 0.95 - ETA: 1s - loss: 0.1512 - accuracy: 0.95 - ETA: 1s - loss: 0.1511 - accuracy: 0.95 - ETA: 1s - loss: 0.1507 - accuracy: 0.95 - ETA: 1s - loss: 0.1501 - accuracy: 0.95 - ETA: 1s - loss: 0.1501 - accuracy: 0.95 - ETA: 1s - loss: 0.1496 - accuracy: 0.95 - ETA: 1s - loss: 0.1502 - accuracy: 0.95 - ETA: 1s - loss: 0.1500 - accuracy: 0.95 - ETA: 1s - loss: 0.1492 - accuracy: 0.95 - ETA: 0s - loss: 0.1493 - accuracy: 0.95 - ETA: 0s - loss: 0.1500 - accuracy: 0.95 - ETA: 0s - loss: 0.1499 - accuracy: 0.95 - ETA: 0s - loss: 0.1497 - accuracy: 0.95 - ETA: 0s - loss: 0.1492 - accuracy: 0.95 - ETA: 0s - loss: 0.1482 - accuracy: 0.95 - ETA: 0s - loss: 0.1479 - accuracy: 0.95 - ETA: 0s - loss: 0.1477 - accuracy: 0.95 - ETA: 0s - loss: 0.1469 - accuracy: 0.95 - ETA: 0s - loss: 0.1457 - accuracy: 0.95 - ETA: 0s - loss: 0.1459 - accuracy: 0.95 - ETA: 0s - loss: 0.1457 - accuracy: 0.95 - ETA: 0s - loss: 0.1468 - accuracy: 0.95 - ETA: 0s - loss: 0.1467 - accuracy: 0.95 - ETA: 0s - loss: 0.1467 - accuracy: 0.95 - ETA: 0s - loss: 0.1464 - accuracy: 0.95 - ETA: 0s - loss: 0.1461 - accuracy: 0.95 - ETA: 0s - loss: 0.1458 - accuracy: 0.95 - ETA: 0s - loss: 0.1454 - accuracy: 0.95 - 2s 40us/sample - loss: 0.1451 - accuracy: 0.9590 Epoch 4/5 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code test_loss, test_acc = model.evaluate(x=test_images, y=test_labels, verbose=2) print('Test accuracy:', test_acc) ###Output 10000/10000 - 1s - loss: 0.1047 - accuracy: 0.9698 Test accuracy: 0.9698 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3, 3), strides=(1,1 )), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3, 3), strides=(1, 1)), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_2 (Conv2D) multiple 240 _________________________________________________________________ max_pooling2d_2 (MaxPooling2 multiple 0 _________________________________________________________________ conv2d_3 (Conv2D) multiple 7812 _________________________________________________________________ max_pooling2d_3 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_2 (Flatten) multiple 0 _________________________________________________________________ dense_3 (Dense) multiple 115328 _________________________________________________________________ dense_4 (Dense) multiple 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' opt = tf.keras.optimizers.Adam(learning_rate=0.005) cnn_model.compile(optimizer=opt, loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' BATCH_SIZE = 64 EPOCHS = 5 cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - ETA: 12s - loss: 0.0323 - accuracy: 0.984 - ETA: 5s - loss: 0.1254 - accuracy: 0.985 - ETA: 4s - loss: 0.0938 - accuracy: 0.98 - ETA: 4s - loss: 0.0820 - accuracy: 0.98 - ETA: 4s - loss: 0.1142 - accuracy: 0.98 - ETA: 3s - loss: 0.1085 - accuracy: 0.98 - ETA: 3s - loss: 0.0975 - accuracy: 0.98 - ETA: 3s - loss: 0.0901 - accuracy: 0.98 - ETA: 3s - loss: 0.0882 - accuracy: 0.98 - ETA: 3s - loss: 0.0806 - accuracy: 0.98 - ETA: 3s - loss: 0.0742 - accuracy: 0.98 - ETA: 3s - loss: 0.0703 - accuracy: 0.99 - ETA: 3s - loss: 0.0692 - accuracy: 0.99 - ETA: 3s - loss: 0.0679 - accuracy: 0.99 - ETA: 3s - loss: 0.0633 - accuracy: 0.99 - ETA: 3s - loss: 0.0608 - accuracy: 0.99 - ETA: 3s - loss: 0.0639 - accuracy: 0.99 - ETA: 3s - loss: 0.0662 - accuracy: 0.99 - ETA: 3s - loss: 0.0635 - accuracy: 0.99 - ETA: 3s - 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loss: 0.0490 - accuracy: 0.99 - ETA: 0s - loss: 0.0500 - accuracy: 0.99 - ETA: 0s - loss: 0.0502 - accuracy: 0.99 - ETA: 0s - loss: 0.0499 - accuracy: 0.99 - ETA: 0s - loss: 0.0507 - accuracy: 0.99 - ETA: 0s - loss: 0.0509 - accuracy: 0.99 - ETA: 0s - loss: 0.0507 - accuracy: 0.99 - ETA: 0s - loss: 0.0510 - accuracy: 0.99 - ETA: 0s - loss: 0.0509 - accuracy: 0.99 - ETA: 0s - loss: 0.0502 - accuracy: 0.99 - ETA: 0s - loss: 0.0504 - accuracy: 0.99 - 4s 68us/sample - loss: 0.0507 - accuracy: 0.9924 Epoch 2/5 60000/60000 [==============================] - ETA: 4s - loss: 4.5461e-06 - accuracy: 1.00 - ETA: 4s - loss: 0.0267 - accuracy: 0.9952 - ETA: 4s - loss: 0.0598 - accuracy: 0.99 - ETA: 4s - loss: 0.0653 - accuracy: 0.99 - ETA: 4s - loss: 0.0721 - accuracy: 0.99 - ETA: 3s - loss: 0.0615 - accuracy: 0.99 - ETA: 3s - loss: 0.0657 - accuracy: 0.99 - ETA: 3s - loss: 0.0610 - accuracy: 0.99 - ETA: 3s - loss: 0.0571 - accuracy: 0.99 - ETA: 3s - loss: 0.0597 - accuracy: 0.99 - ETA: 3s - loss: 0.0574 - 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accuracy: 0.99 - ETA: 0s - loss: 0.0748 - accuracy: 0.99 - ETA: 0s - loss: 0.0762 - accuracy: 0.99 - ETA: 0s - loss: 0.0796 - accuracy: 0.99 - ETA: 0s - loss: 0.0828 - accuracy: 0.99 - ETA: 0s - loss: 0.0840 - accuracy: 0.99 - ETA: 0s - loss: 0.0845 - accuracy: 0.99 - ETA: 0s - loss: 0.0863 - accuracy: 0.99 - ETA: 0s - loss: 0.0858 - accuracy: 0.99 - ETA: 0s - loss: 0.0860 - accuracy: 0.99 - ETA: 0s - loss: 0.0865 - accuracy: 0.99 - ETA: 0s - loss: 0.0865 - accuracy: 0.99 - ETA: 0s - loss: 0.0863 - accuracy: 0.99 - ETA: 0s - loss: 0.0871 - accuracy: 0.99 - ETA: 0s - loss: 0.0879 - accuracy: 0.99 - ETA: 0s - loss: 0.0869 - accuracy: 0.99 - ETA: 0s - loss: 0.0876 - accuracy: 0.99 - 4s 65us/sample - loss: 0.0871 - accuracy: 0.9909 Epoch 3/5 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(x=test_images, y=test_labels, verbose=2) print('Test accuracy:', test_acc) ###Output 10000/10000 - 1s - loss: 0.3903 - accuracy: 0.9825 Test accuracy: 0.9825 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions, axis=1) print(prediction) ###Output [7 2 1 ... 4 5 6] ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 # %tensorflow_version 2.x import tensorflow as tf # !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices("GPU")) > 0 gpus = tf.config.experimental.list_physical_devices("GPU") if gpus: try: # Currently, memory growth needs to be the same across GPUs for gpu in gpus: tf.config.experimental.set_memory_growth(gpu, True) logical_gpus = tf.config.experimental.list_logical_devices("GPU") print(len(gpus), "Physical GPUs,", len(logical_gpus), "Logical GPUs") except RuntimeError as e: # Memory growth must be set before GPUs have been initialized print(e) ###Output 1 Physical GPUs, 1 Logical GPUs ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1) / 255.0).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1) / 255.0).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10, 10)) random_inds = np.random.choice(60000, 36) for i in range(36): plt.subplot(6, 6, i + 1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential( [ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation="relu"), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation="softmax"), ] ) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code """TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?""" model.compile( optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss="sparse_categorical_crossentropy", metrics=["accuracy"], ) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code train_labels[:10] # notice train labels are in raw; in this case use sparse categorial cross entropy # , when the output is one-hot probability # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 1s 1ms/step - loss: 0.2958 - accuracy: 0.9164 Epoch 2/5 938/938 [==============================] - 1s 1ms/step - loss: 0.1356 - accuracy: 0.9603 Epoch 3/5 938/938 [==============================] - 1s 1ms/step - loss: 0.0945 - accuracy: 0.9722 Epoch 4/5 938/938 [==============================] - 1s 1ms/step - loss: 0.0716 - accuracy: 0.9790 Epoch 5/5 938/938 [==============================] - 1s 1ms/step - loss: 0.0567 - accuracy: 0.9832 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code """TODO: Use the evaluate method to test the model!""" test_loss, test_acc = model.evaluate(test_images, test_labels) print("Test accuracy:", test_acc) ###Output 1/313 [..............................] - ETA: 0s - loss: 0.0131 - accuracy: 1.0000WARNING:tensorflow:Callbacks method `on_test_batch_end` is slow compared to the batch time (batch time: 0.0000s vs `on_test_batch_end` time: 0.0010s). Check your callbacks. 313/313 [==============================] - 0s 961us/step - loss: 0.0808 - accuracy: 0.9759 Test accuracy: 0.9758999943733215 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential( [ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3, 3), activation="relu"), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3, 3), activation="relu"), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation="softmax"), ] ) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 900) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 115328 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code """TODO: Define the compile operation with your optimizer and learning rate of choice""" cnn_model.compile( optimizer="adam", loss="sparse_categorical_crossentropy", metrics=["accuracy"] ) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code """TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.""" cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1927 - accuracy: 0.9416 Epoch 2/5 938/938 [==============================] - 1s 2ms/step - loss: 0.0574 - accuracy: 0.9816 Epoch 3/5 938/938 [==============================] - 1s 2ms/step - loss: 0.0380 - accuracy: 0.9883 Epoch 4/5 938/938 [==============================] - 1s 2ms/step - loss: 0.0288 - accuracy: 0.9906 Epoch 5/5 938/938 [==============================] - 1s 2ms/step - loss: 0.0220 - accuracy: 0.9931 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code """TODO: Use the evaluate method to test the model!""" test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print("Test accuracy:", test_acc) ###Output 313/313 [==============================] - 0s 1ms/step - loss: 0.0399 - accuracy: 0.9868 Test accuracy: 0.9868000149726868 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code """TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. """ prediction = tf.math.argmax(predictions, axis=1) print(prediction) ###Output tf.Tensor([7 2 1 ... 4 5 6], shape=(10000,), dtype=int64) ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0, :, :, 0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code # @title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 # @param {type:"slider", min:0, max:100, step:1} plt.subplot(1, 2, 1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1, 2, 2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows * num_cols plt.figure(figsize=(2 * 2 * num_cols, 2 * num_rows)) for i in range(num_images): plt.subplot(num_rows, 2 * num_cols, 2 * i + 1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2 * num_cols, 2 * i + 2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory( smoothing_factor=0.95 ) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter( sec=2, xlabel="Iterations", ylabel="Loss", scale="semilogy" ) optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3) # define our optimizer if hasattr(tqdm, "_instances"): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = ( train_images[idx : idx + batch_size], train_labels[idx : idx + batch_size], ) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) # TODO # this is bad; the outputs are a probability distribution, dont use from_logits # only if output is linear activation, use from logits #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) loss_history.append( loss_value.numpy().mean() ) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation """TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.""" grads = tape.gradient(loss_value, cnn_model.trainable_variables) # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 print("GitHub Copy") ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 21.9MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp36-none-any.whl size=2115443 sha256=df0a542026961a51ea928616268be92b310063185e5dd57b3841607c422ae946 Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 2ms/step - loss: 0.5783 - accuracy: 0.8405 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2139 - accuracy: 0.9388 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1569 - accuracy: 0.9559 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1281 - accuracy: 0.9641 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1069 - accuracy: 0.9696 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1043 - accuracy: 0.9685 Test accuracy: 0.968500018119812 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, 3, activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, 3, activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax), ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_3" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_2 (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d_2 (MaxPooling2 (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_3 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_3 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_3 (Flatten) (None, 900) 0 _________________________________________________________________ dense_6 (Dense) (None, 128) 115328 _________________________________________________________________ dense_7 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-2), loss=tf.keras.losses.sparse_categorical_crossentropy, metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels,batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 1.5165 - accuracy: 0.5091 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2605 - accuracy: 0.9214 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1737 - accuracy: 0.9486 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1276 - accuracy: 0.9611 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1066 - accuracy: 0.9669 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(x=train_images, y=train_labels) print('Test accuracy:', test_acc) ###Output 1875/1875 [==============================] - 3s 2ms/step - loss: 0.0939 - accuracy: 0.9717 Test accuracy: 0.971666693687439 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = tf.math.argmax(predictions[0]) print(prediction) ###Output tf.Tensor(7, shape=(), dtype=int64) ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 89 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 5.4MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=ba6653417f01557b3ff95f63fe0fb7b6fa4356112a869406e7fce52b2259df38 Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10,activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 2ms/step - loss: 0.6001 - accuracy: 0.8318 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2083 - accuracy: 0.9411 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1554 - accuracy: 0.9559 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1233 - accuracy: 0.9655 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1009 - accuracy: 0.9714 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images,test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1015 - accuracy: 0.9704 Test accuracy: 0.9703999757766724 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24,3), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(24,3), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size= (2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 24) 5208 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 24) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 600) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 76928 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 83,666 Trainable params: 83,666 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 5ms/step - loss: 0.5107 - accuracy: 0.8403 Epoch 2/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0696 - accuracy: 0.9777 Epoch 3/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0462 - accuracy: 0.9859 Epoch 4/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0354 - accuracy: 0.9888 Epoch 5/5 938/938 [==============================] - 4s 4ms/step - loss: 0.0287 - accuracy: 0.9911 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images,test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1015 - accuracy: 0.9704 Test accuracy: 0.9703999757766724 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0], axis = 0) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 63 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2022 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning Downloading mitdeeplearning-0.2.0.tar.gz (2.1 MB)  |████████████████████████████████| 2.1 MB 5.4 MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.62.3) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-py3-none-any.whl size=2115442 sha256=952b91ac8700186ceb8d5ac4a3837b999aebfadff82ec1f649db538002da613f Stored in directory: /root/.cache/pip/wheels/9a/b9/4f/99b7c8c5c75355550b83e1fcfc02956fb40c35eb01e2262877 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step 11501568/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation= 'softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 3ms/step - loss: 0.3719 - accuracy: 0.8959 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.2006 - accuracy: 0.9435 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1508 - accuracy: 0.9569 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1221 - accuracy: 0.9648 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1022 - accuracy: 0.9719 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.1042 - accuracy: 0.9679 Test accuracy: 0.9678999781608582 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, 3), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(24, 3), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation= 'softmax'), ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 max_pooling2d (MaxPooling2D (None, 13, 13, 24) 0 ) conv2d_1 (Conv2D) (None, 11, 11, 24) 5208 max_pooling2d_1 (MaxPooling (None, 5, 5, 24) 0 2D) flatten_2 (Flatten) (None, 600) 0 dense_4 (Dense) (None, 128) 76928 dense_5 (Dense) (None, 10) 1290 ================================================================= Total params: 83,666 Trainable params: 83,666 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels) ###Output 1875/1875 [==============================] - 9s 4ms/step - loss: 0.1729 - accuracy: 0.9461 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 4ms/step - loss: 0.0529 - accuracy: 0.9821 Test accuracy: 0.9821000099182129 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation # '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. # Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown 1.5 ConclusionIn this part of the lab, you had the chance to play with different MNIST classifiers with different architectures (fully-connected layers only, CNN), and experiment with how different hyperparameters affect accuracy (learning rate, etc.). The next part of the lab explores another application of CNNs, facial detection, and some drawbacks of AI systems in real world applications, like issues of bias. ###Code ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 #%tensorflow_version 2.x import tensorflow as tf #!pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 2s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' # '''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 1s 1ms/step - loss: 0.3685 - accuracy: 0.8964 Epoch 2/5 938/938 [==============================] - 1s 1ms/step - loss: 0.2011 - accuracy: 0.9425 Epoch 3/5 938/938 [==============================] - 1s 1ms/step - loss: 0.1516 - accuracy: 0.9571 Epoch 4/5 938/938 [==============================] - 1s 1ms/step - loss: 0.1231 - accuracy: 0.9654 Epoch 5/5 938/938 [==============================] - 1s 1ms/step - loss: 0.1038 - accuracy: 0.9709 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) # TODO print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 0s 1ms/step - loss: 0.1053 - accuracy: 0.9692 Test accuracy: 0.9692000150680542 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3, 3), activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3, 3), activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output # '''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_3" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_5 (Flatten) (None, 900) 0 _________________________________________________________________ dense_7 (Dense) (None, 128) 115328 _________________________________________________________________ dense_8 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-4), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0242 - accuracy: 0.9930 Epoch 2/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0170 - accuracy: 0.9948 Epoch 3/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0136 - accuracy: 0.9956 Epoch 4/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0115 - accuracy: 0.9963 Epoch 5/5 938/938 [==============================] - 4s 5ms/step - loss: 0.0099 - accuracy: 0.9967 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) # TODO print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0528 - accuracy: 0.9878 Test accuracy: 0.9878000020980835 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) # TODO print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO''') # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO''') # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO''') # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO''') tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous ***Use data is this web site*** [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. 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mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=5dd9774f524a941806e3bbb116dc1b4d9311a34cccc328e58a4c883aeb641ba1 Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below:[Alt_text](https://github.com/Jagadambass/Intro-to-TensorFlow-Music-Generation/blob/main/lab2/img/mnist_2layers_arch.png ) Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) # [TODO Dense layer to output classification probabilities] ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 2ms/step - loss: 0.5906 - accuracy: 0.8387 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2113 - accuracy: 0.9393 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1549 - accuracy: 0.9561 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1222 - accuracy: 0.9655 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1064 - accuracy: 0.9706 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) # TODO # test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1028 - accuracy: 0.9694 Test accuracy: 0.9693999886512756 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below:[Alt_text 2](https://github.com/Jagadambass/Intro-to-TensorFlow-Music-Generation/blob/main/lab2/img/mnist_model.png) Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # tf.keras.layers.Conv2D('''TODO''') # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # tf.keras.layers.MaxPool2D('''TODO''') # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation=tf.nn.relu), # tf.keras.layers.Conv2D('''TODO''') # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # tf.keras.layers.MaxPool2D('''TODO''') tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) # [TODO Dense layer to output classification probabilities] ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 900) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 115328 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) # cnn_model.fit('''TODO''') ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.4458 - accuracy: 0.8681 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0615 - accuracy: 0.9813 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0378 - accuracy: 0.9887 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0281 - accuracy: 0.9917 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0223 - accuracy: 0.9930 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) # test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0346 - accuracy: 0.9890 Test accuracy: 0.9890000224113464 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) # prediction = # TODO print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) # logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) # grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 4.9MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.18.3) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.38.0) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.1) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.4.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.12.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114586 sha256=2fb8d25e5c19d8aceb1295b7f219dabc22bfb52175abb5f64d3cadb70c70c1f7 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation='relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.3696 - accuracy: 0.8982 Epoch 2/5 938/938 [==============================] - 2s 3ms/step - loss: 0.1973 - accuracy: 0.9435 Epoch 3/5 938/938 [==============================] - 2s 3ms/step - loss: 0.1471 - accuracy: 0.9580 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1188 - accuracy: 0.9661 Epoch 5/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0995 - accuracy: 0.9724 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1021 - accuracy: 0.9701 Test accuracy: 0.9700999855995178 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, 3, activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D((2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, 3, activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D((2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) multiple 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) multiple 0 _________________________________________________________________ conv2d_1 (Conv2D) multiple 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_1 (Flatten) multiple 0 _________________________________________________________________ dense_2 (Dense) multiple 115328 _________________________________________________________________ dense_3 (Dense) multiple 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=64, epochs=5) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1768 - accuracy: 0.9488 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0500 - accuracy: 0.9842 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0356 - accuracy: 0.9888 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0271 - accuracy: 0.9915 Epoch 5/5 938/938 [==============================] - 3s 4ms/step - loss: 0.0208 - accuracy: 0.9934 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0254 - accuracy: 0.9918 Test accuracy: 0.9918000102043152 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 99 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) print(loss_history.get()[-1]) ###Output 0.11113820937167927 ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |▏ | 10kB 24.2MB/s eta 0:00:01  |▎ | 20kB 30.4MB/s eta 0:00:01  |▌ | 30kB 25.6MB/s eta 0:00:01  |▋ | 40kB 29.2MB/s eta 0:00:01  |▉ | 51kB 27.0MB/s eta 0:00:01  |█ | 61kB 29.4MB/s eta 0:00:01  |█ | 71kB 19.3MB/s eta 0:00:01  |█▎ | 81kB 20.5MB/s eta 0:00:01  |█▍ | 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mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=cfa59a6e21e0a4f684315668eeb5a8f9ba442b8322081586eed21b9b1e39cc9d Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer="Adam", loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.9742 - accuracy: 0.6483 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0344 - accuracy: 0.9898 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0238 - accuracy: 0.9932 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0176 - accuracy: 0.9952 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0160 - accuracy: 0.9956 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0742 - accuracy: 0.9805 Test accuracy: 0.9804999828338623 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, 3, activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(2), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, 3, activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(2), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_6" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_10 (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d_10 (MaxPooling (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_11 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_11 (MaxPooling (None, 5, 5, 36) 0 _________________________________________________________________ flatten_6 (Flatten) (None, 900) 0 _________________________________________________________________ dense_12 (Dense) (None, 128) 115328 _________________________________________________________________ dense_13 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.4002 - accuracy: 0.8868 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0524 - accuracy: 0.9839 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0342 - accuracy: 0.9892 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0246 - accuracy: 0.9923 Epoch 5/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0192 - accuracy: 0.9942 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0270 - accuracy: 0.9909 Test accuracy: 0.9908999800682068 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 100 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 8.7MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=5e360b6e574dfb253b60d711107e4b6c7e2f3c22f239f8f4dd30d6c8738834a6 Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() print(train_images.shape) train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) print(train_images.shape) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step (60000, 28, 28) (60000, 28, 28, 1) ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation="relu"), # '''TODO: Define the second Dense layer to output the classification probabilities''' # '''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation="softmax"), ]) return fc_model model = build_fc_model() input_shape = (4, 28, 28, 3) ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) tf.keras.utils.plot_model(model, "my_first_model.png",show_shapes=True) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) test_loss, test_acc = model.evaluate(x=test_images,y=test_labels,batch_size=BATCH_SIZE)# TODO print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 1s 2ms/step - loss: 0.1113 - accuracy: 0.9679 Test accuracy: 0.9678999781608582 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24,3,input_shape=train_images.shape[1:]), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36,3), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output #'''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation="softmax"), ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 900) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 115328 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 4s 3ms/step - loss: 0.2026 - accuracy: 0.9423 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0657 - accuracy: 0.9801 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0455 - accuracy: 0.9863 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0339 - accuracy: 0.9896 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0263 - accuracy: 0.9922 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code # '''TODO: Use the evaluate method to test the model!''' # test_loss, test_acc = # TODO cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) test_loss, test_acc = cnn_model.evaluate(x=test_images,y=test_labels,batch_size=BATCH_SIZE)# TODO print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 1s 2ms/step - loss: 0.0354 - accuracy: 0.9882 Test accuracy: 0.9882000088691711 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] type(predictions) ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = predictions.argmax(axis=1)# TODO print(prediction) ###Output [7 2 1 ... 4 5 6] ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 31 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images,training=True)# TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels,logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Requirement already satisfied: mitdeeplearning in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (0.2.0) Requirement already satisfied: numpy in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from mitdeeplearning) (1.19.1) Requirement already satisfied: gym in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from mitdeeplearning) (0.18.0) Requirement already satisfied: regex in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from mitdeeplearning) (2021.4.4) Requirement already satisfied: tqdm in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from mitdeeplearning) (4.60.0) Requirement already satisfied: Pillow<=7.2.0 in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from gym->mitdeeplearning) (7.2.0) Requirement already satisfied: scipy in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from gym->mitdeeplearning) (1.5.2) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from gym->mitdeeplearning) (1.6.0) Requirement already satisfied: future in c:\users\dell\.conda\envs\tensorflow\lib\site-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.18.2) ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 9s 1us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) # [TODO Dense layer to output classification probabilities] ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - 4s 67us/sample - loss: 0.3751 - accuracy: 0.8956 Epoch 2/5 60000/60000 [==============================] - 3s 51us/sample - loss: 0.2010 - accuracy: 0.9431 Epoch 3/5 60000/60000 [==============================] - 3s 45us/sample - loss: 0.1499 - accuracy: 0.9572 Epoch 4/5 60000/60000 [==============================] - 3s 47us/sample - loss: 0.1208 - accuracy: 0.9658 Epoch 5/5 60000/60000 [==============================] - 3s 48us/sample - loss: 0.1024 - accuracy: 0.9707 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) # TODO # test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output 10000/1 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- 1s 63us/sample - loss: 0.0550 - accuracy: 0.9699 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) multiple 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) multiple 0 _________________________________________________________________ conv2d_1 (Conv2D) multiple 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_2 (Flatten) multiple 0 _________________________________________________________________ dense_4 (Dense) multiple 115328 _________________________________________________________________ dense_5 (Dense) multiple 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - 34s 572us/sample - loss: 0.1722 - accuracy: 0.9489 Epoch 2/5 60000/60000 [==============================] - 36s 605us/sample - loss: 0.0537 - accuracy: 0.9834 Epoch 3/5 60000/60000 [==============================] - 37s 621us/sample - loss: 0.0386 - accuracy: 0.9880 Epoch 4/5 60000/60000 [==============================] - 34s 567us/sample - loss: 0.0294 - accuracy: 0.9908 Epoch 5/5 60000/60000 [==============================] - 29s 476us/sample - loss: 0.0224 - accuracy: 0.9924 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 10000/1 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=] - 2s 191us/sample - loss: 0.0169 - accuracy: 0.9899 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) # logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) # grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |▏ | 10kB 22.6MB/s eta 0:00:01  |▎ | 20kB 29.7MB/s eta 0:00:01  |▌ | 30kB 24.9MB/s eta 0:00:01  |▋ | 40kB 21.2MB/s eta 0:00:01  |▉ | 51kB 22.5MB/s eta 0:00:01  |█ | 61kB 15.5MB/s eta 0:00:01  |█ | 71kB 16.9MB/s eta 0:00:01  |█▎ | 81kB 15.9MB/s eta 0:00:01  |█▍ | 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mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=b6c91ccafe91a17b330997976cd9d04434694bbc005924d4d4f1d2d72a8b0447 Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.5787 - accuracy: 0.8419 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2138 - accuracy: 0.9404 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1586 - accuracy: 0.9549 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1215 - accuracy: 0.9663 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1039 - accuracy: 0.9716 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1016 - accuracy: 0.9700 Test accuracy: 0.9700000286102295 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. ** This gap between training accuracy and test accuracy is an example of *overfitting* ** , when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), #Notice the 128 is the ouput size # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) #Notice that it has to have the number of output channels ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_3" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 24) 5208 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 24) 0 _________________________________________________________________ flatten_5 (Flatten) (None, 600) 0 _________________________________________________________________ dense_6 (Dense) (None, 128) 76928 _________________________________________________________________ dense_7 (Dense) (None, 10) 1290 ================================================================= Total params: 83,666 Trainable params: 83,666 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' BATCH_SIZE = 64 EPOCHS = 5 cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.5692 - accuracy: 0.8222 Epoch 2/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0788 - accuracy: 0.9764 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0530 - accuracy: 0.9835 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0413 - accuracy: 0.9876 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0357 - accuracy: 0.9894 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0388 - accuracy: 0.9864 Test accuracy: 0.9864000082015991 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Do this with WB from spacetp Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |▏ | 10kB 23.3MB/s eta 0:00:01  |▎ | 20kB 6.2MB/s eta 0:00:01  |▌ | 30kB 7.7MB/s eta 0:00:01  |▋ | 40kB 8.4MB/s eta 0:00:01  |▉ | 51kB 7.2MB/s eta 0:00:01  |█ | 61kB 8.1MB/s eta 0:00:01  |█ | 71kB 8.3MB/s eta 0:00:01  |█▎ | 81kB 8.7MB/s eta 0:00:01  |█▍ | 92kB 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/usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114586 sha256=e29958887b55eb74fe74409d4491a0f73f2a91c0cb18b6b53ebd511b9afa3a80 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' # '''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(len(set(train_labels)), activation= 'softmax'), ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.3630 - accuracy: 0.8982 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1938 - accuracy: 0.9449 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1475 - accuracy: 0.9576 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1206 - accuracy: 0.9654 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1015 - accuracy: 0.9715 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1067 - accuracy: 0.9686 Test accuracy: 0.9685999751091003 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, input_shape= (28, 28 ,1), kernel_size=(4,4)), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(12, kernel_size=(2, 2)), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output # '''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(len(set(train_labels)), activation= 'softmax'), ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_4" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 25, 25, 24) 408 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 12, 12, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 12) 1164 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 12) 0 _________________________________________________________________ flatten_5 (Flatten) (None, 300) 0 _________________________________________________________________ dense_8 (Dense) (None, 128) 38528 _________________________________________________________________ dense_9 (Dense) (None, 10) 1290 ================================================================= Total params: 41,390 Trainable params: 41,390 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='adam', loss=tf.losses.sparse_categorical_crossentropy, metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, epochs=EPOCHS, batch_size=BATCH_SIZE) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.2523 - accuracy: 0.9259 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0751 - accuracy: 0.9762 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0516 - accuracy: 0.9837 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0400 - accuracy: 0.9874 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0298 - accuracy: 0.9906 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0400 - accuracy: 0.9872 Test accuracy: 0.9872000217437744 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions, axis=1) print(prediction) ###Output [7 2 1 ... 4 5 6] ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.Adam() # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits, from_logits=True) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) import os checkpoint_dir = './training_checkpoints' checkpoint_prefix = os.path.join(checkpoint_dir, "my_ckpt") cnn_model.save_weights(checkpoint_prefix) cnn_model.compile(optimizer = tf.keras.optimizers.Adam(), loss=tf.losses.sparse_categorical_crossentropy,metrics=['accuracy'] ) cnn_model.load_weights(tf.train.latest_checkpoint(checkpoint_dir)) cnn_model.build(tf.TensorShape([1, None])) test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.3213 - accuracy: 0.9572 Test accuracy: 0.9571999907493591 ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 9.3MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.19.4) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114587 sha256=0f636484fce8708c131ccadb4381e078263ac625b9728df5b64f414020a22751 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation='relu'), tf.keras.layers.Dropout(0.5), tf.keras.layers.Dense(128, activation='relu'), tf.keras.layers.Dropout(0.3), tf.keras.layers.Dense(128, activation='relu'), tf.keras.layers.Dropout(0.1), tf.keras.layers.Dense(128, activation='relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model = build_fc_model() model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 15 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/15 938/938 [==============================] - 3s 3ms/step - loss: 0.8517 - accuracy: 0.7174 Epoch 2/15 938/938 [==============================] - 2s 3ms/step - loss: 0.2946 - accuracy: 0.9132 Epoch 3/15 938/938 [==============================] - 2s 3ms/step - loss: 0.2372 - accuracy: 0.9304 Epoch 4/15 938/938 [==============================] - 2s 3ms/step - loss: 0.2157 - accuracy: 0.9363 Epoch 5/15 938/938 [==============================] - 2s 3ms/step - loss: 0.1911 - accuracy: 0.9428 Epoch 6/15 938/938 [==============================] - 2s 3ms/step - loss: 0.1859 - accuracy: 0.9455 Epoch 7/15 938/938 [==============================] - 2s 3ms/step - loss: 0.1700 - accuracy: 0.9496 Epoch 8/15 938/938 [==============================] - 2s 3ms/step - loss: 0.1556 - accuracy: 0.9528 Epoch 9/15 938/938 [==============================] - 3s 3ms/step - loss: 0.1518 - accuracy: 0.9544 Epoch 10/15 938/938 [==============================] - 3s 3ms/step - loss: 0.1517 - accuracy: 0.9541 Epoch 11/15 938/938 [==============================] - 2s 3ms/step - loss: 0.1409 - accuracy: 0.9575 Epoch 12/15 938/938 [==============================] - 3s 3ms/step - loss: 0.1406 - accuracy: 0.9589 Epoch 13/15 938/938 [==============================] - 3s 3ms/step - loss: 0.1334 - accuracy: 0.9612 Epoch 14/15 938/938 [==============================] - 3s 3ms/step - loss: 0.1279 - accuracy: 0.9628 Epoch 15/15 938/938 [==============================] - 2s 3ms/step - loss: 0.1315 - accuracy: 0.9615 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0809 - accuracy: 0.9764 Test accuracy: 0.9764000177383423 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3, 3), activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3, 3)), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_20" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_2 (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d_2 (MaxPooling2 (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_3 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_3 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_21 (Flatten) (None, 900) 0 _________________________________________________________________ dense_61 (Dense) (None, 128) 115328 _________________________________________________________________ dense_62 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' BATCH_SIZE = 64 EPOCHS = 5 cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 4s 3ms/step - loss: 0.0367 - accuracy: 0.9888 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0284 - accuracy: 0.9912 Epoch 3/5 938/938 [==============================] - 3s 4ms/step - loss: 0.0222 - accuracy: 0.9927 Epoch 4/5 938/938 [==============================] - 3s 4ms/step - loss: 0.0173 - accuracy: 0.9942 Epoch 5/5 938/938 [==============================] - 4s 4ms/step - loss: 0.0133 - accuracy: 0.9955 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0380 - accuracy: 0.9904 Test accuracy: 0.9904000163078308 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 52 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. 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mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114585 sha256=6bd64435b2218856a1e3c9e45c8fe5e5485636d49af4c630853abebe3da55f50 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output [[[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] [[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] [[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] ... [[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] [[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]] [[0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] ... [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0] [0 0 0 ... 0 0 0]]] ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.3630 - accuracy: 0.8982 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1964 - accuracy: 0.9437 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1493 - accuracy: 0.9572 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1204 - accuracy: 0.9656 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1019 - accuracy: 0.9707 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 0s 1ms/step - loss: 0.1052 - accuracy: 0.9682 Test accuracy: 0.9682000279426575 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax), ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_2 (Flatten) (None, 900) 0 _________________________________________________________________ dense_4 (Dense) (None, 128) 115328 _________________________________________________________________ dense_5 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(x=train_images, y=train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0138 - accuracy: 0.9958 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0122 - accuracy: 0.9966 Epoch 3/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0114 - accuracy: 0.9968 Epoch 4/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0110 - accuracy: 0.9970 Epoch 5/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0107 - accuracy: 0.9971 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(x=test_images, y=test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1052 - accuracy: 0.9682 Test accuracy: 0.9682000279426575 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 42 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model.call(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output TensorFlow 2.x selected. Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 2.8MB/s [?25hRequirement already satisfied: numpy in /tensorflow-2.1.0/python3.6 (from mitdeeplearning) (1.18.1) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.28.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.15.6) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.10) Requirement already satisfied: scipy in /tensorflow-2.1.0/python3.6 (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle~=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.2.2) Requirement already satisfied: six in /tensorflow-2.1.0/python3.6 (from gym->mitdeeplearning) (1.14.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114586 sha256=1fc56845e3d197d62e97abd897898c7241bca00c86eb5129546c07e1acf27db3 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation= 'softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - 4s 70us/sample - loss: 0.3772 - accuracy: 0.8952 Epoch 2/5 60000/60000 [==============================] - 2s 36us/sample - loss: 0.2026 - accuracy: 0.9421 Epoch 3/5 60000/60000 [==============================] - 2s 37us/sample - loss: 0.1517 - accuracy: 0.9568 Epoch 4/5 60000/60000 [==============================] - 2s 37us/sample - loss: 0.1216 - accuracy: 0.9656 Epoch 5/5 60000/60000 [==============================] - 2s 37us/sample - loss: 0.1012 - accuracy: 0.9717 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 10000/10000 [==============================] - 1s 65us/sample - loss: 0.1032 - accuracy: 0.9691 Test accuracy: 0.9691 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) multiple 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) multiple 0 _________________________________________________________________ conv2d_1 (Conv2D) multiple 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_1 (Flatten) multiple 0 _________________________________________________________________ dense_2 (Dense) multiple 115328 _________________________________________________________________ dense_3 (Dense) multiple 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - 4s 59us/sample - loss: 0.1761 - accuracy: 0.9474 Epoch 2/5 60000/60000 [==============================] - 3s 49us/sample - loss: 0.0532 - accuracy: 0.9832 Epoch 3/5 60000/60000 [==============================] - 3s 53us/sample - loss: 0.0359 - accuracy: 0.9891 Epoch 4/5 60000/60000 [==============================] - 3s 52us/sample - loss: 0.0278 - accuracy: 0.9912 Epoch 5/5 60000/60000 [==============================] - 3s 51us/sample - loss: 0.0208 - accuracy: 0.9933 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 10000/10000 [==============================] - 1s 76us/sample - loss: 0.0324 - accuracy: 0.9900 Test accuracy: 0.99 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) # TODO print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 6 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images)# TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2022 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning Downloading mitdeeplearning-0.2.0.tar.gz (2.1 MB)  |████████████████████████████████| 2.1 MB 12.3 MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.21.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.63.0) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-py3-none-any.whl size=2115442 sha256=980379039749e11455610d29f5d0b5aaccb513212f3f30010f9f26b450df8c08 Stored in directory: /root/.cache/pip/wheels/9a/b9/4f/99b7c8c5c75355550b83e1fcfc02956fb40c35eb01e2262877 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() print(train_images.shape) train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) print(train_images.shape) train_labels = (train_labels).astype(np.int64) print(train_labels.shape) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 1s 0us/step 11501568/11490434 [==============================] - 1s 0us/step (60000, 28, 28) (60000, 28, 28, 1) (60000,) ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 7s 5ms/step - loss: 0.3707 - accuracy: 0.8971 Epoch 2/5 938/938 [==============================] - 5s 5ms/step - loss: 0.2018 - accuracy: 0.9415 Epoch 3/5 938/938 [==============================] - 6s 6ms/step - loss: 0.1520 - accuracy: 0.9560 Epoch 4/5 938/938 [==============================] - 5s 6ms/step - loss: 0.1237 - accuracy: 0.9641 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1041 - accuracy: 0.9699 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.1054 - accuracy: 0.9695 Test accuracy: 0.9695000052452087 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, 3), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(2, 2), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, 3), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(2, 2), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_7" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_12 (Conv2D) (None, 26, 26, 24) 240 max_pooling2d_12 (MaxPoolin (None, 13, 13, 24) 0 g2D) conv2d_13 (Conv2D) (None, 11, 11, 36) 7812 max_pooling2d_13 (MaxPoolin (None, 5, 5, 36) 0 g2D) flatten_7 (Flatten) (None, 900) 0 dense_14 (Dense) (None, 128) 115328 dense_15 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 6s 6ms/step - loss: 0.1738 - accuracy: 0.9502 Epoch 2/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0535 - accuracy: 0.9839 Epoch 3/5 938/938 [==============================] - 5s 6ms/step - loss: 0.0357 - accuracy: 0.9886 Epoch 4/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0257 - accuracy: 0.9919 Epoch 5/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0202 - accuracy: 0.9937 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.0427 - accuracy: 0.9888 Test accuracy: 0.9887999892234802 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 18 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning Downloading mitdeeplearning-0.2.0.tar.gz (2.1 MB)  |████████████████████████████████| 2.1 MB 5.2 MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.62.3) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-py3-none-any.whl size=2115442 sha256=0242532d948bbb2ea817cf517be28759fca47a7016919efdb9c9d80e97103022 Stored in directory: /root/.cache/pip/wheels/9a/b9/4f/99b7c8c5c75355550b83e1fcfc02956fb40c35eb01e2262877 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step 11501568/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) # print(random_inds) # print(train_images[image_ind]) # print(np.squeeze(train_images[image_ind])) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] # print(image_ind) plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 6s 3ms/step - loss: 0.3636 - accuracy: 0.8999 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1924 - accuracy: 0.9454 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1450 - accuracy: 0.9588 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1184 - accuracy: 0.9661 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1006 - accuracy: 0.9712 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.0996 - accuracy: 0.9688 Test accuracy: 0.9688000082969666 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # tf.keras.layers.Conv2D('''TODO''') # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # tf.keras.layers.MaxPool2D('''TODO''') # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation=tf.nn.relu), # tf.keras.layers.Conv2D('''TODO''') # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # tf.keras.layers.MaxPool2D('''TODO''') tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) # [TODO Dense layer to output classification probabilities] ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 max_pooling2d (MaxPooling2D (None, 13, 13, 24) 0 ) conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 max_pooling2d_1 (MaxPooling (None, 5, 5, 36) 0 2D) flatten_1 (Flatten) (None, 900) 0 dense_2 (Dense) (None, 128) 115328 dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' BATCH_SIZE = 64 EPOCHS = 5 cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 8s 6ms/step - loss: 0.2503 - accuracy: 0.9206 Epoch 2/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0720 - accuracy: 0.9776 Epoch 3/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0506 - accuracy: 0.9840 Epoch 4/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0394 - accuracy: 0.9876 Epoch 5/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0317 - accuracy: 0.9901 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 4ms/step - loss: 0.0297 - accuracy: 0.9901 Test accuracy: 0.9901000261306763 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 80 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. 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/usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114585 sha256=3a496fbe8faa9c0fef74139862e4764241121153772347ca4fce873f9d81fe49 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation='relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10,activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.3663 - accuracy: 0.8985 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1961 - accuracy: 0.9445 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1503 - accuracy: 0.9571 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1222 - accuracy: 0.9656 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1033 - accuracy: 0.9711 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1076 - accuracy: 0.9687 Test accuracy: 0.9686999917030334 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24,(3,3)), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36,(3,3)), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10,activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 900) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 115328 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images,train_labels) ###Output 1875/1875 [==============================] - 4s 2ms/step - loss: 0.1380 - accuracy: 0.9591 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images,test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1076 - accuracy: 0.9687 Test accuracy: 0.9686999917030334 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 88 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels,logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value,cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU print(tf.config.list_physical_devices) assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, kernel_size=3, activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(3,3), strides=2), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, kernel_size=3, activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2), strides=2), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=0.01), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, BATCH_SIZE, EPOCHS) ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 50 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 from tensorflow.python.client import device_lib for device in device_lib.list_local_devices(): if device.device_type=="GPU": print(device.physical_device_desc) mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 4s 2ms/step - loss: 0.5771 - accuracy: 0.8427 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2159 - accuracy: 0.9371 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1586 - accuracy: 0.9544 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1292 - accuracy: 0.9634 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1082 - accuracy: 0.9691 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 0s 2ms/step - loss: 0.1003 - accuracy: 0.9697 Test accuracy: 0.9696999788284302 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, kernel_size=3), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, kernel_size=3), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 900) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 115328 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adagrad (learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # Frank: pretty good # cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), # loss='sparse_categorical_crossentropy', # metrics=['accuracy']) ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0048 - accuracy: 0.9986 Epoch 2/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0048 - accuracy: 0.9986 Epoch 3/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0044 - accuracy: 0.9987 Epoch 4/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0039 - accuracy: 0.9988 Epoch 5/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0046 - accuracy: 0.9987 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0386 - accuracy: 0.9900 Test accuracy: 0.9900000095367432 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 30 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits, from_logits=True) loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown 1.5 ConclusionIn this part of the lab, you had the chance to play with different MNIST classifiers with different architectures (fully-connected layers only, CNN), and experiment with how different hyperparameters affect accuracy (learning rate, etc.). The next part of the lab explores another application of CNNs, facial detection, and some drawbacks of AI systems in real world applications, like issues of bias. ###Code ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 17.8MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=e711273d15c99ae99c63779fdc9edece376462a28462ed3b897bd64565fc50e1 Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'sigmoid'), tf.keras.layers.Dense(128, activation= 'sigmoid'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/10 938/938 [==============================] - 2s 2ms/step - loss: 0.2536 - accuracy: 0.9255 Epoch 2/10 938/938 [==============================] - 2s 2ms/step - loss: 0.2346 - accuracy: 0.9314 Epoch 3/10 938/938 [==============================] - 2s 2ms/step - loss: 0.2181 - accuracy: 0.9364 Epoch 4/10 938/938 [==============================] - 2s 2ms/step - loss: 0.2034 - accuracy: 0.9417 Epoch 5/10 938/938 [==============================] - 2s 2ms/step - loss: 0.1905 - accuracy: 0.9452 Epoch 6/10 938/938 [==============================] - 2s 2ms/step - loss: 0.1788 - accuracy: 0.9480 Epoch 7/10 938/938 [==============================] - 2s 2ms/step - loss: 0.1682 - accuracy: 0.9508 Epoch 8/10 938/938 [==============================] - 2s 2ms/step - loss: 0.1591 - accuracy: 0.9537 Epoch 9/10 938/938 [==============================] - 2s 2ms/step - loss: 0.1502 - accuracy: 0.9564 Epoch 10/10 938/938 [==============================] - 2s 2ms/step - loss: 0.1423 - accuracy: 0.9586 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1444 - accuracy: 0.9579 Test accuracy: 0.9578999876976013 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24,kernel_size=(3,3)), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, (3,3)), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_5" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_2 (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d_2 (MaxPooling2 (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_3 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_3 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_5 (Flatten) (None, 900) 0 _________________________________________________________________ dense_13 (Dense) (None, 128) 115328 _________________________________________________________________ dense_14 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels) ###Output 1875/1875 [==============================] - 5s 2ms/step - loss: 0.1637 - accuracy: 0.9517 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0468 - accuracy: 0.9855 Test accuracy: 0.9854999780654907 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 100 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO''') # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO''') # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO''') # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO''') tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Requirement already satisfied: mitdeeplearning in /usr/local/lib/python3.6/dist-packages (0.1.2) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.19.4) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''output = activation(dot(input, kernel) + bias)''' tf.keras.layers.Dense(128, activation='relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='sigmoid') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 4s 2ms/step - loss: 0.5866 - accuracy: 0.8393 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2138 - accuracy: 0.9391 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1568 - accuracy: 0.9551 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1263 - accuracy: 0.9640 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1078 - accuracy: 0.9700 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(x=test_images, y=test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1075 - accuracy: 0.9685 Test accuracy: 0.968500018119812 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24,3,activation='relu',input_shape=(28,28,1)), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(24,3,activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.sigmoid), ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_4 (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d_4 (MaxPooling2 (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_5 (Conv2D) (None, 11, 11, 24) 5208 _________________________________________________________________ max_pooling2d_5 (MaxPooling2 (None, 5, 5, 24) 0 _________________________________________________________________ flatten_2 (Flatten) (None, 600) 0 _________________________________________________________________ dense_4 (Dense) (None, 128) 76928 _________________________________________________________________ dense_5 (Dense) (None, 10) 1290 ================================================================= Total params: 83,666 Trainable params: 83,666 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) #(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' BATCH_SIZE = 64 EPOCHS = 5 cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.7679 - accuracy: 0.7556 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0876 - accuracy: 0.9724 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0609 - accuracy: 0.9807 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0467 - accuracy: 0.9857 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0370 - accuracy: 0.9882 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code test_loss, test_acc = cnn_model.evaluate(x=test_images, y=test_labels) print('Test accuracy:', test_acc) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0372 - accuracy: 0.9873 Test accuracy: 0.9872999787330627 Test accuracy: 0.9872999787330627 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code a=predictions[0].tolist() a.index(max(a)) '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = predictions[0].tolist().index(max(predictions[0])) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 61 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output TensorFlow 2.x selected. Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 15.7MB/s [?25hRequirement already satisfied: numpy in /tensorflow-2.1.0/python3.6 (from mitdeeplearning) (1.18.1) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.28.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.15.6) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.10) Requirement already satisfied: six in /tensorflow-2.1.0/python3.6 (from gym->mitdeeplearning) (1.14.0) Requirement already satisfied: scipy in /tensorflow-2.1.0/python3.6 (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle~=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.2.2) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114586 sha256=0299eb306304570c0bc8bfad1df201437bcb8abe2312406c15048a12afa835a3 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 1s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' #'''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation= tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - 2s 41us/sample - loss: 0.3712 - accuracy: 0.8969 Epoch 2/5 60000/60000 [==============================] - 2s 37us/sample - loss: 0.1986 - accuracy: 0.9439 Epoch 3/5 60000/60000 [==============================] - 2s 35us/sample - loss: 0.1482 - accuracy: 0.9573 Epoch 4/5 60000/60000 [==============================] - 2s 37us/sample - loss: 0.1186 - accuracy: 0.9657 Epoch 5/5 60000/60000 [==============================] - 2s 40us/sample - loss: 0.0998 - accuracy: 0.9718 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) # TODO print('Test accuracy:', test_acc) ###Output 10000/10000 [==============================] - 1s 60us/sample - loss: 0.1042 - accuracy: 0.9688 Test accuracy: 0.9688 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(16, 2, activation=tf.nn.relu), #'''TODO''' # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # '''TODO''' # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(64, 2,activation=tf.nn.relu), #'''TODO''' # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), #'''TODO''' tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output #'''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation = tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_7" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_6 (Conv2D) multiple 80 _________________________________________________________________ max_pooling2d_6 (MaxPooling2 multiple 0 _________________________________________________________________ conv2d_7 (Conv2D) multiple 4160 _________________________________________________________________ max_pooling2d_7 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_8 (Flatten) multiple 0 _________________________________________________________________ dense_15 (Dense) multiple 295040 _________________________________________________________________ dense_16 (Dense) multiple 1290 ================================================================= Total params: 300,570 Trainable params: 300,570 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO #optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), # loss='sparse_categorical_crossentropy', # metrics=['accuracy'] ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' BATCH_SIZE = 128 EPOCHS = 10 cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS)#'''TODO''') ###Output Train on 60000 samples Epoch 1/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0488 - accuracy: 0.9845 Epoch 2/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0338 - accuracy: 0.9891 Epoch 3/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0285 - accuracy: 0.9912 Epoch 4/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0244 - accuracy: 0.9925 Epoch 5/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0215 - accuracy: 0.9935 Epoch 6/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0178 - accuracy: 0.9944 Epoch 7/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0166 - accuracy: 0.9948 Epoch 8/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0140 - accuracy: 0.9961 Epoch 9/10 60000/60000 [==============================] - 2s 34us/sample - loss: 0.0121 - accuracy: 0.9966 Epoch 10/10 60000/60000 [==============================] - 2s 36us/sample - loss: 0.0107 - accuracy: 0.9969 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels, verbose=False)# TODO print('Test accuracy:', test_acc) ###Output Test accuracy: 0.9919 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' #prediction= np.where(predictions[0] == np.amax(predictions[0])) prediction = np.argmax(prediction[0]) print(prediction) ###Output 0 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 42 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images)# TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables)# TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown 1.5 ConclusionIn this part of the lab, you had the chance to play with different MNIST classifiers with different architectures (fully-connected layers only, CNN), and experiment with how different hyperparameters affect accuracy (learning rate, etc.). The next part of the lab explores another application of CNNs, facial detection, and some drawbacks of AI systems in real world applications, like issues of bias. ###Code ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning Downloading mitdeeplearning-0.2.0.tar.gz (2.1 MB) [?25l  |▏ | 10 kB 20.4 MB/s eta 0:00:01  |▎ | 20 kB 23.5 MB/s eta 0:00:01  |▌ | 30 kB 26.4 MB/s eta 0:00:01  |▋ | 40 kB 25.6 MB/s eta 0:00:01  |▉ | 51 kB 15.3 MB/s eta 0:00:01  |█ | 61 kB 12.9 MB/s eta 0:00:01  |█ | 71 kB 12.1 MB/s eta 0:00:01  |█▎ | 81 kB 13.1 MB/s eta 0:00:01  |█▍ | 92 kB 13.8 MB/s eta 0:00:01  |█▋ | 102 kB 11.4 MB/s eta 0:00:01  |█▊ | 112 kB 11.4 MB/s 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|████████████████████████████████| 2.1 MB 11.4 MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.62.3) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-py3-none-any.whl size=2115442 sha256=489455447acfd4b27d731fad01c8cf05a0616631df5f0b36e00d7227a3b4e191 Stored in directory: /root/.cache/pip/wheels/9a/b9/4f/99b7c8c5c75355550b83e1fcfc02956fb40c35eb01e2262877 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step 11501568/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= 'relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation= 'softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 3ms/step - loss: 0.3699 - accuracy: 0.8962 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1967 - accuracy: 0.9447 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1474 - accuracy: 0.9577 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1186 - accuracy: 0.9662 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1002 - accuracy: 0.9713 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images,test_labels,batch_size=BATCH_SIZE) print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 1s 3ms/step - loss: 0.1026 - accuracy: 0.9695 Test accuracy: 0.9695000052452087 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24,kernel_size=(3,3),activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36,kernel_size=(3,3),activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_2 (Conv2D) (None, 26, 26, 24) 240 max_pooling2d_2 (MaxPooling (None, 13, 13, 24) 0 2D) conv2d_3 (Conv2D) (None, 11, 11, 36) 7812 max_pooling2d_3 (MaxPooling (None, 5, 5, 36) 0 2D) flatten_2 (Flatten) (None, 900) 0 dense_4 (Dense) (None, 128) 115328 dense_5 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 7s 6ms/step - loss: 0.2679 - accuracy: 0.9137 Epoch 2/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0658 - accuracy: 0.9793 Epoch 3/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0468 - accuracy: 0.9855 Epoch 4/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0367 - accuracy: 0.9886 Epoch 5/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0294 - accuracy: 0.9907 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images,test_labels,batch_size=BATCH_SIZE) print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 1s 4ms/step - loss: 0.0332 - accuracy: 0.9888 Test accuracy: 0.9887999892234802 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = max(predictions[0]) print(prediction) ###Output 0.99999774 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 94 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 14.1MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.18.4) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.2) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: cloudpickle<1.4.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114586 sha256=cdeee0bf33b14dd1aa8a89ca1f213858ef2b99ccafd34912a379f8de42cd6a46 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= "relu"), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation= "sigmoid") ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.4467 - accuracy: 0.8766 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.2191 - accuracy: 0.9373 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1652 - accuracy: 0.9527 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1337 - accuracy: 0.9610 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1132 - accuracy: 0.9681 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate( x=test_images, y=test_labels ) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1158 - accuracy: 0.9661 Test accuracy: 0.9660999774932861 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(2, 3), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(2,3), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) multiple 20 _________________________________________________________________ max_pooling2d (MaxPooling2D) multiple 0 _________________________________________________________________ conv2d_1 (Conv2D) multiple 38 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_1 (Flatten) multiple 0 _________________________________________________________________ dense_2 (Dense) multiple 6528 _________________________________________________________________ dense_3 (Dense) multiple 1290 ================================================================= Total params: 7,876 Trainable params: 7,876 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss="sparse_categorical_crossentropy", metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels) ###Output 1875/1875 [==============================] - 4s 2ms/step - loss: 0.1897 - accuracy: 0.9407 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1273 - accuracy: 0.9605 Test accuracy: 0.9605000019073486 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) # TODO print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 43 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables)# TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/9d/ad/650eb53c0d9d1213536fe94bc150f89b564ff5ee784bd662272584bb091b/mitdeeplearning-0.2.0.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 18.7MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-cp37-none-any.whl size=2115442 sha256=7ae055a8a3f01cc518e8b08b09f1be1a8098e85f9e2ec9d2d9270383532a1b84 Stored in directory: /root/.cache/pip/wheels/af/dc/2a/5c3633135e7e4ef4fd31463cfa1942cb1bae7486ab94e7a2ad Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist #mnist.load_data() returns tuples of np arrays (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= "relu"), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation="softmax") #softmax for categorizing ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-2), loss='sparse_categorical_crossentropy', metrics=['accuracy']) print('done') ###Output done ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 #input data, target data, batch_size (bounciness), no. iterations over dataset model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) #noting how accuracy improves over epochs #slower learning rate is better! About 98.38% accuracy for 1e-2 #however, the effect plateaus: 1e-5 yields 98.22% accuracy. Variance in another #trial will likely yield a different answer, but this is probably due to the #limitations of the model itself. ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0607 - accuracy: 0.9827 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0559 - accuracy: 0.9830 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0590 - accuracy: 0.9826 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0550 - accuracy: 0.9836 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0541 - accuracy: 0.9838 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' #some data is kept to evaluate on unseen data test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1026 - accuracy: 0.9709 Test accuracy: 0.9708999991416931 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer #assuming 3 x 3 "window" tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 900) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 115328 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-2), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=64, epochs=5) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0218 - accuracy: 0.9933 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0164 - accuracy: 0.9951 Epoch 3/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0151 - accuracy: 0.9955 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0120 - accuracy: 0.9963 Epoch 5/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0134 - accuracy: 0.9960 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) #Adamax is achieving promising accuracy of about 99% ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0546 - accuracy: 0.9881 Test accuracy: 0.988099992275238 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 89 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Requirement already satisfied: mitdeeplearning in /usr/local/lib/python3.6/dist-packages (0.1.2) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.2) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.18.5) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.4.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation="relu"), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation="softmax") ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.Adam(), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.3008 - accuracy: 0.9143 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.1329 - accuracy: 0.9623 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0934 - accuracy: 0.9730 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0713 - accuracy: 0.9796 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0559 - accuracy: 0.9837 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0791 - accuracy: 0.9758 Test accuracy: 0.9757999777793884 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, 3, input_shape=(28, 28, 1)), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, 3), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation="softmax") ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_1" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_1 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 5, 5, 36) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 900) 0 _________________________________________________________________ dense_2 (Dense) (None, 128) 115328 _________________________________________________________________ dense_3 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 3ms/step - loss: 0.1702 - accuracy: 0.9503 Epoch 2/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0517 - accuracy: 0.9841 Epoch 3/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0343 - accuracy: 0.9894 Epoch 4/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0250 - accuracy: 0.9922 Epoch 5/5 938/938 [==============================] - 2s 3ms/step - loss: 0.0191 - accuracy: 0.9939 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0402 - accuracy: 0.9876 Test accuracy: 0.9876000285148621 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 88 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 9.6MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.19.4) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.41.1) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114587 sha256=99ead65c27abedcc71aabb6f82214c24517b13ada2f4b8faf9d2dee585bc2276 Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation='relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation="sigmoid") ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=3e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0461 - accuracy: 0.9867 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0369 - accuracy: 0.9884 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0274 - accuracy: 0.9919 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0269 - accuracy: 0.9922 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0200 - accuracy: 0.9947 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels, batch_size=BATCH_SIZE) print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 0s 2ms/step - loss: 0.0771 - accuracy: 0.9760 Test accuracy: 0.9760000109672546 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, (3, 3), padding='valid', activation='relu'), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D((2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, (3, 3), padding='valid', activation='relu'), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D((2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation='sigmoid') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_28" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_52 (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d_52 (MaxPooling (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_53 (Conv2D) (None, 11, 11, 36) 7812 _________________________________________________________________ max_pooling2d_53 (MaxPooling (None, 5, 5, 36) 0 _________________________________________________________________ flatten_28 (Flatten) (None, 900) 0 _________________________________________________________________ dense_56 (Dense) (None, 128) 115328 _________________________________________________________________ dense_57 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.4271 - accuracy: 0.8717 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0594 - accuracy: 0.9820 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0399 - accuracy: 0.9872 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0315 - accuracy: 0.9901 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0232 - accuracy: 0.9929 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels, batch_size=BATCH_SIZE) print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 0s 2ms/step - loss: 0.0376 - accuracy: 0.9875 Test accuracy: 0.987500011920929 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output WARNING:tensorflow:8 out of the last 8 calls to <function Model.make_predict_function.<locals>.predict_function at 0x7f0cc8150c80> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has experimental_relax_shapes=True option that relaxes argument shapes that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for more details. ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 10 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.Adam(learning_rate=1e-4) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2022 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning Downloading mitdeeplearning-0.2.0.tar.gz (2.1 MB)  |████████████████████████████████| 2.1 MB 5.4 MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.62.3) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-py3-none-any.whl size=2115442 sha256=2ed1df6c714143169c18785b13cc1a10ab14f91dd67f895feb82ea6f59cf0a77 Stored in directory: /root/.cache/pip/wheels/9a/b9/4f/99b7c8c5c75355550b83e1fcfc02956fb40c35eb01e2262877 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation='relu'), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation='softmax') ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.3673 - accuracy: 0.8978 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1957 - accuracy: 0.9452 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1483 - accuracy: 0.9579 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1205 - accuracy: 0.9658 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1019 - accuracy: 0.9711 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(x=test_images, y=test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.1085 - accuracy: 0.9664 Test accuracy: 0.9664000272750854 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), input_shape=(28,28,1)), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D((2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(36, (3,3)), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D((2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10,activation='softmax') ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_7" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_4 (Conv2D) (None, 26, 26, 24) 240 max_pooling2d_4 (MaxPooling (None, 13, 13, 24) 0 2D) conv2d_5 (Conv2D) (None, 11, 11, 36) 7812 max_pooling2d_5 (MaxPooling (None, 5, 5, 36) 0 2D) flatten_7 (Flatten) (None, 900) 0 dense_14 (Dense) (None, 128) 115328 dense_15 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss=tf.keras.losses.sparse_categorical_crossentropy, metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 6s 6ms/step - loss: 0.2212 - accuracy: 0.9316 Epoch 2/5 938/938 [==============================] - 6s 6ms/step - loss: 0.0667 - accuracy: 0.9793 Epoch 3/5 938/938 [==============================] - 5s 6ms/step - loss: 0.0461 - accuracy: 0.9852 Epoch 4/5 938/938 [==============================] - 5s 6ms/step - loss: 0.0344 - accuracy: 0.9891 Epoch 5/5 938/938 [==============================] - 5s 6ms/step - loss: 0.0268 - accuracy: 0.9915 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.1085 - accuracy: 0.9664 Test accuracy: 0.9664000272750854 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = tf.math.argmax(predictions[0]) print(prediction) ###Output tf.Tensor(7, shape=(), dtype=int64) ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 87 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits, from_logits=True) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning Downloading mitdeeplearning-0.2.0.tar.gz (2.1 MB)  |████████████████████████████████| 2.1 MB 4.1 MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.62.3) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-py3-none-any.whl size=2115442 sha256=0e9f6b41af138df346e55d93b4b27f4fb6fbb6efc89937c6aa998ce3c5b80fb1 Stored in directory: /root/.cache/pip/wheels/9a/b9/4f/99b7c8c5c75355550b83e1fcfc02956fb40c35eb01e2262877 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step 11501568/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= "relu"), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation="softmax") ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 3ms/step - loss: 0.3645 - accuracy: 0.8974 Epoch 2/5 938/938 [==============================] - 2s 3ms/step - loss: 0.1992 - accuracy: 0.9433 Epoch 3/5 938/938 [==============================] - 2s 3ms/step - loss: 0.1518 - accuracy: 0.9568 Epoch 4/5 938/938 [==============================] - 2s 3ms/step - loss: 0.1231 - accuracy: 0.9647 Epoch 5/5 938/938 [==============================] - 2s 3ms/step - loss: 0.1030 - accuracy: 0.9702 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.1023 - accuracy: 0.9676 Test accuracy: 0.9675999879837036 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(24, 3, activation="relu"), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D((2, 2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(24, 3, activation="relu"), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D((2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation="softmax") ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_6" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_10 (Conv2D) (None, 26, 26, 24) 240 _________________________________________________________________ max_pooling2d_10 (MaxPooling (None, 13, 13, 24) 0 _________________________________________________________________ conv2d_11 (Conv2D) (None, 11, 11, 24) 5208 _________________________________________________________________ max_pooling2d_11 (MaxPooling (None, 5, 5, 24) 0 _________________________________________________________________ flatten_6 (Flatten) (None, 600) 0 _________________________________________________________________ dense_12 (Dense) (None, 128) 76928 _________________________________________________________________ dense_13 (Dense) (None, 10) 1290 ================================================================= Total params: 83,666 Trainable params: 83,666 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 5ms/step - loss: 0.0057 - accuracy: 0.9983 Epoch 2/5 938/938 [==============================] - 5s 5ms/step - loss: 0.0029 - accuracy: 0.9992 Epoch 3/5 938/938 [==============================] - 5s 5ms/step - loss: 0.0023 - accuracy: 0.9995 Epoch 4/5 938/938 [==============================] - 5s 5ms/step - loss: 0.0017 - accuracy: 0.9997 Epoch 5/5 938/938 [==============================] - 5s 5ms/step - loss: 0.0014 - accuracy: 0.9996 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.0313 - accuracy: 0.9917 Test accuracy: 0.9916999936103821 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model.call(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Run in Google Colab Copyright Information ###Code # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Collecting mitdeeplearning Downloading mitdeeplearning-0.2.0.tar.gz (2.1 MB)  |████████████████████████████████| 2.1 MB 5.3 MB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (1.19.5) Requirement already satisfied: regex in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (4.62.3) Requirement already satisfied: gym in /usr/local/lib/python3.7/dist-packages (from mitdeeplearning) (0.17.3) Requirement already satisfied: cloudpickle<1.7.0,>=1.2.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.7/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.7/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.2.0-py3-none-any.whl size=2115442 sha256=203fd8da218480bd5e7fe624befb9e8e60f778fbef3c567f23943fdf9e588ab6 Stored in directory: /root/.cache/pip/wheels/9a/b9/4f/99b7c8c5c75355550b83e1fcfc02956fb40c35eb01e2262877 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.2.0 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step 11501568/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(units=10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.Adagrad(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 10 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/10 938/938 [==============================] - 3s 3ms/step - loss: 0.2633 - accuracy: 0.9226 Epoch 2/10 938/938 [==============================] - 3s 3ms/step - loss: 0.1194 - accuracy: 0.9651 Epoch 3/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0854 - accuracy: 0.9756 Epoch 4/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0653 - accuracy: 0.9812 Epoch 5/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0536 - accuracy: 0.9846 Epoch 6/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0446 - accuracy: 0.9870 Epoch 7/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0373 - accuracy: 0.9895 Epoch 8/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0311 - accuracy: 0.9918 Epoch 9/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0270 - accuracy: 0.9930 Epoch 10/10 938/938 [==============================] - 3s 3ms/step - loss: 0.0227 - accuracy: 0.9948 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 3ms/step - loss: 0.0598 - accuracy: 0.9810 Test accuracy: 0.9810000061988831 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code from tensorflow.python.ops.gen_nn_ops import softmax def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), strides=(1,1), padding='valid', activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2), strides=(2,2), padding='valid'), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), strides=(1,1), padding='valid', activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2), strides=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_17" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_8 (Conv2D) (None, 26, 26, 24) 240 max_pooling2d_6 (MaxPooling (None, 13, 13, 24) 0 2D) conv2d_9 (Conv2D) (None, 11, 11, 36) 7812 max_pooling2d_7 (MaxPooling (None, 5, 5, 36) 0 2D) flatten_25 (Flatten) (None, 900) 0 dense_34 (Dense) (None, 128) 115328 dense_35 (Dense) (None, 10) 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adagrad(learning_rate=1e-1), loss=tf.keras.losses.sparse_categorical_crossentropy, metrics=['accuracy']) ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, BATCH_SIZE, EPOCHS) ###Output Epoch 1/10 938/938 [==============================] - 8s 7ms/step - loss: 0.1845 - accuracy: 0.9424 Epoch 2/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0455 - accuracy: 0.9859 Epoch 3/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0303 - accuracy: 0.9907 Epoch 4/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0233 - accuracy: 0.9924 Epoch 5/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0169 - accuracy: 0.9947 Epoch 6/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0127 - accuracy: 0.9961 Epoch 7/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0098 - accuracy: 0.9971 Epoch 8/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0078 - accuracy: 0.9977 Epoch 9/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0062 - accuracy: 0.9983 Epoch 10/10 938/938 [==============================] - 6s 7ms/step - loss: 0.0044 - accuracy: 0.9990 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(test_images, test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 4ms/step - loss: 0.0464 - accuracy: 0.9871 Test accuracy: 0.9871000051498413 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for some images in the test dataset: ###Code predictions[:10] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = tf.argmax(predictions[0]) print(prediction) ###Output tf.Tensor(7, shape=(), dtype=int64) ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels, logits, from_logits=True) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value, cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output TensorFlow 2.x selected. Collecting mitdeeplearning [?25l Downloading https://files.pythonhosted.org/packages/8b/3b/b9174b68dc10832356d02a2d83a64b43a24f1762c172754407d22fc8f960/mitdeeplearning-0.1.2.tar.gz (2.1MB)  |████████████████████████████████| 2.1MB 110kB/s [?25hRequirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.18.2) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.38.0) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.1) Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.12.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: cloudpickle<1.4.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) Building wheels for collected packages: mitdeeplearning Building wheel for mitdeeplearning (setup.py) ... [?25l[?25hdone Created wheel for mitdeeplearning: filename=mitdeeplearning-0.1.2-cp36-none-any.whl size=2114586 sha256=51d5d6174a6c9f5f3ecb5a59410742dd8c68759a33bf401ca7e19c9eba7ddc0b Stored in directory: /root/.cache/pip/wheels/27/e1/73/5f01c787621d8a3c857f59876c79e304b9b64db9ff5bd61b74 Successfully built mitdeeplearning Installing collected packages: mitdeeplearning Successfully installed mitdeeplearning-0.1.2 ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz 11493376/11490434 [==============================] - 0s 0us/step ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - 4s 68us/sample - loss: 0.3668 - accuracy: 0.8981 Epoch 2/5 60000/60000 [==============================] - 2s 39us/sample - loss: 0.1962 - accuracy: 0.9444 Epoch 3/5 60000/60000 [==============================] - 2s 37us/sample - loss: 0.1485 - accuracy: 0.9570 Epoch 4/5 60000/60000 [==============================] - 2s 36us/sample - loss: 0.1216 - accuracy: 0.9657 Epoch 5/5 60000/60000 [==============================] - 2s 37us/sample - loss: 0.1026 - accuracy: 0.9703 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(x=test_images,y=test_labels,batch_size=BATCH_SIZE) print('Test accuracy:', test_acc) ###Output 10000/10000 [==============================] - 0s 37us/sample - loss: 0.1055 - accuracy: 0.9681 Test accuracy: 0.9681 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters = 24,kernel_size=(3,3),activation = tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size = (2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters = 36, kernel_size = (3,3), activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_2 (Conv2D) multiple 240 _________________________________________________________________ max_pooling2d_2 (MaxPooling2 multiple 0 _________________________________________________________________ conv2d_3 (Conv2D) multiple 7812 _________________________________________________________________ max_pooling2d_3 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_2 (Flatten) multiple 0 _________________________________________________________________ dense_4 (Dense) multiple 115328 _________________________________________________________________ dense_5 (Dense) multiple 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=0.01) , loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(x = train_images, y= train_labels,batch_size=BATCH_SIZE,epochs=EPOCHS) ###Output Train on 60000 samples Epoch 1/5 60000/60000 [==============================] - 4s 62us/sample - loss: 0.7445 - accuracy: 0.7860 Epoch 2/5 60000/60000 [==============================] - 3s 51us/sample - loss: 0.2026 - accuracy: 0.9384 Epoch 3/5 60000/60000 [==============================] - 3s 50us/sample - loss: 0.1426 - accuracy: 0.9563 Epoch 4/5 60000/60000 [==============================] - 3s 52us/sample - loss: 0.1145 - accuracy: 0.9650 Epoch 5/5 60000/60000 [==============================] - 3s 53us/sample - loss: 0.0978 - accuracy: 0.9704 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = cnn_model.evaluate(x=test_images,y=test_labels,batch_size=BATCH_SIZE) print('Test accuracy:', test_acc) ###Output 10000/10000 [==============================] - 0s 42us/sample - loss: 0.0852 - accuracy: 0.9717 Test accuracy: 0.9717 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' nums = np.array(range(0,len(predictions[0]))) prediction = nums[predictions[0]==max(predictions[0])] print(prediction) ###Output [7] ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 100 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(target = labels,output=logits,from_logits=True) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value,cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2021 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation= '''TODO'''), # '''TODO: Define the second Dense layer to output the classification probabilities''' '''TODO: Dense layer to output classification probabilities''' ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output _____no_output_____ ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D('''TODO'''), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output '''TODO: Dense layer to output classification probabilities''' ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output _____no_output_____ ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer='''TODO''', loss='''TODO''', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit('''TODO''') ###Output _____no_output_____ ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = # TODO print('Test accuracy:', test_acc) ###Output _____no_output_____ ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = # TODO print(prediction) ###Output _____no_output_____ ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output _____no_output_____ ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2022 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 #%tensorflow_version 2.x import tensorflow as tf #!pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output _____no_output_____ ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' #'''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(128, activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model.** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 5s 6ms/step - loss: 0.4299 - accuracy: 0.8817 Epoch 2/5 938/938 [==============================] - 5s 5ms/step - loss: 0.2194 - accuracy: 0.9376 Epoch 3/5 938/938 [==============================] - 5s 5ms/step - loss: 0.1639 - accuracy: 0.9537 Epoch 4/5 938/938 [==============================] - 5s 5ms/step - loss: 0.1322 - accuracy: 0.9625 Epoch 5/5 938/938 [==============================] - 5s 5ms/step - loss: 0.1107 - accuracy: 0.9682 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate( x=test_images, y=test_labels, batch_size=BATCH_SIZE)#, #verbose=1, #sample_weight=None, #steps=None, #callbacks=None, #max_queue_size=10, #workers=1, #use_multiprocessing=False, #return_dict=False, #**kwargs #) print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 1s 5ms/step - loss: 0.1066 - accuracy: 0.9694 Test accuracy: 0.9693999886512756 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the first max pooling layer ##tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.MaxPooling2D(pool_size=(2, 2)), # TODO: Define the second convolutional layer ##tf.keras.layers.Conv2D('''TODO'''), tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the second max pooling layer ##tf.keras.layers.MaxPool2D('''TODO'''), tf.keras.layers.MaxPooling2D(pool_size=(2, 2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output #'''TODO: Dense layer to output classification probabilities''' tf.keras.layers.Dense(10, activation=tf.keras.activations.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output 2022-03-28 14:34:43.418149: I tensorflow/stream_executor/cuda/cuda_dnn.cc:368] Loaded cuDNN version 8303 ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 7s 7ms/step - loss: 0.1806 - accuracy: 0.9467 Epoch 2/5 938/938 [==============================] - 6s 7ms/step - loss: 0.0578 - accuracy: 0.9819 Epoch 3/5 938/938 [==============================] - 6s 7ms/step - loss: 0.0395 - accuracy: 0.9878 Epoch 4/5 938/938 [==============================] - 7s 7ms/step - loss: 0.0300 - accuracy: 0.9906 Epoch 5/5 938/938 [==============================] - 7s 7ms/step - loss: 0.0232 - accuracy: 0.9924 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate( x=test_images, y=test_labels, batch_size=BATCH_SIZE) print('Test accuracy:', test_acc) ###Output 157/157 [==============================] - 1s 5ms/step - loss: 0.1066 - accuracy: 0.9694 Test accuracy: 0.9693999886512756 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 79 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are grey. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = # TODO #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy() # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = # TODO optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____ ###Markdown Visit MIT Deep Learning Run in Google Colab View Source on GitHub Copyright Information ###Code # Copyright 2020 MIT 6.S191 Introduction to Deep Learning. All Rights Reserved. # # Licensed under the MIT License. You may not use this file except in compliance # with the License. Use and/or modification of this code outside of 6.S191 must # reference: # # © MIT 6.S191: Introduction to Deep Learning # http://introtodeeplearning.com # ###Output _____no_output_____ ###Markdown Laboratory 2: Computer Vision Part 1: MNIST Digit ClassificationIn the first portion of this lab, we will build and train a convolutional neural network (CNN) for classification of handwritten digits from the famous [MNIST](http://yann.lecun.com/exdb/mnist/) dataset. The MNIST dataset consists of 60,000 training images and 10,000 test images. Our classes are the digits 0-9.First, let's download the course repository, install dependencies, and import the relevant packages we'll need for this lab. ###Code # Import Tensorflow 2.0 %tensorflow_version 2.x import tensorflow as tf !pip install mitdeeplearning import mitdeeplearning as mdl import matplotlib.pyplot as plt import numpy as np import random from tqdm import tqdm # Check that we are using a GPU, if not switch runtimes # using Runtime > Change Runtime Type > GPU assert len(tf.config.list_physical_devices('GPU')) > 0 ###Output Requirement already satisfied: mitdeeplearning in /usr/local/lib/python3.6/dist-packages (0.1.2) Requirement already satisfied: regex in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (2019.12.20) Requirement already satisfied: tqdm in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (4.38.0) Requirement already satisfied: numpy in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (1.18.3) Requirement already satisfied: gym in /usr/local/lib/python3.6/dist-packages (from mitdeeplearning) (0.17.1) Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.12.0) Requirement already satisfied: cloudpickle<1.4.0,>=1.2.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.3.0) Requirement already satisfied: pyglet<=1.5.0,>=1.4.0 in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.5.0) Requirement already satisfied: scipy in /usr/local/lib/python3.6/dist-packages (from gym->mitdeeplearning) (1.4.1) Requirement already satisfied: future in /usr/local/lib/python3.6/dist-packages (from pyglet<=1.5.0,>=1.4.0->gym->mitdeeplearning) (0.16.0) ###Markdown 1.1 MNIST dataset Let's download and load the dataset and display a few random samples from it: ###Code mnist = tf.keras.datasets.mnist (train_images, train_labels), (test_images, test_labels) = mnist.load_data() train_images = (np.expand_dims(train_images, axis=-1)/255.).astype(np.float32) train_labels = (train_labels).astype(np.int64) test_images = (np.expand_dims(test_images, axis=-1)/255.).astype(np.float32) test_labels = (test_labels).astype(np.int64) ###Output _____no_output_____ ###Markdown Our training set is made up of 28x28 grayscale images of handwritten digits. Let's visualize what some of these images and their corresponding training labels look like. ###Code plt.figure(figsize=(10,10)) random_inds = np.random.choice(60000,36) for i in range(36): plt.subplot(6,6,i+1) plt.xticks([]) plt.yticks([]) plt.grid(False) image_ind = random_inds[i] plt.imshow(np.squeeze(train_images[image_ind]), cmap=plt.cm.binary) plt.xlabel(train_labels[image_ind]) ###Output _____no_output_____ ###Markdown 1.2 Neural Network for Handwritten Digit ClassificationWe'll first build a simple neural network consisting of two fully connected layers and apply this to the digit classification task. Our network will ultimately output a probability distribution over the 10 digit classes (0-9). This first architecture we will be building is depicted below: Fully connected neural network architectureTo define the architecture of this first fully connected neural network, we'll once again use the Keras API and define the model using the [`Sequential`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequential) class. Note how we first use a [`Flatten`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Flatten) layer, which flattens the input so that it can be fed into the model. In this next block, you'll define the fully connected layers of this simple work. ###Code def build_fc_model(): fc_model = tf.keras.Sequential([ # First define a Flatten layer tf.keras.layers.Flatten(), # '''TODO: Define the activation function for the first fully connected (Dense) layer.''' tf.keras.layers.Dense(128, activation=tf.nn.relu), # '''TODO: Define the second Dense layer to output the classification probabilities''' tf.keras.layers.Dense(10,activation=tf.nn.softmax) ]) return fc_model model = build_fc_model() ###Output _____no_output_____ ###Markdown As we progress through this next portion, you may find that you'll want to make changes to the architecture defined above. **Note that in order to update the model later on, you'll need to re-run the above cell to re-initialize the model. ** Let's take a step back and think about the network we've just created. The first layer in this network, `tf.keras.layers.Flatten`, transforms the format of the images from a 2d-array (28 x 28 pixels), to a 1d-array of 28 * 28 = 784 pixels. You can think of this layer as unstacking rows of pixels in the image and lining them up. There are no learned parameters in this layer; it only reformats the data.After the pixels are flattened, the network consists of a sequence of two `tf.keras.layers.Dense` layers. These are fully-connected neural layers. The first `Dense` layer has 128 nodes (or neurons). The second (and last) layer (which you've defined!) should return an array of probability scores that sum to 1. Each node contains a score that indicates the probability that the current image belongs to one of the handwritten digit classes.That defines our fully connected model! Compile the modelBefore training the model, we need to define a few more settings. These are added during the model's [`compile`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialcompile) step:* *Loss function* — This defines how we measure how accurate the model is during training. As was covered in lecture, during training we want to minimize this function, which will "steer" the model in the right direction.* *Optimizer* — This defines how the model is updated based on the data it sees and its loss function.* *Metrics* — Here we can define metrics used to monitor the training and testing steps. In this example, we'll look at the *accuracy*, the fraction of the images that are correctly classified.We'll start out by using a stochastic gradient descent (SGD) optimizer initialized with a learning rate of 0.1. Since we are performing a categorical classification task, we'll want to use the [cross entropy loss](https://www.tensorflow.org/api_docs/python/tf/keras/metrics/sparse_categorical_crossentropy).You'll want to experiment with both the choice of optimizer and learning rate and evaluate how these affect the accuracy of the trained model. ###Code '''TODO: Experiment with different optimizers and learning rates. How do these affect the accuracy of the trained model? Which optimizers and/or learning rates yield the best performance?''' model.compile(optimizer=tf.keras.optimizers.SGD(learning_rate=1e-1), loss='sparse_categorical_crossentropy', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown Train the modelWe're now ready to train our model, which will involve feeding the training data (`train_images` and `train_labels`) into the model, and then asking it to learn the associations between images and labels. We'll also need to define the batch size and the number of epochs, or iterations over the MNIST dataset, to use during training. In Lab 1, we saw how we can use `GradientTape` to optimize losses and train models with stochastic gradient descent. After defining the model settings in the `compile` step, we can also accomplish training by calling the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) method on an instance of the `Model` class. We will use this to train our fully connected model ###Code # Define the batch size and the number of epochs to use during training BATCH_SIZE = 64 EPOCHS = 5 model.fit(train_images, train_labels, batch_size=BATCH_SIZE, epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0888 - accuracy: 0.9753 Epoch 2/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0784 - accuracy: 0.9780 Epoch 3/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0697 - accuracy: 0.9806 Epoch 4/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0633 - accuracy: 0.9822 Epoch 5/5 938/938 [==============================] - 2s 2ms/step - loss: 0.0574 - accuracy: 0.9839 ###Markdown As the model trains, the loss and accuracy metrics are displayed. With five epochs and a learning rate of 0.01, this fully connected model should achieve an accuracy of approximatley 0.97 (or 97%) on the training data. Evaluate accuracy on the test datasetNow that we've trained the model, we can ask it to make predictions about a test set that it hasn't seen before. In this example, the `test_images` array comprises our test dataset. To evaluate accuracy, we can check to see if the model's predictions match the labels from the `test_labels` array. Use the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method to evaluate the model on the test dataset! ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images,test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0815 - accuracy: 0.9750 Test accuracy: 0.9750000238418579 ###Markdown You may observe that the accuracy on the test dataset is a little lower than the accuracy on the training dataset. This gap between training accuracy and test accuracy is an example of *overfitting*, when a machine learning model performs worse on new data than on its training data. What is the highest accuracy you can achieve with this first fully connected model? Since the handwritten digit classification task is pretty straightforward, you may be wondering how we can do better... 1.3 Convolutional Neural Network (CNN) for handwritten digit classification As we saw in lecture, convolutional neural networks (CNNs) are particularly well-suited for a variety of tasks in computer vision, and have achieved near-perfect accuracies on the MNIST dataset. We will now build a CNN composed of two convolutional layers and pooling layers, followed by two fully connected layers, and ultimately output a probability distribution over the 10 digit classes (0-9). The CNN we will be building is depicted below: Define the CNN modelWe'll use the same training and test datasets as before, and proceed similarly as our fully connected network to define and train our new CNN model. To do this we will explore two layers we have not encountered before: you can use [`keras.layers.Conv2D` ](https://www.tensorflow.org/api_docs/python/tf/keras/layers/Conv2D) to define convolutional layers and [`keras.layers.MaxPool2D`](https://www.tensorflow.org/api_docs/python/tf/keras/layers/MaxPool2D) to define the pooling layers. Use the parameters shown in the network architecture above to define these layers and build the CNN model. ###Code def build_cnn_model(): cnn_model = tf.keras.Sequential([ # TODO: Define the first convolutional layer tf.keras.layers.Conv2D(filters=24, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the first max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), # TODO: Define the second convolutional layer tf.keras.layers.Conv2D(filters=36, kernel_size=(3,3), activation=tf.nn.relu), # TODO: Define the second max pooling layer tf.keras.layers.MaxPool2D(pool_size=(2,2)), tf.keras.layers.Flatten(), tf.keras.layers.Dense(128, activation=tf.nn.relu), # TODO: Define the last Dense layer to output the classification # probabilities. Pay attention to the activation needed a probability # output tf.keras.layers.Dense(10, activation=tf.nn.softmax) ]) return cnn_model cnn_model = build_cnn_model() # Initialize the model by passing some data through cnn_model.predict(train_images[[0]]) # Print the summary of the layers in the model. print(cnn_model.summary()) ###Output Model: "sequential_2" _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d (Conv2D) multiple 240 _________________________________________________________________ max_pooling2d (MaxPooling2D) multiple 0 _________________________________________________________________ conv2d_1 (Conv2D) multiple 7812 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 multiple 0 _________________________________________________________________ flatten_2 (Flatten) multiple 0 _________________________________________________________________ dense_4 (Dense) multiple 115328 _________________________________________________________________ dense_5 (Dense) multiple 1290 ================================================================= Total params: 124,670 Trainable params: 124,670 Non-trainable params: 0 _________________________________________________________________ None ###Markdown Train and test the CNN modelNow, as before, we can define the loss function, optimizer, and metrics through the `compile` method. Compile the CNN model with an optimizer and learning rate of choice: ###Code '''TODO: Define the compile operation with your optimizer and learning rate of choice''' cnn_model.compile(optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3), loss='sparse_categorical_crossentropy', metrics=['accuracy']) # TODO ###Output _____no_output_____ ###Markdown As was the case with the fully connected model, we can train our CNN using the `fit` method via the Keras API. ###Code '''TODO: Use model.fit to train the CNN model, with the same batch_size and number of epochs previously used.''' cnn_model.fit(train_images,train_labels,batch_size=BATCH_SIZE,epochs=EPOCHS) ###Output Epoch 1/5 938/938 [==============================] - 3s 3ms/step - loss: 0.1904 - accuracy: 0.9430 Epoch 2/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0529 - accuracy: 0.9838 Epoch 3/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0366 - accuracy: 0.9891 Epoch 4/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0276 - accuracy: 0.9912 Epoch 5/5 938/938 [==============================] - 3s 3ms/step - loss: 0.0212 - accuracy: 0.9936 ###Markdown Great! Now that we've trained the model, let's evaluate it on the test dataset using the [`evaluate`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialevaluate) method: ###Code '''TODO: Use the evaluate method to test the model!''' test_loss, test_acc = model.evaluate(test_images,test_labels) print('Test accuracy:', test_acc) ###Output 313/313 [==============================] - 1s 2ms/step - loss: 0.0815 - accuracy: 0.9750 Test accuracy: 0.9750000238418579 ###Markdown What is the highest accuracy you're able to achieve using the CNN model, and how does the accuracy of the CNN model compare to the accuracy of the simple fully connected network? What optimizers and learning rates seem to be optimal for training the CNN model? Make predictions with the CNN modelWith the model trained, we can use it to make predictions about some images. The [`predict`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialpredict) function call generates the output predictions given a set of input samples. ###Code predictions = cnn_model.predict(test_images) ###Output _____no_output_____ ###Markdown With this function call, the model has predicted the label for each image in the testing set. Let's take a look at the prediction for the first image in the test dataset: ###Code predictions[0] ###Output _____no_output_____ ###Markdown As you can see, a prediction is an array of 10 numbers. Recall that the output of our model is a probability distribution over the 10 digit classes. Thus, these numbers describe the model's "confidence" that the image corresponds to each of the 10 different digits. Let's look at the digit that has the highest confidence for the first image in the test dataset: ###Code '''TODO: identify the digit with the highest confidence prediction for the first image in the test dataset. ''' prediction = np.argmax(predictions[0]) print(prediction) ###Output 7 ###Markdown So, the model is most confident that this image is a "???". We can check the test label (remember, this is the true identity of the digit) to see if this prediction is correct: ###Code print("Label of this digit is:", test_labels[0]) plt.imshow(test_images[0,:,:,0], cmap=plt.cm.binary) ###Output Label of this digit is: 7 ###Markdown It is! Let's visualize the classification results on the MNIST dataset. We will plot images from the test dataset along with their predicted label, as well as a histogram that provides the prediction probabilities for each of the digits: ###Code #@title Change the slider to look at the model's predictions! { run: "auto" } image_index = 99 #@param {type:"slider", min:0, max:100, step:1} plt.subplot(1,2,1) mdl.lab2.plot_image_prediction(image_index, predictions, test_labels, test_images) plt.subplot(1,2,2) mdl.lab2.plot_value_prediction(image_index, predictions, test_labels) ###Output _____no_output_____ ###Markdown We can also plot several images along with their predictions, where correct prediction labels are blue and incorrect prediction labels are red. The number gives the percent confidence (out of 100) for the predicted label. Note the model can be very confident in an incorrect prediction! ###Code # Plots the first X test images, their predicted label, and the true label # Color correct predictions in blue, incorrect predictions in red num_rows = 5 num_cols = 4 num_images = num_rows*num_cols plt.figure(figsize=(2*2*num_cols, 2*num_rows)) for i in range(num_images): plt.subplot(num_rows, 2*num_cols, 2*i+1) mdl.lab2.plot_image_prediction(i, predictions, test_labels, test_images) plt.subplot(num_rows, 2*num_cols, 2*i+2) mdl.lab2.plot_value_prediction(i, predictions, test_labels) ###Output _____no_output_____ ###Markdown 1.4 Training the model 2.0Earlier in the lab, we used the [`fit`](https://www.tensorflow.org/api_docs/python/tf/keras/models/Sequentialfit) function call to train the model. This function is quite high-level and intuitive, which is really useful for simpler models. As you may be able to tell, this function abstracts away many details in the training call, and we have less control over training model, which could be useful in other contexts. As an alternative to this, we can use the [`tf.GradientTape`](https://www.tensorflow.org/api_docs/python/tf/GradientTape) class to record differentiation operations during training, and then call the [`tf.GradientTape.gradient`](https://www.tensorflow.org/api_docs/python/tf/GradientTapegradient) function to actually compute the gradients. You may recall seeing this in Lab 1 Part 1, but let's take another look at this here.We'll use this framework to train our `cnn_model` using stochastic gradient descent. ###Code # Rebuild the CNN model cnn_model = build_cnn_model() batch_size = 12 loss_history = mdl.util.LossHistory(smoothing_factor=0.95) # to record the evolution of the loss plotter = mdl.util.PeriodicPlotter(sec=2, xlabel='Iterations', ylabel='Loss', scale='semilogy') optimizer = tf.keras.optimizers.SGD(learning_rate=1e-2) # define our optimizer if hasattr(tqdm, '_instances'): tqdm._instances.clear() # clear if it exists for idx in tqdm(range(0, train_images.shape[0], batch_size)): # First grab a batch of training data and convert the input images to tensors (images, labels) = (train_images[idx:idx+batch_size], train_labels[idx:idx+batch_size]) images = tf.convert_to_tensor(images, dtype=tf.float32) # GradientTape to record differentiation operations with tf.GradientTape() as tape: #'''TODO: feed the images into the model and obtain the predictions''' logits = cnn_model(images) #'''TODO: compute the categorical cross entropy loss loss_value = tf.keras.backend.sparse_categorical_crossentropy(labels,logits) # TODO loss_history.append(loss_value.numpy().mean()) # append the loss to the loss_history record plotter.plot(loss_history.get()) # Backpropagation '''TODO: Use the tape to compute the gradient against all parameters in the CNN model. Use cnn_model.trainable_variables to access these parameters.''' grads = tape.gradient(loss_value,cnn_model.trainable_variables) optimizer.apply_gradients(zip(grads, cnn_model.trainable_variables)) ###Output _____no_output_____

notebooks/zipcodes_import.ipynb

###Markdown zipcodes_import.ipynb README As noted in the master README this notebook's usage is generally not required unless the geo_zipcodes.db has to be created from scratch. Assuming that the data folder structure is still in place, this notebook should run as is without alteration of the config.yml file. ###Code import json import os import sqlite3 import sys from datetime import datetime import logzero import numpy as np import pandas as pd import yaml from logzero import logger sys.path.append("../source") import queries log_path = "logs/" log_file = "zip_code_import.log" logzero.logfile(log_path + log_file, maxBytes=1e6, backupCount=5, disableStderrLogger=True) logger.info(f"{log_path}, {log_file}") logger.info(sys.path) try: with open("../source/config.yml", "r") as config_in: configs = yaml.load(config_in, Loader=yaml.SafeLoader) logger.info(configs) except: logger.error(f"config file open failure.") exit(1) data_path = configs["file_paths"]["data_path_gaz"] data_file = configs["file_names"]["data_file_gaz"] db_path = configs["file_paths"]["downloads_path_db"] db_file = configs["file_names"]["db_file_gzc"] logger.info(f"{data_path}, {data_file}") logger.info(f"{db_path}, {db_file}") downloads_dir = os.path.isdir(configs["file_paths"]["downloads_path"]) if not downloads_dir: os.makedirs(configs["file_paths"]["downloads_path"]) os.makedirs(configs["file_paths"]["downloads_path_db"]) logger.info(f"created downloads directory structure") print(f"created downloads directory structure") else: logger.info(f"directory {configs['file_paths']['downloads_path']} present") print(f"directory {configs['file_paths']['downloads_path']} present") original = ["GEOID", "ALAND", "AWATER", "ALAND_SQMI", "AWATER_SQMI", "INTPTLAT", "INTPTLONG"] header = [ "ZIPCODE", "LAND_AREA_MSQ", "WATER_AREA_MSQ", "LAND_AREA_SQMI", "WATER_AREA_SQMI", "LAT_ZC", "LON_ZC", ] names = [x.lower() for x in header] logger.info("Dataframe and db column names") logger.info(names) dtypes = { names[0]: object, names[1]: np.float64, names[2]: np.float64, names[3]: np.float64, names[4]: np.float64, names[5]: np.float64, names[6]: np.float64, } try: df_raw = pd.read_csv(data_path + data_file, sep="\t", dtype=dtypes, names=names, header=0) logger.info("CSV file successfully read.") except: logger.error("error reading CSV file.") df_raw # establish db connection and cursor conn = sqlite3.connect(db_path + db_file) cursor = conn.cursor() df_raw.to_sql( "geo_zipcodes", conn, if_exists="append", index=False, method="multi", ) conn.commit() conn.close() ###Output _____no_output_____

scripts/data/process_ecmwf.ipynb

###Markdown Load IFS data ###Code ds_ifs_pl = xr.open_mfdataset('../data/raw/ifs/pl_*.nc', parallel=True, chunks={'time': 2}) ds_ifs_sfc = xr.open_mfdataset('../data/raw/ifs/sfc_*.nc', parallel=True, chunks={'time': 2}) ds_ifs_t = ds_ifs_pl['t'].to_dataset('level') ds_ifs_t = ds_ifs_t.rename({500: 't_500', 850: 't_850'}) ds_ifs_gh = ds_ifs_pl['gh'].to_dataset('level') ds_ifs_gh = ds_ifs_gh.rename({500: 'gh_500', 850: 'gh_850'}) ds_ifs_merged = xr.merge([ds_ifs_sfc, ds_ifs_t, ds_ifs_gh]) ds_ifs_merged = ds_ifs_merged.isel(latitude=slice(None, None, -1)) ds_ifs_merged = ds_ifs_merged.rename({'number': 'ensemble'}) ds_ifs_train = ds_ifs_merged.sel(time=slice('2017-01-01 00:00', '2018-12-31 12:00')) ds_ifs_train.to_zarr( '../data/processed/ifs/ds_train', encoding={ 't2m': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 't_500': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 't_850': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 'gh_500': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 'gh_850': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, } ) ds_ifs_test = ds_ifs_merged.sel(time=slice('2019-01-01 00:00', '2019-12-31 12:00')) ds_ifs_test.to_zarr( '../data/processed/ifs/ds_test', encoding={ 't2m': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 't_500': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 't_850': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 'gh_500': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, 'gh_850': {'dtype': 'float32', 'scale_factor': 1.0, 'add_offset': 0.0}, } ) ###Output _____no_output_____

examples/notebooks/46_local_rf_training.ipynb

###Markdown Uncomment the following line to install [geemap](https://geemap.org) if needed. ###Code # !pip install geemap scikit-learn ###Output _____no_output_____ ###Markdown How to use locally trained machine learning models with GEEThis notebook illustrates how to train a random forest (or any other ensemble tree estimator) locally using scikit-learn, convert the estimator into a string representation that Earth Engine can interpret, and how to apply the machine learning model with EE. **The notebook and the geemap machine learning module ([ml.py](https://geemap.org/ml/)) were contributed by [Kel Markert](https://github.com/KMarkert). A huge thank you to him.** ###Code import ee import geemap import pandas as pd from geemap import ml from sklearn import ensemble geemap.ee_initialize() ###Output _____no_output_____ ###Markdown Train a model locally using scikit-learnIn this demo, we are going to use the training data from [here](https://github.com/giswqs/geemap/blob/master/examples/data/rf_example.csv). ###Code # read the feature table to train our RandomForest model # data taken from ee.FeatureCollection('GOOGLE/EE/DEMOS/demo_landcover_labels') url = "https://raw.githubusercontent.com/giswqs/geemap/master/examples/data/rf_example.csv" df = pd.read_csv(url) df # specify the names of the features (i.e. band names) and label # feature names used to extract out features and define what bands feature_names = ['B2', 'B3', 'B4', 'B5', 'B6', 'B7'] label = "landcover" # get the features and labels into seperate variables X = df[feature_names] y = df[label] # create a classifier and fit n_trees = 10 rf = ensemble.RandomForestClassifier(n_trees).fit(X,y) ###Output _____no_output_____ ###Markdown Convert a sklearn classifier object to a list of strings ###Code # convert the estimator into a list of strings # this function also works with the ensemble.ExtraTrees estimator trees = ml.rf_to_strings(rf,feature_names) # print the first tree to see the result print(trees[0]) print(trees[1]) # number of trees we converted should equal the number of trees we defined for the model len(trees) == n_trees ###Output _____no_output_____ ###Markdown Convert sklearn classifier to GEE classifierAt this point you can take the list of strings and save them locally to avoid training again. However, we want to use the model with EE so we need to create an ee.Classifier and persist the data on ee for best results. ###Code # create a ee classifier to use with ee objects from the trees ee_classifier = ml.strings_to_classifier(trees) # ee_classifier.getInfo() ###Output _____no_output_____ ###Markdown Classify image using GEE classifier ###Code # Make a cloud-free Landsat 8 TOA composite (from raw imagery). l8 = ee.ImageCollection('LANDSAT/LC08/C01/T1'); image = ee.Algorithms.Landsat.simpleComposite( collection= l8.filterDate('2018-01-01', '2018-12-31'), asFloat= True ) # classify the image using the classifier we created from the local training # note: here we select the feature_names from the image that way the classifier knows which bands to use classified = image.select(feature_names).classify(ee_classifier) # display results Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Yay!! 🎉 Looks like our example works. Don't party too much because there is a catch...This workflow has several limitations particularly due to how much data you can pass from the client to the server and how large of a model ee can acutally handle. EE can only handle 40MB of data passed to the server, so if you have a lot of large decision tree strings then this will not work. Also, creating a classifier from strings has limitation (see this ee-forum discussion: https://groups.google.com/g/google-earth-engine-developers/c/lFFU1GBPzi8/m/6MewQk1FBwAJ), this is again limited by string lengths when ee creates a computation graph.So, you can use this but know you will probably run into errors when training large models. Save trees to the cloudNow we have the strings in a format that ee can use, we want to save it for later use. There is a function to export a list of tree strings to a feature collection. The feature collection will have a pro ###Code user_id = geemap.ee_user_id() user_id # specify asset id where to save trees # be sure to change <user_name> to your ee user name asset_id = user_id + "/random_forest_strings_test" asset_id # kick off an export process so it will be saved to the ee asset ml.export_trees_to_fc(trees,asset_id) # this will kick off an export task, so wait a few minutes before moving on # read the exported tree feature collection rf_fc = ee.FeatureCollection(asset_id) # convert it to a classifier, very similar to the `ml.trees_to_classifier` function another_classifier = ml.fc_to_classifier(rf_fc) # classify the image again but with the classifier from the persisted trees classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Save trees locally ###Code import os out_csv = os.path.expanduser("~/Downloads/trees.csv") ml.trees_to_csv(trees, out_csv) another_classifier = ml.csv_to_classifier(out_csv) classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Uncomment the following line to install [geemap](https://geemap.org) if needed. ###Code # !pip install geemap scikit-learn ###Output _____no_output_____ ###Markdown How to use locally trained machine learning models with GEEThis notebook illustrates how to train a random forest (or any other ensemble tree estimator) locally using scikit-learn, convert the estimator into a string representation that Earth Engine can interpret, and how to apply the machine learning model with EE. **The notebook and the geemap machine learning module ([ml.py](https://geemap.org/ml/)) were contributed by [Kel Markert](https://github.com/KMarkert). A huge thank you to him.** ###Code import ee import geemap import pandas as pd from geemap import ml from sklearn import ensemble geemap.ee_initialize() ###Output _____no_output_____ ###Markdown Train a model locally using scikit-learnIn this demo, we are going to use the training data from [here](https://github.com/giswqs/geemap/blob/master/examples/data/rf_example.csv). ###Code # read the feature table to train our RandomForest model # data taken from ee.FeatureCollection('GOOGLE/EE/DEMOS/demo_landcover_labels') url = "https://raw.githubusercontent.com/giswqs/geemap/master/examples/data/rf_example.csv" df = pd.read_csv(url) df # specify the names of the features (i.e. band names) and label # feature names used to extract out features and define what bands feature_names = ['B2', 'B3', 'B4', 'B5', 'B6', 'B7'] label = "landcover" # get the features and labels into seperate variables X = df[feature_names] y = df[label] # create a classifier and fit n_trees = 100 rf = ensemble.RandomForestClassifier(n_trees).fit(X,y) ###Output _____no_output_____ ###Markdown Convert a sklearn classifier object to a list of strings ###Code # convert the estimator into a list of strings # this function also works with the ensemble.ExtraTrees estimator trees = ml.rf_to_strings(rf,feature_names) # print the first tree to see the result print(trees[0]) print(trees[1]) # number of trees we converted should equal the number of trees we defined for the model len(trees) == n_trees ###Output _____no_output_____ ###Markdown Convert sklearn classifier to GEE classifierAt this point you can take the list of strings and save them locally to avoid training again. However, we want to use the model with EE so we need to create an ee.Classifier and persist the data on ee for best results. ###Code # create a ee classifier to use with ee objects from the trees ee_classifier = ml.strings_to_classifier(trees) # ee_classifier.getInfo() ###Output _____no_output_____ ###Markdown Classify image using GEE classifier ###Code # Make a cloud-free Landsat 8 TOA composite (from raw imagery). l8 = ee.ImageCollection('LANDSAT/LC08/C01/T1'); image = ee.Algorithms.Landsat.simpleComposite( collection= l8.filterDate('2018-01-01', '2018-12-31'), asFloat= True ) # classify the image using the classifier we created from the local training # note: here we select the feature_names from the image that way the classifier knows which bands to use classified = image.select(feature_names).classify(ee_classifier) # display results Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Yay!! 🎉 Looks like our example works. Don't party too much because there is a catch...This workflow has several limitations particularly due to how much data you can pass from the client to the server and how large of a model ee can acutally handle. EE can only handle 40MB of data passed to the server, so if you have a lot of large decision tree strings then this will not work. Also, creating a classifier from strings has limitation (see this ee-forum discussion: https://groups.google.com/g/google-earth-engine-developers/c/lFFU1GBPzi8/m/6MewQk1FBwAJ), this is again limited by string lengths when ee creates a computation graph.So, you can use this but know you will probably run into errors when training large models. Save trees to the cloudNow we have the strings in a format that ee can use, we want to save it for later use. There is a function to export a list of tree strings to a feature collection. The feature collection will have a pro ###Code user_id = geemap.ee_user_id() user_id # specify asset id where to save trees # be sure to change <user_name> to your ee user name asset_id = user_id + "/random_forest_strings_test" asset_id # kick off an export process so it will be saved to the ee asset # ml.export_trees_to_fc(trees,asset_id) # this will kick off an export task, so wait a few minutes before moving on # read the exported tree feature collection rf_fc = ee.FeatureCollection(asset_id) # convert it to a classifier, very similar to the `ml.trees_to_classifier` function another_classifier = ml.fc_to_classifier(rf_fc) # classify the image again but with the classifier from the persisted trees classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Save trees locally ###Code import os out_csv = os.path.expanduser("~/Downloads/trees.csv") ml.trees_to_csv(trees, out_csv) another_classifier = ml.csv_to_classifier(out_csv) classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Uncomment the following line to install [geemap](https://geemap.org) if needed. ###Code # !pip install geemap scikit-learn ###Output _____no_output_____ ###Markdown How to use locally trained machine learning models with GEEThis notebook illustrates how to train a random forest (or any other ensemble tree estimator) locally using scikit-learn, convert the estimator into a string representation that Earth Engine can interpret, and how to apply the machine learning model with EE. **The notebook and the geemap machine learning module ([ml.py](https://geemap.org/ml/)) were contributed by [Kel Markert](https://github.com/KMarkert). A huge thank you to him.** ###Code import ee import geemap import pandas as pd from geemap import ml from sklearn import ensemble geemap.ee_initialize() ###Output _____no_output_____ ###Markdown Train a model locally using scikit-learnIn this demo, we are going to use the training data from [here](https://github.com/giswqs/geemap/blob/master/examples/data/rf_example.csv). ###Code # read the feature table to train our RandomForest model # data taken from ee.FeatureCollection('GOOGLE/EE/DEMOS/demo_landcover_labels') url = "https://raw.githubusercontent.com/giswqs/geemap/master/examples/data/rf_example.csv" df = pd.read_csv(url) df # specify the names of the features (i.e. band names) and label # feature names used to extract out features and define what bands feature_names = ['B2', 'B3', 'B4', 'B5', 'B6', 'B7'] label = "landcover" # get the features and labels into separate variables X = df[feature_names] y = df[label] # create a classifier and fit n_trees = 10 rf = ensemble.RandomForestClassifier(n_trees).fit(X,y) ###Output _____no_output_____ ###Markdown Convert a sklearn classifier object to a list of strings ###Code # convert the estimator into a list of strings # this function also works with the ensemble.ExtraTrees estimator trees = ml.rf_to_strings(rf,feature_names) # print the first tree to see the result print(trees[0]) print(trees[1]) # number of trees we converted should equal the number of trees we defined for the model len(trees) == n_trees ###Output _____no_output_____ ###Markdown Convert sklearn classifier to GEE classifierAt this point you can take the list of strings and save them locally to avoid training again. However, we want to use the model with EE so we need to create an ee.Classifier and persist the data on ee for best results. ###Code # create a ee classifier to use with ee objects from the trees ee_classifier = ml.strings_to_classifier(trees) # ee_classifier.getInfo() ###Output _____no_output_____ ###Markdown Classify image using GEE classifier ###Code # Make a cloud-free Landsat 8 TOA composite (from raw imagery). l8 = ee.ImageCollection('LANDSAT/LC08/C01/T1'); image = ee.Algorithms.Landsat.simpleComposite( collection= l8.filterDate('2018-01-01', '2018-12-31'), asFloat= True ) # classify the image using the classifier we created from the local training # note: here we select the feature_names from the image that way the classifier knows which bands to use classified = image.select(feature_names).classify(ee_classifier) # display results Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Yay!! 🎉 Looks like our example works. Don't party too much because there is a catch...This workflow has several limitations particularly due to how much data you can pass from the client to the server and how large of a model ee can actually handle. EE can only handle 40MB of data passed to the server, so if you have a lot of large decision tree strings then this will not work. Also, creating a classifier from strings has limitation (see this ee-forum discussion: https://groups.google.com/g/google-earth-engine-developers/c/lFFU1GBPzi8/m/6MewQk1FBwAJ), this is again limited by string lengths when ee creates a computation graph.So, you can use this but know you will probably run into errors when training large models. Save trees to the cloudNow we have the strings in a format that ee can use, we want to save it for later use. There is a function to export a list of tree strings to a feature collection. The feature collection will have a pro ###Code user_id = geemap.ee_user_id() user_id # specify asset id where to save trees # be sure to change <user_name> to your ee user name asset_id = user_id + "/random_forest_strings_test" asset_id # kick off an export process so it will be saved to the ee asset ml.export_trees_to_fc(trees,asset_id) # this will kick off an export task, so wait a few minutes before moving on # read the exported tree feature collection rf_fc = ee.FeatureCollection(asset_id) # convert it to a classifier, very similar to the `ml.trees_to_classifier` function another_classifier = ml.fc_to_classifier(rf_fc) # classify the image again but with the classifier from the persisted trees classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Save trees locally ###Code import os out_csv = os.path.expanduser("~/Downloads/trees.csv") ml.trees_to_csv(trees, out_csv) another_classifier = ml.csv_to_classifier(out_csv) classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75,-122.25), zoom=11) Map.addLayer(image,{"bands": ['B7', 'B5', 'B3'], "min":0.05, "max": 0.55, "gamma":1.5}, 'image') Map.addLayer(classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']},'classification') Map ###Output _____no_output_____ ###Markdown Uncomment the following line to install [geemap](https://geemap.org) if needed. ###Code # !pip install geemap scikit-learn ###Output _____no_output_____ ###Markdown How to use locally trained machine learning models with GEEThis notebook illustrates how to train a random forest (or any other ensemble tree estimator) locally using scikit-learn, convert the estimator into a string representation that Earth Engine can interpret, and how to apply the machine learning model with EE. **The notebook and the geemap machine learning module ([ml.py](https://geemap.org/ml/)) were contributed by [Kel Markert](https://github.com/KMarkert). A huge thank you to him.** ###Code import ee import geemap import pandas as pd from geemap import ml from sklearn import ensemble geemap.ee_initialize() ###Output _____no_output_____ ###Markdown Train a model locally using scikit-learnIn this demo, we are going to use the training data from [here](https://github.com/giswqs/geemap/blob/master/examples/data/rf_example.csv). ###Code # read the feature table to train our RandomForest model # data taken from ee.FeatureCollection('GOOGLE/EE/DEMOS/demo_landcover_labels') url = "https://raw.githubusercontent.com/giswqs/geemap/master/examples/data/rf_example.csv" df = pd.read_csv(url) df # specify the names of the features (i.e. band names) and label # feature names used to extract out features and define what bands feature_names = ['B2', 'B3', 'B4', 'B5', 'B6', 'B7'] label = "landcover" # get the features and labels into separate variables X = df[feature_names] y = df[label] # create a classifier and fit n_trees = 10 rf = ensemble.RandomForestClassifier(n_trees).fit(X, y) ###Output _____no_output_____ ###Markdown Convert a sklearn classifier object to a list of strings ###Code # convert the estimator into a list of strings # this function also works with the ensemble.ExtraTrees estimator trees = ml.rf_to_strings(rf, feature_names) # print the first tree to see the result print(trees[0]) print(trees[1]) # number of trees we converted should equal the number of trees we defined for the model len(trees) == n_trees ###Output _____no_output_____ ###Markdown Convert sklearn classifier to GEE classifierAt this point you can take the list of strings and save them locally to avoid training again. However, we want to use the model with EE so we need to create an ee.Classifier and persist the data on ee for best results. ###Code # create a ee classifier to use with ee objects from the trees ee_classifier = ml.strings_to_classifier(trees) # ee_classifier.getInfo() ###Output _____no_output_____ ###Markdown Classify image using GEE classifier ###Code # Make a cloud-free Landsat 8 TOA composite (from raw imagery). l8 = ee.ImageCollection('LANDSAT/LC08/C01/T1') image = ee.Algorithms.Landsat.simpleComposite( collection=l8.filterDate('2018-01-01', '2018-12-31'), asFloat=True ) # classify the image using the classifier we created from the local training # note: here we select the feature_names from the image that way the classifier knows which bands to use classified = image.select(feature_names).classify(ee_classifier) # display results Map = geemap.Map(center=(37.75, -122.25), zoom=11) Map.addLayer( image, {"bands": ['B7', 'B5', 'B3'], "min": 0.05, "max": 0.55, "gamma": 1.5}, 'image', ) Map.addLayer( classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']}, 'classification', ) Map ###Output _____no_output_____ ###Markdown Yay!! 🎉 Looks like our example works. Don't party too much because there is a catch...This workflow has several limitations particularly due to how much data you can pass from the client to the server and how large of a model ee can actually handle. EE can only handle 40MB of data passed to the server, so if you have a lot of large decision tree strings then this will not work. Also, creating a classifier from strings has limitation (see this ee-forum discussion: https://groups.google.com/g/google-earth-engine-developers/c/lFFU1GBPzi8/m/6MewQk1FBwAJ), this is again limited by string lengths when ee creates a computation graph.So, you can use this but know you will probably run into errors when training large models. Save trees to the cloudNow we have the strings in a format that ee can use, we want to save it for later use. There is a function to export a list of tree strings to a feature collection. The feature collection will have a pro ###Code user_id = geemap.ee_user_id() user_id # specify asset id where to save trees # be sure to change <user_name> to your ee user name asset_id = user_id + "/random_forest_strings_test" asset_id # kick off an export process so it will be saved to the ee asset ml.export_trees_to_fc(trees, asset_id) # this will kick off an export task, so wait a few minutes before moving on # read the exported tree feature collection rf_fc = ee.FeatureCollection(asset_id) # convert it to a classifier, very similar to the `ml.trees_to_classifier` function another_classifier = ml.fc_to_classifier(rf_fc) # classify the image again but with the classifier from the persisted trees classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75, -122.25), zoom=11) Map.addLayer( image, {"bands": ['B7', 'B5', 'B3'], "min": 0.05, "max": 0.55, "gamma": 1.5}, 'image', ) Map.addLayer( classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']}, 'classification', ) Map ###Output _____no_output_____ ###Markdown Save trees locally ###Code import os out_csv = os.path.expanduser("~/Downloads/trees.csv") ml.trees_to_csv(trees, out_csv) another_classifier = ml.csv_to_classifier(out_csv) classified = image.select(feature_names).classify(another_classifier) # display results # we should get the exact same results as before Map = geemap.Map(center=(37.75, -122.25), zoom=11) Map.addLayer( image, {"bands": ['B7', 'B5', 'B3'], "min": 0.05, "max": 0.55, "gamma": 1.5}, 'image', ) Map.addLayer( classified, {"min": 0, "max": 2, "palette": ['red', 'green', 'blue']}, 'classification', ) Map ###Output _____no_output_____

week2_model_based/practice_vi.ipynb

###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely areare you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0': { 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1': { 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2': { 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2': 0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output _____no_output_____ ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output _____no_output_____ ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ <YOUR CODE> return Q import numpy as np test_Vs = {s: i for i, s in enumerate(mdp.get_all_states())} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 return <YOUR CODE> test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : new_V(state)} new_state_values = <YOUR CODE> assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | " % (i, diff), end="") print(' '.join("V(%s) = %.3f" % (s, v) for s, v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated") break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output _____no_output_____ ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None <YOUR CODE> return <YOUR CODE> assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert 0.85 < np.mean(rewards) < 1.0 ###Output _____no_output_____ ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma=0.9, num_iter=1000, min_difference=1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : new_V(state)} new_state_values = <YOUR CODE> assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f " % (i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated") break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output _____no_output_____ ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3, 3)) h, w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w, h), cmap='gray', interpolation='none', clim=(0, 1)) ax = plt.gca() ax.set_xticks(np.arange(h) - .5) ax.set_yticks(np.arange(w) - .5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down': (0, -1), 'right': (1, 0), 'up': (-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y, x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y, u * .3, -v * .3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s: 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from time import sleep from IPython.display import clear_output mdp = FrozenLakeEnv(map_name='8x8', slip_chance=0.1) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output _____no_output_____ ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 1.0 <= np.mean(total_rewards) <= 1.0 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.8 <= np.mean(total_rewards) <= 0.95 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.6 <= np.mean(total_rewards) <= 0.7 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.6 <= np.mean(total_rewards) <= 0.8 print("Well done!") ###Output _____no_output_____ ###Markdown Submit to coursera ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, <EMAIL>, <TOKEN>) ###Output _____no_output_____ ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely are you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience._This notebook is inspired by the awesome_ [CS294](https://github.com/berkeleydeeprlcourse/homework/blob/36a0b58261acde756abd55306fbe63df226bf62b/hw2/HW2.ipynb) _by Berkeley_ For starters, let's define a simple MDP from this picture: ###Code import sys, os if 'google.colab' in sys.modules and not os.path.exists('.setup_complete'): !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/master/setup_colab.sh -O- | bash !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/coursera/grading.py -O ../grading.py !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/coursera/week2_model_based/submit.py !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/coursera/week2_model_based/mdp.py !touch .setup_complete # This code creates a virtual display to draw game images on. # It will have no effect if your machine has a monitor. if type(os.environ.get("DISPLAY")) is not str or len(os.environ.get("DISPLAY")) == 0: !bash ../xvfb start os.environ['DISPLAY'] = ':1' transition_probs = { 's0': { 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1': { 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2': { 'a0': {'s0': 0.4, 's2': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2': 0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s0', 's1', 's2') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s0': 0.7, 's1': 0.1, 's2': 0.2} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Optional: Visualizing MDPsYou can also visualize any MDP with the drawing fuction donated by [neer201](https://github.com/neer201).You have to install graphviz for system and for python. 1. * For ubuntu just run: `sudo apt-get install graphviz` * For OSX: `brew install graphviz`2. `pip install graphviz`3. restart the notebook__Note:__ Installing graphviz on some OS (esp. Windows) may be tricky. However, you can ignore this part alltogether and use the standart vizualization. ###Code from mdp import has_graphviz from IPython.display import display print("Graphviz available:", has_graphviz) if has_graphviz: from mdp import plot_graph, plot_graph_with_state_values, plot_graph_optimal_strategy_and_state_values display(plot_graph(mdp)) ###Output _____no_output_____ ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0 for next_state in mdp.get_all_states(): Q += mdp.get_transition_prob(state, action, next_state)\ * (mdp.get_reward(state, action, next_state) + gamma * state_values[next_state]) return Q import numpy as np test_Vs = {s: i for i, s in enumerate(sorted(mdp.get_all_states()))} assert np.isclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.isclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as in formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 Qs = [] for action in mdp.get_possible_actions(state): Q = get_action_value(mdp, state_values, state, action, gamma) Qs.append(Q) return np.max(Qs) test_Vs_copy = dict(test_Vs) assert np.isclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.isclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 1.08) assert np.isclose(get_new_state_value(mdp, {'s0': -1e10, 's1': 0, 's2': -2e10}, 's0', 0.9), -13500000000.0), \ "Please ensure that you handle negative Q-values of arbitrary magnitude correctly" assert test_Vs == test_Vs_copy, "Please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization # stop VI if new values are this close to old values (or closer) min_difference = 0.001 # initialize V(s) state_values = {s: 0 for s in mdp.get_all_states()} if has_graphviz: display(plot_graph_with_state_values(mdp, state_values)) for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : float V_new(state)} new_state_values = { state: get_new_state_value(mdp, state_values, state, gamma) for state in mdp.get_all_states() } assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | " % (i, diff), end="") print(' '.join("V(%s) = %.3f" % (s, v) for s, v in state_values.items())) state_values = new_state_values if diff < min_difference: print("Terminated") break if has_graphviz: display(plot_graph_with_state_values(mdp, state_values)) print("Final state values:", state_values) assert abs(state_values['s0'] - 3.781) < 0.01 assert abs(state_values['s1'] - 7.294) < 0.01 assert abs(state_values['s2'] - 4.202) < 0.01 ###Output Final state values: {'s0': 3.7810348735476405, 's1': 7.294006423867229, 's2': 4.202140275227048} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None Qs = [] possible_actions = mdp.get_possible_actions(state) for action in possible_actions: Q = get_action_value(mdp, state_values, state, action, gamma) Qs.append(Q) return possible_actions[np.argmax(Qs)] assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a1' assert get_optimal_action(mdp, {'s0': -1e10, 's1': 0, 's2': -2e10}, 's0', 0.9) == 'a0', \ "Please ensure that you handle negative Q-values of arbitrary magnitude correctly" assert get_optimal_action(mdp, {'s0': -2e10, 's1': 0, 's2': -1e10}, 's0', 0.9) == 'a1', \ "Please ensure that you handle negative Q-values of arbitrary magnitude correctly" if has_graphviz: display(plot_graph_optimal_strategy_and_state_values(mdp, state_values, get_action_value)) # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.40 < np.mean(rewards) < 0.55) ###Output average reward: 0.4374 ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma=0.9, num_iter=1000, min_difference=1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = { state: get_new_state_value(mdp, state_values, state, gamma) for state in mdp.get_all_states() } assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f " % (i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG down SFFF *HFH FFFH HFFG down SFFF FHFH *FFH HFFG right SFFF FHFH F*FH HFFG down SFFF FHFH FFFH H*FG right SFFF FHFH FFFH HF*G right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3, 3)) h, w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w, h), cmap='gray', interpolation='none', clim=(0, 1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down': (0, -1), 'right': (1, 0), 'up': (0, 1)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y, x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y, u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s: 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8', slip_chance=0.1) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output iter 0 | diff: 0.80000 | V(start): 0.000 iter 1 | diff: 0.57600 | V(start): 0.000 iter 2 | diff: 0.41472 | V(start): 0.000 iter 3 | diff: 0.29860 | V(start): 0.000 iter 4 | diff: 0.24186 | V(start): 0.000 iter 5 | diff: 0.19349 | V(start): 0.000 iter 6 | diff: 0.15325 | V(start): 0.000 iter 7 | diff: 0.12288 | V(start): 0.000 iter 8 | diff: 0.09930 | V(start): 0.000 iter 9 | diff: 0.08037 | V(start): 0.000 iter 10 | diff: 0.06426 | V(start): 0.000 iter 11 | diff: 0.05129 | V(start): 0.000 iter 12 | diff: 0.04330 | V(start): 0.000 iter 13 | diff: 0.03802 | V(start): 0.033 iter 14 | diff: 0.03332 | V(start): 0.058 iter 15 | diff: 0.02910 | V(start): 0.087 iter 16 | diff: 0.01855 | V(start): 0.106 iter 17 | diff: 0.01403 | V(start): 0.120 iter 18 | diff: 0.00810 | V(start): 0.128 iter 19 | diff: 0.00555 | V(start): 0.133 iter 20 | diff: 0.00321 | V(start): 0.137 iter 21 | diff: 0.00247 | V(start): 0.138 iter 22 | diff: 0.00147 | V(start): 0.139 iter 23 | diff: 0.00104 | V(start): 0.140 iter 24 | diff: 0.00058 | V(start): 0.140 iter 25 | diff: 0.00036 | V(start): 0.141 iter 26 | diff: 0.00024 | V(start): 0.141 iter 27 | diff: 0.00018 | V(start): 0.141 iter 28 | diff: 0.00012 | V(start): 0.141 iter 29 | diff: 0.00007 | V(start): 0.141 iter 30 | diff: 0.00004 | V(start): 0.141 iter 31 | diff: 0.00003 | V(start): 0.141 iter 32 | diff: 0.00001 | V(start): 0.141 iter 33 | diff: 0.00001 | V(start): 0.141 average reward: 0.74 Well done! ###Markdown Submit to courseraIf your submission doesn't finish in 30 seconds, set `verbose=True` and try again. ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, '[email protected]', 'gzLgy6As5x1xGmOM', verbose=False, ) ###Output Submitted to Coursera platform. See results on assignment page! ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely areare you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0':{ 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1':{ 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2':{ 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2':0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output _____no_output_____ ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output _____no_output_____ ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ <YOUR CODE> return Q import numpy as np test_Vs = {s : i for i, s in enumerate(mdp.get_all_states())} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 return <YOUR CODE> test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = <YOUR CODE> assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | "%(i, diff), end="") print(' '.join("V(%s) = %.3f"%(s, v) for s,v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated"); break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output _____no_output_____ ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None <YOUR CODE> return <YOUR CODE> assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.85 < np.mean(rewards) < 1.0) ###Output _____no_output_____ ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma = 0.9, num_iter = 1000, min_difference = 1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = <YOUR CODE> assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f "%(i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated"); break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output _____no_output_____ ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3,3)) h,w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w,h), cmap='gray', interpolation='none', clim=(0,1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down':(0, -1), 'right':(1,0), 'up':(-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y,x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y,u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s : 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8',slip_chance=0.1) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output _____no_output_____ ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output _____no_output_____ ###Markdown Submit to coursera ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, <EMAIL>, <TOKEN>) ###Output _____no_output_____ ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely areare you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0':{ 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1':{ 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2':{ 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2':0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output _____no_output_____ ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output _____no_output_____ ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ <YOUR CODE> return Q import numpy as np test_Vs = {s : i for i, s in enumerate(mdp.get_all_states())} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 return <YOUR CODE> test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = <YOUR CODE> assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | "%(i, diff), end="") print(' '.join("V(%s) = %.3f"%(s, v) for s,v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated"); break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output _____no_output_____ ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None <YOUR CODE> return <YOUR CODE> assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.85 < np.mean(rewards) < 1.0) ###Output _____no_output_____ ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma = 0.9, num_iter = 1000, min_difference = 1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = <YOUR CODE> assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f "%(i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated"); break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output _____no_output_____ ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3,3)) h,w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w,h), cmap='gray', interpolation='none', clim=(0,1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down':(0, -1), 'right':(1,0), 'up':(-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y,x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y,u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s : 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8',slip_chance=0.1) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output _____no_output_____ ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output _____no_output_____ ###Markdown Submit to coursera ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, <EMAIL>, <TOKEN>) ###Output _____no_output_____ ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely are you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience._This notebook is inspired by the awesome_ [CS294](https://github.com/berkeleydeeprlcourse/homework/blob/36a0b58261acde756abd55306fbe63df226bf62b/hw2/HW2.ipynb) _by Berkeley_ For starters, let's define a simple MDP from this picture: ###Code # If you Colab, uncomment this please # !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/master/week02_value_based/mdp.py transition_probs = { 's0': { 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1': { 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2': { 'a0': {'s0': 0.4, 's2': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2': 0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s2', 's1', 's0') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s2': 0.2, 's1': 0.1, 's0': 0.7} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Optional: Visualizing MDPsYou can also visualize any MDP with the drawing fuction donated by [neer201](https://github.com/neer201).You have to install graphviz for system and for python. For ubuntu just run:1. `sudo apt-get install graphviz`2. `pip install graphviz`3. restart the notebook__Note:__ Installing graphviz on some OS (esp. Windows) may be tricky. However, you can ignore this part alltogether and use the standart vizualization. ###Code from mdp import has_graphviz from IPython.display import display print("Graphviz available:", has_graphviz) if has_graphviz: from mdp import plot_graph, plot_graph_with_state_values, \ plot_graph_optimal_strategy_and_state_values display(plot_graph(mdp)) ###Output _____no_output_____ ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code %%writefile mdp_get_action_value.py def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ # YOUR CODE HERE # state_values: dictionary of state:index Q = 0 for state_prime in mdp.get_next_states(state, action): reward = mdp.get_reward(state, action, state_prime) Q += mdp.get_transition_prob(state, action, state_prime) * (reward+gamma*state_values[state_prime]) return Q from mdp_get_action_value import get_action_value import numpy as np test_Vs = {s: i for i, s in enumerate(sorted(mdp.get_all_states()))} print(test_Vs) assert np.isclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.isclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output {'s2': 2, 's1': 1, 's0': 0} ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as in formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 Qi = [] possible_actions = mdp.get_possible_actions(state) for action_prime in possible_actions: Q = get_action_value(mdp, state_values, state, action_prime, gamma) Qi.append(Q) return np.max(Qi) test_Vs_copy = dict(test_Vs) assert np.isclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.isclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 1.08) assert test_Vs == test_Vs_copy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization # stop VI if new values are this close to old values (or closer) min_difference = 0.001 # initialize V(s) state_values = {s: 0 for s in mdp.get_all_states()} if has_graphviz: display(plot_graph_with_state_values(mdp, state_values)) for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : float V_new(state)} new_state_values = {state:get_new_state_value(mdp, state_values, state, gamma) for state in mdp.get_all_states()} # print(new_state_values) assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | " % (i, diff), end="") print(' '.join("V(%s) = %.3f" % (s, v) for s, v in state_values.items())) state_values = new_state_values if diff < min_difference: print("Terminated") break if has_graphviz: display(plot_graph_with_state_values(mdp, state_values)) print("Final state values:", state_values) assert abs(state_values['s0'] - 3.781) < 0.01 assert abs(state_values['s1'] - 7.294) < 0.01 assert abs(state_values['s2'] - 4.202) < 0.01 ###Output Final state values: {'s2': 4.202140275227047, 's1': 7.294006423867229, 's0': 3.7810348735476396} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None # <YOUR CODE HERE> Qi = [] possible_actions = mdp.get_possible_actions(state) # print(possible_actions) for action_prime in possible_actions: Q = get_action_value(mdp, state_values, state, action_prime, gamma) Qi.append(Q) # print(Qi) return possible_actions[np.argmax(Qi)] assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a1' if has_graphviz: try: display(plot_graph_optimal_strategy_and_state_values(mdp, state_values)) except ImportError: raise ImportError("Run the cell that starts with \"%%writefile mdp_get_action_value.py\"") # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.40 < np.mean(rewards) < 0.55) ###Output average reward: 0.4466 ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma=0.9, num_iter=1000, min_difference=1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {state:get_new_state_value(mdp, state_values, state, gamma) for state in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f " % (i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG right S*FF FHFH FFFH HFFG right SF*F FHFH FFFH HFFG down SFFF FH*H FFFH HFFG down SFFF FHFH FF*H HFFG down SFFF FHFH FFFH HF*G right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3, 3)) h, w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w, h), cmap='gray', interpolation='none', clim=(0, 1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down': (0, -1), 'right': (1, 0), 'up': (0, 1)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y, x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y, u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s: 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8', slip_chance=0.1) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output iter 0 | diff: 0.80000 | V(start): 0.000 iter 1 | diff: 0.57600 | V(start): 0.000 iter 2 | diff: 0.41472 | V(start): 0.000 iter 3 | diff: 0.29860 | V(start): 0.000 iter 4 | diff: 0.24186 | V(start): 0.000 iter 5 | diff: 0.19349 | V(start): 0.000 iter 6 | diff: 0.15325 | V(start): 0.000 iter 7 | diff: 0.12288 | V(start): 0.000 iter 8 | diff: 0.09930 | V(start): 0.000 iter 9 | diff: 0.08037 | V(start): 0.000 iter 10 | diff: 0.06426 | V(start): 0.000 iter 11 | diff: 0.05129 | V(start): 0.000 iter 12 | diff: 0.04330 | V(start): 0.000 iter 13 | diff: 0.03802 | V(start): 0.033 iter 14 | diff: 0.03332 | V(start): 0.058 iter 15 | diff: 0.02910 | V(start): 0.087 iter 16 | diff: 0.01855 | V(start): 0.106 iter 17 | diff: 0.01403 | V(start): 0.120 iter 18 | diff: 0.00810 | V(start): 0.128 iter 19 | diff: 0.00555 | V(start): 0.133 iter 20 | diff: 0.00321 | V(start): 0.137 iter 21 | diff: 0.00247 | V(start): 0.138 iter 22 | diff: 0.00147 | V(start): 0.139 iter 23 | diff: 0.00104 | V(start): 0.140 iter 24 | diff: 0.00058 | V(start): 0.140 iter 25 | diff: 0.00036 | V(start): 0.141 iter 26 | diff: 0.00024 | V(start): 0.141 iter 27 | diff: 0.00018 | V(start): 0.141 iter 28 | diff: 0.00012 | V(start): 0.141 iter 29 | diff: 0.00007 | V(start): 0.141 iter 30 | diff: 0.00004 | V(start): 0.141 iter 31 | diff: 0.00003 | V(start): 0.141 iter 32 | diff: 0.00001 | V(start): 0.141 iter 33 | diff: 0.00001 | V(start): 0.141 average reward: 0.748 Well done! ###Markdown Submit to courseraIf your submission doesn't finish in 30 seconds, set `verbose=True` and try again. ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, "", "", verbose=False, ) ###Output Submitted to Coursera platform. See results on assignment page! ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely are you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0': { 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1': { 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2': { 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2': 0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s0', 's1', 's2') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s0': 0.7, 's1': 0.1, 's2': 0.2} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0 for s, p in mdp.get_next_states(state, action).items(): Q += p * (mdp.get_reward(state, action, s) + gamma * state_values[s]) return Q import numpy as np test_Vs = {s: i for i, s in enumerate(sorted(mdp.get_all_states()))} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 return max([get_action_value(mdp, state_values, state, a, gamma) for a in mdp.get_possible_actions(state)]) test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : new_V(state)} new_state_values = {state: get_new_state_value(mdp, state_values, state, gamma) for state in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | " % (i, diff), end="") print(' '.join("V(%s) = %.3f" % (s, v) for s, v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated") break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output Final state values: {'s0': 8.023123818663871, 's1': 11.163174814980803, 's2': 8.915559364985523} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None Q = {action: get_action_value(mdp, state_values, state, action, gamma) for action in mdp.get_possible_actions(state)} return sorted(Q.keys(), key=lambda x: Q[x], reverse=True)[0] assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert 0.85 < np.mean(rewards) < 1.0 ###Output average reward: 0.9275 ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma=0.9, num_iter=1000, min_difference=1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : new_V(state)} new_state_values = {state: get_new_state_value(mdp, state_values, state, gamma) for state in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f " % (i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated") break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG down SFFF *HFH FFFH HFFG down SFFF FHFH *FFH HFFG right SFFF FHFH F*FH HFFG down SFFF FHFH FFFH H*FG right SFFF FHFH FFFH HF*G right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3, 3)) h, w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w, h), cmap='gray', interpolation='none', clim=(0, 1)) ax = plt.gca() ax.set_xticks(np.arange(h) - .5) ax.set_yticks(np.arange(w) - .5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down': (0, -1), 'right': (1, 0), 'up': (-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y, x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y, u * .3, -v * .3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s: 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from time import sleep from IPython.display import clear_output mdp = FrozenLakeEnv(map_name='8x8', slip_chance=0.1) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 Terminated ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 1.0 <= np.mean(total_rewards) <= 1.0 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.8 <= np.mean(total_rewards) <= 0.95 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.6 <= np.mean(total_rewards) <= 0.7 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.6 <= np.mean(total_rewards) <= 0.8 print("Well done!") ###Output iter 0 | diff: 0.80000 | V(start): 0.000 iter 1 | diff: 0.57600 | V(start): 0.000 iter 2 | diff: 0.41472 | V(start): 0.000 iter 3 | diff: 0.29860 | V(start): 0.000 iter 4 | diff: 0.24186 | V(start): 0.000 iter 5 | diff: 0.19349 | V(start): 0.000 iter 6 | diff: 0.15325 | V(start): 0.000 iter 7 | diff: 0.12288 | V(start): 0.000 iter 8 | diff: 0.09930 | V(start): 0.000 iter 9 | diff: 0.08037 | V(start): 0.000 iter 10 | diff: 0.06426 | V(start): 0.000 iter 11 | diff: 0.05129 | V(start): 0.000 iter 12 | diff: 0.04330 | V(start): 0.000 iter 13 | diff: 0.03802 | V(start): 0.033 iter 14 | diff: 0.03332 | V(start): 0.058 iter 15 | diff: 0.02910 | V(start): 0.087 iter 16 | diff: 0.01855 | V(start): 0.106 iter 17 | diff: 0.01403 | V(start): 0.120 iter 18 | diff: 0.00810 | V(start): 0.128 iter 19 | diff: 0.00555 | V(start): 0.133 iter 20 | diff: 0.00321 | V(start): 0.137 iter 21 | diff: 0.00247 | V(start): 0.138 iter 22 | diff: 0.00147 | V(start): 0.139 iter 23 | diff: 0.00104 | V(start): 0.140 iter 24 | diff: 0.00058 | V(start): 0.140 iter 25 | diff: 0.00036 | V(start): 0.141 iter 26 | diff: 0.00024 | V(start): 0.141 iter 27 | diff: 0.00018 | V(start): 0.141 iter 28 | diff: 0.00012 | V(start): 0.141 iter 29 | diff: 0.00007 | V(start): 0.141 iter 30 | diff: 0.00004 | V(start): 0.141 iter 31 | diff: 0.00003 | V(start): 0.141 iter 32 | diff: 0.00001 | V(start): 0.141 iter 33 | diff: 0.00001 | V(start): 0.141 Terminated average reward: 0.737 Well done! ###Markdown Submit to courseraIf your submission doesn't finish in 30 seconds, set `verbose=True` and try again. ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, "[email protected]", "QUavadG12vbE12ht", verbose=False, ) ###Output Submitted to Coursera platform. See results on assignment page! ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely areare you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0':{ 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1':{ 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2':{ 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2':0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s2', 's0', 's1') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s2': 0.2, 's0': 0.7, 's1': 0.1} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0. state_values = {s : i for i, s in enumerate(sorted(state_values))} state_probs = mdp.get_next_states(state, action) for next_s, p in state_probs.items(): r = float(mdp.get_reward(state, action, next_s)) v = float(state_values[next_s]) Q += p*(r+gamma*v) return Q import numpy as np test_Vs = {s : i for i, s in enumerate(mdp.get_all_states())} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 actions = mdp.get_possible_actions(state) values = [get_action_value(mdp, state_values, state, action, gamma) \ for action in actions] new_state_value = np.max(values) return new_state_value test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0. state_probs = mdp.get_next_states(state, action) for next_s, p in state_probs.items(): r = float(mdp.get_reward(state, action, next_s)) v = float(state_values[next_s]) Q += p*(r+gamma*v) return Q # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s : 0 for s in mdp.get_all_states()} print(state_values) for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {s : get_new_state_value(mdp, state_values, s, gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | "%(i, diff), end="") print(' '.join("V(%s) = %.3f"%(s, v) for s,v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated"); break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output Final state values: {'s2': 8.915559364985523, 's0': 8.023123818663871, 's1': 11.163174814980803} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None action_values = {action : get_action_value(mdp, state_values, state, action, gamma) \ for action in mdp.get_possible_actions(state)} print(action_values) optimal_action = max(action_values, key=action_values.get) return optimal_action get_optimal_action(mdp, state_values, 's0', gamma) d = {'a':0, 'b':1, 'c':3} d.get('a') get_optimal_action(mdp, state_values, 's0', gamma) get_optimal_action(mdp, state_values, 's1', gamma) assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.85 < np.mean(rewards) < 1.0) ###Output {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 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8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 11.164054424803906, 'a1': 9.945714638232934} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} {'a0': 7.622407432642227, 'a1': 8.02400342848697} {'a0': 8.916438974808628, 'a1': 8.089902002478851} ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma = 0.9, num_iter = 1000, min_difference = 1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {s : get_new_state_value(mdp, state_values, s, gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f "%(i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated"); break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG {'right': 0.5904900000000002, 'left': 0.5314410000000002, 'down': 0.5904900000000002, 'up': 0.5314410000000002} right S*FF FHFH FFFH HFFG {'right': 0.6561000000000001, 'left': 0.5314410000000002, 'down': 0.0, 'up': 0.5904900000000002} right SF*F FHFH FFFH HFFG {'right': 0.5904900000000002, 'left': 0.5904900000000002, 'down': 0.7290000000000001, 'up': 0.6561000000000001} down SFFF FH*H FFFH HFFG {'right': 0.0, 'left': 0.0, 'down': 0.81, 'up': 0.6561000000000001} down SFFF FHFH FF*H HFFG {'right': 0.0, 'left': 0.7290000000000001, 'down': 0.9, 'up': 0.7290000000000001} down SFFF FHFH FFFH HF*G {'right': 1.0, 'left': 0.81, 'down': 0.9, 'up': 0.81} right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3,3)) h,w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w,h), cmap='gray', interpolation='none', clim=(0,1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down':(0, -1), 'right':(1,0), 'up':(-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y,x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y,u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s : 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8',slip_chance=0.1) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 Terminated ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output _____no_output_____ ###Markdown Submit to coursera ###Code transition_probs = { 's0':{ 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1':{ 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2':{ 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2':0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0. state_values = {s : i for i, s in enumerate(sorted(state_values))} state_probs = mdp.get_next_states(state, action) for next_s, p in state_probs.items(): r = float(mdp.get_reward(state, action, next_s)) v = float(state_values[next_s]) Q += p*(r+gamma*v) return Q def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0. state_values = {s : i for i, s in enumerate(sorted(state_values))} state_probs = mdp.get_next_states(state, action) for next_s, p in state_probs.items(): r = float(mdp.get_reward(state, action, next_s)) v = float(state_values[next_s]) Q += p*(r+gamma*v) return Q if mdp.is_terminal(state): return 0 actions = mdp.get_possible_actions(state) values = [get_action_value(mdp, state_values, state, action, gamma) \ for action in actions] new_state_value = np.max(values) return new_state_value def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0. state_probs = mdp.get_next_states(state, action) for next_s, p in state_probs.items(): r = float(mdp.get_reward(state, action, next_s)) v = float(state_values[next_s]) Q += p*(r+gamma*v) return Q def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 actions = mdp.get_possible_actions(state) values = [get_action_value(mdp, state_values, state, action, gamma) \ for action in actions] new_state_value = np.max(values) return new_state_value if mdp.is_terminal(state): return None action_values = {action : get_action_value(mdp, state_values, state, action, gamma) \ for action in mdp.get_possible_actions(state)} print(action_values) optimal_action = max(action_values, key=action_values.get) return optimal_action def value_iteration(mdp, state_values=None, gamma = 0.9, num_iter = 1000, min_difference = 1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ Q = 0. state_probs = mdp.get_next_states(state, action) for next_s, p in state_probs.items(): r = float(mdp.get_reward(state, action, next_s)) v = float(state_values[next_s]) Q += p*(r+gamma*v) return Q def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 actions = mdp.get_possible_actions(state) values = [get_action_value(mdp, state_values, state, action, gamma) \ for action in actions] new_state_value = np.max(values) return new_state_value state_values = state_values or {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {s : get_new_state_value(mdp, state_values, s, gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f "%(i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated"); break return state_values import numpy as np test_Vs = {s : i for i, s in enumerate(mdp.get_all_states())} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, '[email protected]', 'TyhMT4GKfmegJgom' ) ###Output _____no_output_____ ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely are you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0':{ 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1':{ 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2':{ 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2':0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s0', 's1', 's2') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s0': 0.7, 's1': 0.1, 's2': 0.2} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ #<YOUR CODE> Q = sum(p*(mdp.get_reward(state,action,next_state) + gamma*state_values[next_state]) for next_state,p in mdp.get_next_states(state,action,).items()) return Q import numpy as np test_Vs = {s : i for i, s in enumerate(mdp.get_all_states())} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 #<YOUR CODE> return max(get_action_value(mdp,state_values,state,action,gamma) for action in mdp.get_possible_actions(state)) test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {s:get_new_state_value(mdp,state_values,s,gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | "%(i, diff), end="") print(' '.join("V(%s) = %.3f"%(s, v) for s,v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated"); break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output Final state values: {'s0': 8.023123818663871, 's1': 11.163174814980803, 's2': 8.915559364985523} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None #<YOUR CODE> max_Q = float("-inf") max_action = None for action in mdp.get_possible_actions(state): q = get_action_value(mdp,state_values,state,action,gamma) if q > max_Q: max_Q = q max_action = action return max_action assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.85 < np.mean(rewards) < 1.0) ###Output average reward: 0.902 ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma = 0.9, num_iter = 1000, min_difference = 1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {s:get_new_state_value(mdp,state_values,s,gamma) for s in mdp.get_all_states()}#<YOUR CODE> assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f "%(i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated"); break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG down SFFF *HFH FFFH HFFG down SFFF FHFH *FFH HFFG right SFFF FHFH F*FH HFFG down SFFF FHFH FFFH H*FG right SFFF FHFH FFFH HF*G right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3,3)) h,w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w,h), cmap='gray', interpolation='none', clim=(0,1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down':(0, -1), 'right':(1,0), 'up':(-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y,x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y,u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s : 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8',slip_chance=0.1) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 Terminated ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output iter 0 | diff: 0.80000 | V(start): 0.000 iter 1 | diff: 0.57600 | V(start): 0.000 iter 2 | diff: 0.41472 | V(start): 0.000 iter 3 | diff: 0.29860 | V(start): 0.000 iter 4 | diff: 0.24186 | V(start): 0.000 iter 5 | diff: 0.19349 | V(start): 0.000 iter 6 | diff: 0.15325 | V(start): 0.000 iter 7 | diff: 0.12288 | V(start): 0.000 iter 8 | diff: 0.09930 | V(start): 0.000 iter 9 | diff: 0.08037 | V(start): 0.000 iter 10 | diff: 0.06426 | V(start): 0.000 iter 11 | diff: 0.05129 | V(start): 0.000 iter 12 | diff: 0.04330 | V(start): 0.000 iter 13 | diff: 0.03802 | V(start): 0.033 iter 14 | diff: 0.03332 | V(start): 0.058 iter 15 | diff: 0.02910 | V(start): 0.087 iter 16 | diff: 0.01855 | V(start): 0.106 iter 17 | diff: 0.01403 | V(start): 0.120 iter 18 | diff: 0.00810 | V(start): 0.128 iter 19 | diff: 0.00555 | V(start): 0.133 iter 20 | diff: 0.00321 | V(start): 0.137 iter 21 | diff: 0.00247 | V(start): 0.138 iter 22 | diff: 0.00147 | V(start): 0.139 iter 23 | diff: 0.00104 | V(start): 0.140 iter 24 | diff: 0.00058 | V(start): 0.140 iter 25 | diff: 0.00036 | V(start): 0.141 iter 26 | diff: 0.00024 | V(start): 0.141 iter 27 | diff: 0.00018 | V(start): 0.141 iter 28 | diff: 0.00012 | V(start): 0.141 iter 29 | diff: 0.00007 | V(start): 0.141 iter 30 | diff: 0.00004 | V(start): 0.141 iter 31 | diff: 0.00003 | V(start): 0.141 iter 32 | diff: 0.00001 | V(start): 0.141 iter 33 | diff: 0.00001 | V(start): 0.141 Terminated average reward: 0.748 Well done! ###Markdown Submit to coursera ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, "[email protected]","QH1sshvv6H3WRnWg") #<EMAIL>, #<TOKEN>) ###Output _____no_output_____ ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely areare you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0': { 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1': { 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2': { 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2': 0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s0', 's1', 's2') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s0': 0.7, 's1': 0.1, 's2': 0.2} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ next_possible_states = mdp.get_next_states(state, action) Q = 0 for next_state, prob in next_possible_states.items(): reward = mdp.get_reward(state, action, next_state) Q += prob * (reward + gamma * state_values[next_state]) return Q import numpy as np test_Vs = {s: i for i, s in enumerate(mdp.get_all_states())} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 possible_actions = mdp.get_possible_actions(state) Qs = [get_action_value(mdp, state_values, state, action, gamma) for action in possible_actions] return max(Qs) test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : new_V(state)} new_state_values = {s: get_new_state_value(mdp, state_values, s, gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | " % (i, diff), end="") print(' '.join("V(%s) = %.3f" % (s, v) for s, v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated") break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output Final state values: {'s0': 8.023123818663871, 's1': 11.163174814980803, 's2': 8.915559364985523} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None best_action = None highest_Q = 0 for action in mdp.get_possible_actions(state): Q = get_action_value(mdp, state_values, state, action, gamma) if best_action is None or Q > highest_Q: highest_Q = Q best_action = action return best_action assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert 0.85 < np.mean(rewards) < 1.0 ###Output average reward: 0.928 ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma=0.9, num_iter=1000, min_difference=1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : new_V(state)} new_state_values = {s: get_new_state_value(mdp, state_values, s, gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f " % (i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated") break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG down SFFF *HFH FFFH HFFG down SFFF FHFH *FFH HFFG right SFFF FHFH F*FH HFFG down SFFF FHFH FFFH H*FG right SFFF FHFH FFFH HF*G right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3, 3)) h, w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w, h), cmap='gray', interpolation='none', clim=(0, 1)) ax = plt.gca() ax.set_xticks(np.arange(h) - .5) ax.set_yticks(np.arange(w) - .5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down': (0, -1), 'right': (1, 0), 'up': (-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y, x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y, u * .3, -v * .3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s: 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from time import sleep from IPython.display import clear_output mdp = FrozenLakeEnv(map_name='8x8', slip_chance=0.1) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 Terminated ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 1.0 <= np.mean(total_rewards) <= 1.0 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.8 <= np.mean(total_rewards) <= 0.95 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.6 <= np.mean(total_rewards) <= 0.7 print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert 0.6 <= np.mean(total_rewards) <= 0.8 print("Well done!") ###Output iter 0 | diff: 0.80000 | V(start): 0.000 iter 1 | diff: 0.57600 | V(start): 0.000 iter 2 | diff: 0.41472 | V(start): 0.000 iter 3 | diff: 0.29860 | V(start): 0.000 iter 4 | diff: 0.24186 | V(start): 0.000 iter 5 | diff: 0.19349 | V(start): 0.000 iter 6 | diff: 0.15325 | V(start): 0.000 iter 7 | diff: 0.12288 | V(start): 0.000 iter 8 | diff: 0.09930 | V(start): 0.000 iter 9 | diff: 0.08037 | V(start): 0.000 iter 10 | diff: 0.06426 | V(start): 0.000 iter 11 | diff: 0.05129 | V(start): 0.000 iter 12 | diff: 0.04330 | V(start): 0.000 iter 13 | diff: 0.03802 | V(start): 0.033 iter 14 | diff: 0.03332 | V(start): 0.058 iter 15 | diff: 0.02910 | V(start): 0.087 iter 16 | diff: 0.01855 | V(start): 0.106 iter 17 | diff: 0.01403 | V(start): 0.120 iter 18 | diff: 0.00810 | V(start): 0.128 iter 19 | diff: 0.00555 | V(start): 0.133 iter 20 | diff: 0.00321 | V(start): 0.137 iter 21 | diff: 0.00247 | V(start): 0.138 iter 22 | diff: 0.00147 | V(start): 0.139 iter 23 | diff: 0.00104 | V(start): 0.140 iter 24 | diff: 0.00058 | V(start): 0.140 iter 25 | diff: 0.00036 | V(start): 0.141 iter 26 | diff: 0.00024 | V(start): 0.141 iter 27 | diff: 0.00018 | V(start): 0.141 iter 28 | diff: 0.00012 | V(start): 0.141 iter 29 | diff: 0.00007 | V(start): 0.141 iter 30 | diff: 0.00004 | V(start): 0.141 iter 31 | diff: 0.00003 | V(start): 0.141 iter 32 | diff: 0.00001 | V(start): 0.141 iter 33 | diff: 0.00001 | V(start): 0.141 Terminated average reward: 0.748 Well done! ###Markdown Submit to coursera ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, '[email protected]', 'WfbisWTMXT62ZOhU') ###Output _____no_output_____ ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely areare you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience. For starters, let's define a simple MDP from this picture:_img by MistWiz (Own work) [Public domain], via Wikimedia Commons_ ###Code transition_probs = { 's0':{ 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1':{ 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2':{ 'a0': {'s0': 0.4, 's1': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2':0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s2', 's1', 's0') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s2': 0.2, 's1': 0.1, 's0': 0.7} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ get_next_states = mdp.get_next_states(state, action) Q = sum([p*(mdp.get_reward(state, action, s) + gamma*state_values[s]) for s,p in get_next_states.items()]) return Q import numpy as np test_Vs = {s : i for i, s in enumerate(sorted(mdp.get_all_states()))} #test_Vs = {'s0':0, 's1':1, 's2':2} assert np.allclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.allclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as per formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 new_state_value = sorted([(a, get_action_value(mdp, state_values, state, a, gamma)) for a in mdp.get_possible_actions(state)], key=lambda s: s[1], reverse=True)[0][1] return new_state_value test_Vs_vopy = dict(test_Vs) assert np.allclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.allclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 0.69) assert test_Vs == test_Vs_vopy, "please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization min_difference = 0.001 # stop VI if new values are this close to old values (or closer) # initialize V(s) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {s:get_new_state_value(mdp, state_values, s, gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | "%(i, diff), end="") print(' '.join("V(%s) = %.3f"%(s, v) for s,v in state_values.items()), end='\n\n') state_values = new_state_values if diff < min_difference: print("Terminated"); break print("Final state values:", state_values) assert abs(state_values['s0'] - 8.032) < 0.01 assert abs(state_values['s1'] - 11.169) < 0.01 assert abs(state_values['s2'] - 8.921) < 0.01 ###Output Final state values: {'s2': 8.915559364985523, 's1': 11.163174814980799, 's0': 8.023123818663871} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None opt_action = sorted([(a, get_action_value(mdp, state_values, state, a, gamma))\ for a in mdp.get_possible_actions(state)], key=lambda s: s[1], reverse=True)[0][0] return opt_action assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a0' # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.85 < np.mean(rewards) < 1.0) ###Output average reward: 0.924 ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() mdp.desc def value_iteration(mdp, state_values=None, gamma = 0.9, num_iter = 1000, min_difference = 1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s : 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {s:get_new_state_value(mdp, state_values, s, gamma) for s in mdp.get_all_states()} assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f "%(i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: print("Terminated"); break return state_values state_values = value_iteration(mdp) s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG down SFFF *HFH FFFH HFFG down SFFF FHFH *FFH HFFG right SFFF FHFH F*FH HFFG down SFFF FHFH FFFH H*FG right SFFF FHFH FFFH HF*G right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3,3)) h,w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w,h), cmap='gray', interpolation='none', clim=(0,1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down':(0, -1), 'right':(1,0), 'up':(-1, 0)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y,x].item()), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y,u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s : 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8',slip_chance=0.1) state_values = {s : 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i"%i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 Terminated ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output iter 0 | diff: 0.80000 | V(start): 0.000 iter 1 | diff: 0.57600 | V(start): 0.000 iter 2 | diff: 0.41472 | V(start): 0.000 iter 3 | diff: 0.29860 | V(start): 0.000 iter 4 | diff: 0.24186 | V(start): 0.000 iter 5 | diff: 0.19349 | V(start): 0.000 iter 6 | diff: 0.15325 | V(start): 0.000 iter 7 | diff: 0.12288 | V(start): 0.000 iter 8 | diff: 0.09930 | V(start): 0.000 iter 9 | diff: 0.08037 | V(start): 0.000 iter 10 | diff: 0.06426 | V(start): 0.000 iter 11 | diff: 0.05129 | V(start): 0.000 iter 12 | diff: 0.04330 | V(start): 0.000 iter 13 | diff: 0.03802 | V(start): 0.033 iter 14 | diff: 0.03332 | V(start): 0.058 iter 15 | diff: 0.02910 | V(start): 0.087 iter 16 | diff: 0.01855 | V(start): 0.106 iter 17 | diff: 0.01403 | V(start): 0.120 iter 18 | diff: 0.00810 | V(start): 0.128 iter 19 | diff: 0.00555 | V(start): 0.133 iter 20 | diff: 0.00321 | V(start): 0.137 iter 21 | diff: 0.00247 | V(start): 0.138 iter 22 | diff: 0.00147 | V(start): 0.139 iter 23 | diff: 0.00104 | V(start): 0.140 iter 24 | diff: 0.00058 | V(start): 0.140 iter 25 | diff: 0.00036 | V(start): 0.141 iter 26 | diff: 0.00024 | V(start): 0.141 iter 27 | diff: 0.00018 | V(start): 0.141 iter 28 | diff: 0.00012 | V(start): 0.141 iter 29 | diff: 0.00007 | V(start): 0.141 iter 30 | diff: 0.00004 | V(start): 0.141 iter 31 | diff: 0.00003 | V(start): 0.141 iter 32 | diff: 0.00001 | V(start): 0.141 iter 33 | diff: 0.00001 | V(start): 0.141 Terminated average reward: 0.739 Well done! ###Markdown Submit to coursera ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, '[email protected]', 'rOwd2RgHZtnySFKb') ###Output iter 0 | diff: 0.75000 | V(start): 0.000 iter 1 | diff: 0.50625 | V(start): 0.000 iter 2 | diff: 0.39867 | V(start): 0.000 iter 3 | diff: 0.26910 | V(start): 0.000 iter 4 | diff: 0.18164 | V(start): 0.000 iter 5 | diff: 0.14013 | V(start): 0.140 iter 6 | diff: 0.07028 | V(start): 0.199 iter 7 | diff: 0.06030 | V(start): 0.260 iter 8 | diff: 0.02594 | V(start): 0.285 iter 9 | diff: 0.01918 | V(start): 0.305 iter 10 | diff: 0.00858 | V(start): 0.313 iter 11 | diff: 0.00560 | V(start): 0.319 iter 12 | diff: 0.00260 | V(start): 0.321 iter 13 | diff: 0.00159 | V(start): 0.323 iter 14 | diff: 0.00076 | V(start): 0.324 iter 15 | diff: 0.00045 | V(start): 0.324 iter 16 | diff: 0.00022 | V(start): 0.324 iter 17 | diff: 0.00012 | V(start): 0.325 iter 18 | diff: 0.00006 | V(start): 0.325 iter 19 | diff: 0.00003 | V(start): 0.325 iter 20 | diff: 0.00002 | V(start): 0.325 iter 21 | diff: 0.00001 | V(start): 0.325 Terminated iter 0 | diff: 0.75000 | V(start): 0.000 iter 1 | diff: 0.50625 | V(start): 0.000 iter 2 | diff: 0.34172 | V(start): 0.000 iter 3 | diff: 0.23066 | V(start): 0.000 iter 4 | diff: 0.18164 | V(start): 0.000 iter 5 | diff: 0.14013 | V(start): 0.000 iter 6 | diff: 0.10641 | V(start): 0.000 iter 7 | diff: 0.08247 | V(start): 0.000 iter 8 | diff: 0.06464 | V(start): 0.000 iter 9 | diff: 0.05474 | V(start): 0.000 iter 10 | diff: 0.04729 | V(start): 0.000 iter 11 | diff: 0.04105 | V(start): 0.000 iter 12 | diff: 0.03516 | V(start): 0.000 iter 13 | diff: 0.02994 | V(start): 0.018 iter 14 | diff: 0.02535 | V(start): 0.035 iter 15 | diff: 0.02133 | V(start): 0.056 iter 16 | diff: 0.01610 | V(start): 0.072 iter 17 | diff: 0.01357 | V(start): 0.086 iter 18 | diff: 0.00912 | V(start): 0.095 iter 19 | diff: 0.00674 | V(start): 0.101 iter 20 | diff: 0.00440 | V(start): 0.106 iter 21 | diff: 0.00383 | V(start): 0.109 iter 22 | diff: 0.00252 | V(start): 0.111 iter 23 | diff: 0.00184 | V(start): 0.112 iter 24 | diff: 0.00116 | V(start): 0.113 iter 25 | diff: 0.00078 | V(start): 0.113 iter 26 | diff: 0.00061 | V(start): 0.113 iter 27 | diff: 0.00049 | V(start): 0.114 iter 28 | diff: 0.00037 | V(start): 0.114 iter 29 | diff: 0.00028 | V(start): 0.114 iter 30 | diff: 0.00022 | V(start): 0.114 iter 31 | diff: 0.00015 | V(start): 0.114 iter 32 | diff: 0.00010 | V(start): 0.114 iter 33 | diff: 0.00006 | V(start): 0.114 iter 34 | diff: 0.00004 | V(start): 0.114 iter 35 | diff: 0.00002 | V(start): 0.114 iter 36 | diff: 0.00001 | V(start): 0.114 iter 37 | diff: 0.00001 | V(start): 0.114 Terminated ###Markdown Markov decision processThis week's methods are all built to solve __M__arkov __D__ecision __P__rocesses. In the broadest sense, an MDP is defined by how it changes states and how rewards are computed.State transition is defined by $P(s' |s,a)$ - how likely are you to end at state $s'$ if you take action $a$ from state $s$. Now there's more than one way to define rewards, but we'll use $r(s,a,s')$ function for convenience._This notebook is inspired by the awesome_ [CS294](https://github.com/berkeleydeeprlcourse/homework/blob/36a0b58261acde756abd55306fbe63df226bf62b/hw2/HW2.ipynb) _by Berkeley_ For starters, let's define a simple MDP from this picture: ###Code import sys, os if 'google.colab' in sys.modules and not os.path.exists('.setup_complete'): !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/master/setup_colab.sh -O- | bash !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/coursera/grading.py -O ../grading.py !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/coursera/week2_model_based/submit.py !wget -q https://raw.githubusercontent.com/yandexdataschool/Practical_RL/coursera/week2_model_based/mdp.py !touch .setup_complete # This code creates a virtual display to draw game images on. # It will have no effect if your machine has a monitor. if type(os.environ.get("DISPLAY")) is not str or len(os.environ.get("DISPLAY")) == 0: !bash ../xvfb start os.environ['DISPLAY'] = ':1' transition_probs = { 's0': { 'a0': {'s0': 0.5, 's2': 0.5}, 'a1': {'s2': 1} }, 's1': { 'a0': {'s0': 0.7, 's1': 0.1, 's2': 0.2}, 'a1': {'s1': 0.95, 's2': 0.05} }, 's2': { 'a0': {'s0': 0.4, 's2': 0.6}, 'a1': {'s0': 0.3, 's1': 0.3, 's2': 0.4} } } rewards = { 's1': {'a0': {'s0': +5}}, 's2': {'a1': {'s0': -1}} } from mdp import MDP mdp = MDP(transition_probs, rewards, initial_state='s0') ###Output _____no_output_____ ###Markdown We can now use MDP just as any other gym environment: ###Code print('initial state =', mdp.reset()) next_state, reward, done, info = mdp.step('a1') print('next_state = %s, reward = %s, done = %s' % (next_state, reward, done)) ###Output initial state = s0 next_state = s2, reward = 0.0, done = False ###Markdown but it also has other methods that you'll need for Value Iteration ###Code print("mdp.get_all_states =", mdp.get_all_states()) print("mdp.get_possible_actions('s1') = ", mdp.get_possible_actions('s1')) print("mdp.get_next_states('s1', 'a0') = ", mdp.get_next_states('s1', 'a0')) print("mdp.get_reward('s1', 'a0', 's0') = ", mdp.get_reward('s1', 'a0', 's0')) print("mdp.get_transition_prob('s1', 'a0', 's0') = ", mdp.get_transition_prob('s1', 'a0', 's0')) ###Output mdp.get_all_states = ('s0', 's1', 's2') mdp.get_possible_actions('s1') = ('a0', 'a1') mdp.get_next_states('s1', 'a0') = {'s0': 0.7, 's1': 0.1, 's2': 0.2} mdp.get_reward('s1', 'a0', 's0') = 5 mdp.get_transition_prob('s1', 'a0', 's0') = 0.7 ###Markdown Optional: Visualizing MDPsYou can also visualize any MDP with the drawing fuction donated by [neer201](https://github.com/neer201).You have to install graphviz for system and for python. 1. * For ubuntu just run: `sudo apt-get install graphviz` * For OSX: `brew install graphviz`2. `pip install graphviz`3. restart the notebook__Note:__ Installing graphviz on some OS (esp. Windows) may be tricky. However, you can ignore this part alltogether and use the standart vizualization. ###Code from mdp import has_graphviz from IPython.display import display print("Graphviz available:", has_graphviz) if has_graphviz: from mdp import plot_graph, plot_graph_with_state_values, plot_graph_optimal_strategy_and_state_values display(plot_graph(mdp)) ###Output _____no_output_____ ###Markdown Value IterationNow let's build something to solve this MDP. The simplest algorithm so far is __V__alue __I__terationHere's the pseudo-code for VI:---`1.` Initialize $V^{(0)}(s)=0$, for all $s$`2.` For $i=0, 1, 2, \dots$ `3.` $ \quad V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$, for all $s$--- First, let's write a function to compute the state-action value function $Q^{\pi}$, defined as follows$$Q_i(s, a) = \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')]$$ ###Code {s: i for i, s in enumerate(sorted(mdp.get_all_states()))} def get_action_value(mdp, state_values, state, action, gamma): """ Computes Q(s,a) as in formula above """ q = 0 for s, p in mdp.get_next_states(state,action).items(): q+=p*(mdp.get_reward(state,action,s) + gamma * state_values[s]) return q import numpy as np test_Vs = {s: i for i, s in enumerate(sorted(mdp.get_all_states()))} assert np.isclose(get_action_value(mdp, test_Vs, 's2', 'a1', 0.9), 0.69) assert np.isclose(get_action_value(mdp, test_Vs, 's1', 'a0', 0.9), 3.95) ###Output _____no_output_____ ###Markdown Using $Q(s,a)$ we can now define the "next" V(s) for value iteration. $$V_{(i+1)}(s) = \max_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = \max_a Q_i(s,a)$$ ###Code def get_new_state_value(mdp, state_values, state, gamma): """ Computes next V(s) as in formula above. Please do not change state_values in process. """ if mdp.is_terminal(state): return 0 max_v = [] for a in mdp.get_possible_actions(state): q_a = get_action_value(mdp,state_values,state,a,gamma) max_v.append(q_a) return max(max_v) test_Vs_copy = dict(test_Vs) assert np.isclose(get_new_state_value(mdp, test_Vs, 's0', 0.9), 1.8) assert np.isclose(get_new_state_value(mdp, test_Vs, 's2', 0.9), 1.08) assert np.isclose(get_new_state_value(mdp, {'s0': -1e10, 's1': 0, 's2': -2e10}, 's0', 0.9), -13500000000.0), \ "Please ensure that you handle negative Q-values of arbitrary magnitude correctly" assert test_Vs == test_Vs_copy, "Please do not change state_values in get_new_state_value" ###Output _____no_output_____ ###Markdown Finally, let's combine everything we wrote into a working value iteration algo. ###Code # parameters gamma = 0.9 # discount for MDP num_iter = 100 # maximum iterations, excluding initialization # stop VI if new values are this close to old values (or closer) min_difference = 0.001 # initialize V(s) state_values = {s: 0 for s in mdp.get_all_states()} if has_graphviz: display(plot_graph_with_state_values(mdp, state_values)) for i in range(num_iter): # Compute new state values using the functions you defined above. # It must be a dict {state : float V_new(state)} new_state_values = {} for s in state_values.keys(): new_state_values[s] = get_new_state_value(mdp,state_values,s,gamma) # print(new_state_values) assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | " % (i, diff), end="") print(' '.join("V(%s) = %.3f" % (s, v) for s, v in state_values.items())) state_values = new_state_values if diff < min_difference: print("Terminated") break if has_graphviz: display(plot_graph_with_state_values(mdp, state_values)) print("Final state values:", state_values) assert abs(state_values['s0'] - 3.781) < 0.01 assert abs(state_values['s1'] - 7.294) < 0.01 assert abs(state_values['s2'] - 4.202) < 0.01 ###Output Final state values: {'s0': 3.7810348735476405, 's1': 7.294006423867229, 's2': 4.202140275227048} ###Markdown Now let's use those $V^{*}(s)$ to find optimal actions in each state $$\pi^*(s) = argmax_a \sum_{s'} P(s' | s,a) \cdot [ r(s,a,s') + \gamma V_{i}(s')] = argmax_a Q_i(s,a)$$ The only difference vs V(s) is that here we take not max but argmax: find action such with maximum Q(s,a). ###Code def get_optimal_action(mdp, state_values, state, gamma=0.9): """ Finds optimal action using formula above. """ if mdp.is_terminal(state): return None max_v = None action = None for a in mdp.get_possible_actions(state): q_a = get_action_value(mdp,state_values,state,a,gamma) if max_v is None or max_v < q_a: max_v = q_a action = a return action assert get_optimal_action(mdp, state_values, 's0', gamma) == 'a1' assert get_optimal_action(mdp, state_values, 's1', gamma) == 'a0' assert get_optimal_action(mdp, state_values, 's2', gamma) == 'a1' assert get_optimal_action(mdp, {'s0': -1e10, 's1': 0, 's2': -2e10}, 's0', 0.9) == 'a0', \ "Please ensure that you handle negative Q-values of arbitrary magnitude correctly" assert get_optimal_action(mdp, {'s0': -2e10, 's1': 0, 's2': -1e10}, 's0', 0.9) == 'a1', \ "Please ensure that you handle negative Q-values of arbitrary magnitude correctly" if has_graphviz: display(plot_graph_optimal_strategy_and_state_values(mdp, state_values, get_action_value)) # Measure agent's average reward s = mdp.reset() rewards = [] for _ in range(10000): s, r, done, _ = mdp.step(get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) print("average reward: ", np.mean(rewards)) assert(0.40 < np.mean(rewards) < 0.55) ###Output average reward: 0.4672 ###Markdown Frozen lake ###Code from mdp import FrozenLakeEnv mdp = FrozenLakeEnv(slip_chance=0) mdp.render() def value_iteration(mdp, state_values=None, gamma=0.9, num_iter=1000, min_difference=1e-5): """ performs num_iter value iteration steps starting from state_values. Same as before but in a function """ state_values = state_values or {s: 0 for s in mdp.get_all_states()} for i in range(num_iter): # Compute new state values using the functions you defined above. It must be a dict {state : new_V(state)} new_state_values = {} for s in state_values.keys(): new_state_values[s] = get_new_state_value(mdp,state_values,s,gamma) assert isinstance(new_state_values, dict) # Compute difference diff = max(abs(new_state_values[s] - state_values[s]) for s in mdp.get_all_states()) print("iter %4i | diff: %6.5f | V(start): %.3f " % (i, diff, new_state_values[mdp._initial_state])) state_values = new_state_values if diff < min_difference: break return state_values state_values = value_iteration(mdp) f"{state_values[(3,2)]:.1f}" s = mdp.reset() mdp.render() for t in range(100): a = get_optimal_action(mdp, state_values, s, gamma) print(a, end='\n\n') s, r, done, _ = mdp.step(a) mdp.render() if done: break ###Output *FFF FHFH FFFH HFFG down SFFF *HFH FFFH HFFG down SFFF FHFH *FFH HFFG right SFFF FHFH F*FH HFFG down SFFF FHFH FFFH H*FG right SFFF FHFH FFFH HF*G right SFFF FHFH FFFH HFF* ###Markdown Let's visualize!It's usually interesting to see what your algorithm actually learned under the hood. To do so, we'll plot state value functions and optimal actions at each VI step. ###Code import matplotlib.pyplot as plt %matplotlib inline def draw_policy(mdp, state_values): plt.figure(figsize=(3, 3)) h, w = mdp.desc.shape states = sorted(mdp.get_all_states()) V = np.array([state_values[s] for s in states]) Pi = {s: get_optimal_action(mdp, state_values, s, gamma) for s in states} plt.imshow(V.reshape(w, h), cmap='gray', interpolation='none', clim=(0, 1)) ax = plt.gca() ax.set_xticks(np.arange(h)-.5) ax.set_yticks(np.arange(w)-.5) ax.set_xticklabels([]) ax.set_yticklabels([]) # Y, X = np.mgrid[0:4, 0:4] a2uv = {'left': (-1, 0), 'down': (0, -1), 'right': (1, 0), 'up': (0, 1)} for y in range(h): for x in range(w): plt.text(x, y, str(mdp.desc[y, x].item()+":"+f"{state_values[(x,y)]:.1f}"), color='g', size=12, verticalalignment='center', horizontalalignment='center', fontweight='bold') a = Pi[y, x] if a is None: continue u, v = a2uv[a] plt.arrow(x, y, u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) plt.grid(color='b', lw=2, ls='-') plt.show() state_values = {s: 0 for s in mdp.get_all_states()} for i in range(10): print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) # please ignore iter 0 at each step from IPython.display import clear_output from time import sleep mdp = FrozenLakeEnv(map_name='8x8', slip_chance=0.1) state_values = {s: 0 for s in mdp.get_all_states()} for i in range(30): clear_output(True) print("after iteration %i" % i) state_values = value_iteration(mdp, state_values, num_iter=1) draw_policy(mdp, state_values) sleep(0.5) # please ignore iter 0 at each step ###Output after iteration 29 iter 0 | diff: 0.00000 | V(start): 0.198 ###Markdown Massive tests ###Code mdp = FrozenLakeEnv(slip_chance=0) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(1.0 <= np.mean(total_rewards) <= 1.0) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.1) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.8 <= np.mean(total_rewards) <= 0.95) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.25) state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.7) print("Well done!") # Measure agent's average reward mdp = FrozenLakeEnv(slip_chance=0.2, map_name='8x8') state_values = value_iteration(mdp) total_rewards = [] for game_i in range(1000): s = mdp.reset() rewards = [] for t in range(100): s, r, done, _ = mdp.step( get_optimal_action(mdp, state_values, s, gamma)) rewards.append(r) if done: break total_rewards.append(np.sum(rewards)) print("average reward: ", np.mean(total_rewards)) assert(0.6 <= np.mean(total_rewards) <= 0.8) print("Well done!") ###Output iter 0 | diff: 0.80000 | V(start): 0.000 iter 1 | diff: 0.57600 | V(start): 0.000 iter 2 | diff: 0.41472 | V(start): 0.000 iter 3 | diff: 0.29860 | V(start): 0.000 iter 4 | diff: 0.24186 | V(start): 0.000 iter 5 | diff: 0.19349 | V(start): 0.000 iter 6 | diff: 0.15325 | V(start): 0.000 iter 7 | diff: 0.12288 | V(start): 0.000 iter 8 | diff: 0.09930 | V(start): 0.000 iter 9 | diff: 0.08037 | V(start): 0.000 iter 10 | diff: 0.06426 | V(start): 0.000 iter 11 | diff: 0.05129 | V(start): 0.000 iter 12 | diff: 0.04330 | V(start): 0.000 iter 13 | diff: 0.03802 | V(start): 0.033 iter 14 | diff: 0.03332 | V(start): 0.058 iter 15 | diff: 0.02910 | V(start): 0.087 iter 16 | diff: 0.01855 | V(start): 0.106 iter 17 | diff: 0.01403 | V(start): 0.120 iter 18 | diff: 0.00810 | V(start): 0.128 iter 19 | diff: 0.00555 | V(start): 0.133 iter 20 | diff: 0.00321 | V(start): 0.137 iter 21 | diff: 0.00247 | V(start): 0.138 iter 22 | diff: 0.00147 | V(start): 0.139 iter 23 | diff: 0.00104 | V(start): 0.140 iter 24 | diff: 0.00058 | V(start): 0.140 iter 25 | diff: 0.00036 | V(start): 0.141 iter 26 | diff: 0.00024 | V(start): 0.141 iter 27 | diff: 0.00018 | V(start): 0.141 iter 28 | diff: 0.00012 | V(start): 0.141 iter 29 | diff: 0.00007 | V(start): 0.141 iter 30 | diff: 0.00004 | V(start): 0.141 iter 31 | diff: 0.00003 | V(start): 0.141 iter 32 | diff: 0.00001 | V(start): 0.141 iter 33 | diff: 0.00001 | V(start): 0.141 average reward: 0.729 Well done! ###Markdown Submit to courseraIf your submission doesn't finish in 30 seconds, set `verbose=True` and try again. ###Code from submit import submit_assigment submit_assigment( get_action_value, get_new_state_value, get_optimal_action, value_iteration, '[email protected]', 'syIAF2jgbRAd7VGB', verbose=False, ) ###Output Submitted to Coursera platform. 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colabs/bigquery_census_correlate.ipynb

###Markdown 1. Install DependenciesFirst install the libraries needed to execute recipes, this only needs to be done once, then click play. ###Code !pip install git+https://github.com/google/starthinker ###Output _____no_output_____ ###Markdown 2. Get Cloud Project IDTo run this recipe [requires a Google Cloud Project](https://github.com/google/starthinker/blob/master/tutorials/cloud_project.md), this only needs to be done once, then click play. ###Code CLOUD_PROJECT = 'PASTE PROJECT ID HERE' print("Cloud Project Set To: %s" % CLOUD_PROJECT) ###Output _____no_output_____ ###Markdown 3. Get Client CredentialsTo read and write to various endpoints requires [downloading client credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_client_installed.md), this only needs to be done once, then click play. ###Code CLIENT_CREDENTIALS = 'PASTE CREDENTIALS HERE' print("Client Credentials Set To: %s" % CLIENT_CREDENTIALS) ###Output _____no_output_____ ###Markdown 4. Enter Census Data Correlation ParametersCorrelate another table with US Census data. Expands a data set dimensions by finding population segments that correlate with the master table. 1. Pre-requisite is Census Normalize, run that at least once. 1. Specify JOIN, PASS, SUM, and CORRELATE columns to build the correlation query. 1. Define the DATASET and TABLE for the joinable source. Can be a view. 1. Choose the significance level. More significance usually means more NULL results, balance quantity and quality using this value. 1. Specify where to write the results. 1. IMPORTANT: If you use VIEWS, you will have to delete them manually if the recipe changes.Modify the values below for your use case, can be done multiple times, then click play. ###Code FIELDS = { 'auth': 'service', # Credentials used for writing data. 'join': '', # Name of column to join on, must match Census Geo_Id column. 'pass': [], # Comma seperated list of columns to pass through. 'sum': [], # Comma seperated list of columns to sum, optional. 'correlate': [], # Comma seperated list of percentage columns to correlate. 'from_dataset': '', # Existing BigQuery dataset. 'from_table': '', # Table to use as join data. 'significance': '80', # Select level of significance to test. 'to_dataset': '', # Existing BigQuery dataset. 'type': 'table', # Write Census_Percent as table or view. } print("Parameters Set To: %s" % FIELDS) ###Output _____no_output_____ ###Markdown 5. Execute Census Data CorrelationThis does NOT need to be modified unles you are changing the recipe, click play. ###Code from starthinker.util.project import project from starthinker.script.parse import json_set_fields USER_CREDENTIALS = '/content/user.json' TASKS = [ { 'census': { 'auth': 'user', 'correlate': { 'join': {'field': {'name': 'join','kind': 'string','order': 1,'default': '','description': 'Name of column to join on, must match Census Geo_Id column.'}}, 'pass': {'field': {'name': 'pass','kind': 'string_list','order': 2,'default': [],'description': 'Comma seperated list of columns to pass through.'}}, 'sum': {'field': {'name': 'sum','kind': 'string_list','order': 3,'default': [],'description': 'Comma seperated list of columns to sum, optional.'}}, 'correlate': {'field': {'name': 'correlate','kind': 'string_list','order': 4,'default': [],'description': 'Comma seperated list of percentage columns to correlate.'}}, 'dataset': {'field': {'name': 'from_dataset','kind': 'string','order': 5,'default': '','description': 'Existing BigQuery dataset.'}}, 'table': {'field': {'name': 'from_table','kind': 'string','order': 6,'default': '','description': 'Table to use as join data.'}}, 'significance': {'field': {'name': 'significance','kind': 'choice','order': 7,'default': '80','description': 'Select level of significance to test.','choices': ['80','90','98','99','99.5','99.95']}} }, 'to': { 'dataset': {'field': {'name': 'to_dataset','kind': 'string','order': 9,'default': '','description': 'Existing BigQuery dataset.'}}, 'type': {'field': {'name': 'type','kind': 'choice','order': 10,'default': 'table','description': 'Write Census_Percent as table or view.','choices': ['table','view']}} } } } ] json_set_fields(TASKS, FIELDS) project.initialize(_recipe={ 'tasks':TASKS }, _project=CLOUD_PROJECT, _user=USER_CREDENTIALS, _client=CLIENT_CREDENTIALS, _verbose=True, _force=True) project.execute(_force=True) ###Output _____no_output_____ ###Markdown 1. Install DependenciesFirst install the libraries needed to execute recipes, this only needs to be done once, then click play. ###Code !pip install git+https://github.com/google/starthinker ###Output _____no_output_____ ###Markdown 2. Get Cloud Project IDTo run this recipe [requires a Google Cloud Project](https://github.com/google/starthinker/blob/master/tutorials/cloud_project.md), this only needs to be done once, then click play. ###Code CLOUD_PROJECT = 'PASTE PROJECT ID HERE' print("Cloud Project Set To: %s" % CLOUD_PROJECT) ###Output _____no_output_____ ###Markdown 3. Get Client CredentialsTo read and write to various endpoints requires [downloading client credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_client_installed.md), this only needs to be done once, then click play. ###Code CLIENT_CREDENTIALS = 'PASTE CREDENTIALS HERE' print("Client Credentials Set To: %s" % CLIENT_CREDENTIALS) ###Output _____no_output_____ ###Markdown 4. Enter Census Data Correlation ParametersCorrelate another table with US Census data. Expands a data set dimensions by finding population segments that correlate with the master table. 1. Pre-requisite is Census Normalize, run that at least once. 1. Specify JOIN, PASS, SUM, and CORRELATE columns to build the correlation query. 1. Define the DATASET and TABLE for the joinable source. Can be a view. 1. Choose the significance level. More significance usually means more NULL results, balance quantity and quality using this value. 1. Specify where to write the results. 1. IMPORTANT: If you use VIEWS, you will have to delete them manually if the recipe changes.Modify the values below for your use case, can be done multiple times, then click play. ###Code FIELDS = { 'auth': 'service', # Credentials used for writing data. 'join': '', # Name of column to join on, must match Census Geo_Id column. 'pass': [], # Comma seperated list of columns to pass through. 'sum': [], # Comma seperated list of columns to sum, optional. 'correlate': [], # Comma seperated list of percentage columns to correlate. 'from_dataset': '', # Existing BigQuery dataset. 'from_table': '', # Table to use as join data. 'significance': '80', # Select level of significance to test. 'to_dataset': '', # Existing BigQuery dataset. 'type': 'table', # Write Census_Percent as table or view. } print("Parameters Set To: %s" % FIELDS) ###Output _____no_output_____ ###Markdown 5. Execute Census Data CorrelationThis does NOT need to be modified unless you are changing the recipe, click play. ###Code from starthinker.util.project import project from starthinker.script.parse import json_set_fields USER_CREDENTIALS = '/content/user.json' TASKS = [ { 'census': { 'auth': 'user', 'correlate': { 'join': {'field': {'name': 'join','kind': 'string','order': 1,'default': '','description': 'Name of column to join on, must match Census Geo_Id column.'}}, 'pass': {'field': {'name': 'pass','kind': 'string_list','order': 2,'default': [],'description': 'Comma seperated list of columns to pass through.'}}, 'sum': {'field': {'name': 'sum','kind': 'string_list','order': 3,'default': [],'description': 'Comma seperated list of columns to sum, optional.'}}, 'correlate': {'field': {'name': 'correlate','kind': 'string_list','order': 4,'default': [],'description': 'Comma seperated list of percentage columns to correlate.'}}, 'dataset': {'field': {'name': 'from_dataset','kind': 'string','order': 5,'default': '','description': 'Existing BigQuery dataset.'}}, 'table': {'field': {'name': 'from_table','kind': 'string','order': 6,'default': '','description': 'Table to use as join data.'}}, 'significance': {'field': {'name': 'significance','kind': 'choice','order': 7,'default': '80','description': 'Select level of significance to test.','choices': ['80','90','98','99','99.5','99.95']}} }, 'to': { 'dataset': {'field': {'name': 'to_dataset','kind': 'string','order': 9,'default': '','description': 'Existing BigQuery dataset.'}}, 'type': {'field': {'name': 'type','kind': 'choice','order': 10,'default': 'table','description': 'Write Census_Percent as table or view.','choices': ['table','view']}} } } } ] json_set_fields(TASKS, FIELDS) project.initialize(_recipe={ 'tasks':TASKS }, _project=CLOUD_PROJECT, _user=USER_CREDENTIALS, _client=CLIENT_CREDENTIALS, _verbose=True, _force=True) project.execute(_force=True) ###Output _____no_output_____ ###Markdown 1. Install DependenciesFirst install the libraries needed to execute recipes, this only needs to be done once, then click play. ###Code !pip install git+https://github.com/google/starthinker ###Output _____no_output_____ ###Markdown 2. Get Cloud Project IDTo run this recipe [requires a Google Cloud Project](https://github.com/google/starthinker/blob/master/tutorials/cloud_project.md), this only needs to be done once, then click play. ###Code CLOUD_PROJECT = 'PASTE PROJECT ID HERE' print("Cloud Project Set To: %s" % CLOUD_PROJECT) ###Output _____no_output_____ ###Markdown 3. Get Client CredentialsTo read and write to various endpoints requires [downloading client credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_client_installed.md), this only needs to be done once, then click play. ###Code CLIENT_CREDENTIALS = 'PASTE CREDENTIALS HERE' print("Client Credentials Set To: %s" % CLIENT_CREDENTIALS) ###Output _____no_output_____ ###Markdown 4. Enter Census Data Correlation ParametersCorrelate another table with US Census data. Expands a data set dimensions by finding population segments that correlate with the master table. 1. Pre-requisite is Census Normalize, run that at least once. 1. Specify JOIN, PASS, SUM, and CORRELATE columns to build the correlation query. 1. Define the DATASET and TABLE for the joinable source. Can be a view. 1. Choose the significance level. More significance usually means more NULL results, balance quantity and quality using this value. 1. Specify where to write the results. 1. IMPORTANT: If you use VIEWS, you will have to delete them manually if the recipe changes.Modify the values below for your use case, can be done multiple times, then click play. ###Code FIELDS = { 'auth': 'service', # Credentials used for writing data. 'join': '', # Name of column to join on, must match Census Geo_Id column. 'pass': [], # Comma seperated list of columns to pass through. 'sum': [], # Comma seperated list of columns to sum, optional. 'correlate': [], # Comma seperated list of percentage columns to correlate. 'from_dataset': '', # Existing BigQuery dataset. 'from_table': '', # Table to use as join data. 'significance': '80', # Select level of significance to test. 'to_dataset': '', # Existing BigQuery dataset. 'type': 'table', # Write Census_Percent as table or view. } print("Parameters Set To: %s" % FIELDS) ###Output _____no_output_____ ###Markdown 5. Execute Census Data CorrelationThis does NOT need to be modified unles you are changing the recipe, click play. ###Code from starthinker.util.project import project from starthinker.script.parse import json_set_fields USER_CREDENTIALS = '/content/user.json' TASKS = [ { 'census': { 'auth': 'user', 'correlate': { 'join': {'field': {'name': 'join','kind': 'string','order': 1,'default': '','description': 'Name of column to join on, must match Census Geo_Id column.'}}, 'pass': {'field': {'name': 'pass','kind': 'string_list','order': 2,'default': [],'description': 'Comma seperated list of columns to pass through.'}}, 'sum': {'field': {'name': 'sum','kind': 'string_list','order': 3,'default': [],'description': 'Comma seperated list of columns to sum, optional.'}}, 'correlate': {'field': {'name': 'correlate','kind': 'string_list','order': 4,'default': [],'description': 'Comma seperated list of percentage columns to correlate.'}}, 'dataset': {'field': {'name': 'from_dataset','kind': 'string','order': 5,'default': '','description': 'Existing BigQuery dataset.'}}, 'table': {'field': {'name': 'from_table','kind': 'string','order': 6,'default': '','description': 'Table to use as join data.'}}, 'significance': {'field': {'name': 'significance','kind': 'choice','order': 7,'default': '80','description': 'Select level of significance to test.','choices': ['80','90','98','99','99.5','99.95']}} }, 'to': { 'dataset': {'field': {'name': 'to_dataset','kind': 'string','order': 9,'default': '','description': 'Existing BigQuery dataset.'}}, 'type': {'field': {'name': 'type','kind': 'choice','order': 10,'default': 'table','description': 'Write Census_Percent as table or view.','choices': ['table','view']}} } } } ] json_set_fields(TASKS, FIELDS) project.initialize(_recipe={ 'tasks':TASKS }, _project=CLOUD_PROJECT, _user=USER_CREDENTIALS, _client=CLIENT_CREDENTIALS, _verbose=True, _force=True) project.execute(_force=True) ###Output _____no_output_____ ###Markdown 1. Install DependenciesFirst install the libraries needed to execute recipes, this only needs to be done once, then click play. ###Code !pip install git+https://github.com/google/starthinker ###Output _____no_output_____ ###Markdown 2. Get Cloud Project IDTo run this recipe [requires a Google Cloud Project](https://github.com/google/starthinker/blob/master/tutorials/cloud_project.md), this only needs to be done once, then click play. ###Code CLOUD_PROJECT = 'PASTE PROJECT ID HERE' print("Cloud Project Set To: %s" % CLOUD_PROJECT) ###Output _____no_output_____ ###Markdown 3. Get Client CredentialsTo read and write to various endpoints requires [downloading client credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_client_installed.md), this only needs to be done once, then click play. ###Code CLIENT_CREDENTIALS = 'PASTE CREDENTIALS HERE' print("Client Credentials Set To: %s" % CLIENT_CREDENTIALS) ###Output _____no_output_____ ###Markdown 4. Enter Census Data Correlation ParametersCorrelate another table with US Census data. Expands a data set dimensions by finding population segments that correlate with the master table. 1. Pre-requisite is Census Normalize, run that at least once. 1. Specify JOIN, PASS, SUM, and CORRELATE columns to build the correlation query. 1. Define the DATASET and TABLE for the joinable source. Can be a view. 1. Choose the significance level. More significance usually means more NULL results, balance quantity and quality using this value. 1. Specify where to write the results. 1. IMPORTANT: If you use VIEWS, you will have to delete them manually if the recipe changes.Modify the values below for your use case, can be done multiple times, then click play. ###Code FIELDS = { 'auth': 'service', # Credentials used for writing data. 'join': '', # Name of column to join on, must match Census Geo_Id column. 'pass': [], # Comma seperated list of columns to pass through. 'sum': [], # Comma seperated list of columns to sum, optional. 'correlate': [], # Comma seperated list of percentage columns to correlate. 'from_dataset': '', # Existing BigQuery dataset. 'from_table': '', # Table to use as join data. 'significance': '80', # Select level of significance to test. 'to_dataset': '', # Existing BigQuery dataset. 'type': 'table', # Write Census_Percent as table or view. } print("Parameters Set To: %s" % FIELDS) ###Output _____no_output_____ ###Markdown 5. Execute Census Data CorrelationThis does NOT need to be modified unless you are changing the recipe, click play. ###Code from starthinker.util.configuration import Configuration from starthinker.util.configuration import commandline_parser from starthinker.util.configuration import execute from starthinker.util.recipe import json_set_fields USER_CREDENTIALS = '/content/user.json' TASKS = [ { 'census': { 'auth': 'user', 'correlate': { 'join': {'field': {'name': 'join','kind': 'string','order': 1,'default': '','description': 'Name of column to join on, must match Census Geo_Id column.'}}, 'pass': {'field': {'name': 'pass','kind': 'string_list','order': 2,'default': [],'description': 'Comma seperated list of columns to pass through.'}}, 'sum': {'field': {'name': 'sum','kind': 'string_list','order': 3,'default': [],'description': 'Comma seperated list of columns to sum, optional.'}}, 'correlate': {'field': {'name': 'correlate','kind': 'string_list','order': 4,'default': [],'description': 'Comma seperated list of percentage columns to correlate.'}}, 'dataset': {'field': {'name': 'from_dataset','kind': 'string','order': 5,'default': '','description': 'Existing BigQuery dataset.'}}, 'table': {'field': {'name': 'from_table','kind': 'string','order': 6,'default': '','description': 'Table to use as join data.'}}, 'significance': {'field': {'name': 'significance','kind': 'choice','order': 7,'default': '80','description': 'Select level of significance to test.','choices': ['80','90','98','99','99.5','99.95']}} }, 'to': { 'dataset': {'field': {'name': 'to_dataset','kind': 'string','order': 9,'default': '','description': 'Existing BigQuery dataset.'}}, 'type': {'field': {'name': 'type','kind': 'choice','order': 10,'default': 'table','description': 'Write Census_Percent as table or view.','choices': ['table','view']}} } } } ] json_set_fields(TASKS, FIELDS) execute(Configuration(project=CLOUD_PROJECT, client=CLIENT_CREDENTIALS, user=USER_CREDENTIALS, verbose=True), TASKS, force=True) ###Output _____no_output_____ ###Markdown 1. Install DependenciesFirst install the libraries needed to execute recipes, this only needs to be done once, then click play. ###Code !pip install git+https://github.com/google/starthinker ###Output _____no_output_____ ###Markdown 2. Get Cloud Project IDTo run this recipe [requires a Google Cloud Project](https://github.com/google/starthinker/blob/master/tutorials/cloud_project.md), this only needs to be done once, then click play. ###Code CLOUD_PROJECT = 'PASTE PROJECT ID HERE' print("Cloud Project Set To: %s" % CLOUD_PROJECT) ###Output _____no_output_____ ###Markdown 3. Get Client CredentialsTo read and write to various endpoints requires [downloading client credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_client_installed.md), this only needs to be done once, then click play. ###Code CLIENT_CREDENTIALS = 'PASTE CLIENT CREDENTIALS HERE' print("Client Credentials Set To: %s" % CLIENT_CREDENTIALS) ###Output _____no_output_____ ###Markdown 4. Enter Census Data Correlation ParametersCorrelate another table with US Census data. Expands a data set dimensions by finding population segments that correlate with the master table. 1. Pre-requisite is Census Normalize, run that at least once. 1. Specify JOIN, PASS, SUM, and CORRELATE columns to build the correlation query. 1. Define the DATASET and TABLE for the joinable source. Can be a view. 1. Choose the significance level. More significance usually means more NULL results, balance quantity and quality using this value. 1. Specify where to write the results. 1. IMPORTANT: If you use VIEWS, you will have to delete them manually if the recipe changes.Modify the values below for your use case, can be done multiple times, then click play. ###Code FIELDS = { 'auth': 'service', # Credentials used for writing data. 'join': '', # Name of column to join on, must match Census Geo_Id column. 'pass': [], # Comma seperated list of columns to pass through. 'sum': [], # Comma seperated list of columns to sum, optional. 'correlate': [], # Comma seperated list of percentage columns to correlate. 'from_dataset': '', # Existing BigQuery dataset. 'from_table': '', # Table to use as join data. 'significance': '80', # Select level of significance to test. 'to_dataset': '', # Existing BigQuery dataset. 'type': 'table', # Write Census_Percent as table or view. } print("Parameters Set To: %s" % FIELDS) ###Output _____no_output_____ ###Markdown 5. Execute Census Data CorrelationThis does NOT need to be modified unless you are changing the recipe, click play. ###Code from starthinker.util.configuration import Configuration from starthinker.util.configuration import execute from starthinker.util.recipe import json_set_fields USER_CREDENTIALS = '/content/user.json' TASKS = [ { 'census': { 'auth': 'user', 'correlate': { 'join': {'field': {'name': 'join','kind': 'string','order': 1,'default': '','description': 'Name of column to join on, must match Census Geo_Id column.'}}, 'pass': {'field': {'name': 'pass','kind': 'string_list','order': 2,'default': [],'description': 'Comma seperated list of columns to pass through.'}}, 'sum': {'field': {'name': 'sum','kind': 'string_list','order': 3,'default': [],'description': 'Comma seperated list of columns to sum, optional.'}}, 'correlate': {'field': {'name': 'correlate','kind': 'string_list','order': 4,'default': [],'description': 'Comma seperated list of percentage columns to correlate.'}}, 'dataset': {'field': {'name': 'from_dataset','kind': 'string','order': 5,'default': '','description': 'Existing BigQuery dataset.'}}, 'table': {'field': {'name': 'from_table','kind': 'string','order': 6,'default': '','description': 'Table to use as join data.'}}, 'significance': {'field': {'name': 'significance','kind': 'choice','order': 7,'default': '80','description': 'Select level of significance to test.','choices': ['80','90','98','99','99.5','99.95']}} }, 'to': { 'dataset': {'field': {'name': 'to_dataset','kind': 'string','order': 9,'default': '','description': 'Existing BigQuery dataset.'}}, 'type': {'field': {'name': 'type','kind': 'choice','order': 10,'default': 'table','description': 'Write Census_Percent as table or view.','choices': ['table','view']}} } } } ] json_set_fields(TASKS, FIELDS) execute(Configuration(project=CLOUD_PROJECT, client=CLIENT_CREDENTIALS, user=USER_CREDENTIALS, verbose=True), TASKS, force=True) ###Output _____no_output_____ ###Markdown Census Data CorrelationCorrelate another table with US Census data. Expands a data set dimensions by finding population segments that correlate with the master table. LicenseCopyright 2020 Google LLC,Licensed under the Apache License, Version 2.0 (the "License");you may not use this file except in compliance with the License.You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0Unless required by applicable law or agreed to in writing, softwaredistributed under the License is distributed on an "AS IS" BASIS,WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.See the License for the specific language governing permissions andlimitations under the License. DisclaimerThis is not an officially supported Google product. It is a reference implementation. There is absolutely NO WARRANTY provided for using this code. The code is Apache Licensed and CAN BE fully modified, white labeled, and disassembled by your team.This code generated (see starthinker/scripts for possible source): - **Command**: "python starthinker_ui/manage.py colab" - **Command**: "python starthinker/tools/colab.py [JSON RECIPE]" 1. Install DependenciesFirst install the libraries needed to execute recipes, this only needs to be done once, then click play. ###Code !pip install git+https://github.com/google/starthinker ###Output _____no_output_____ ###Markdown 2. Set ConfigurationThis code is required to initialize the project. Fill in required fields and press play.1. If the recipe uses a Google Cloud Project: - Set the configuration **project** value to the project identifier from [these instructions](https://github.com/google/starthinker/blob/master/tutorials/cloud_project.md).1. If the recipe has **auth** set to **user**: - If you have user credentials: - Set the configuration **user** value to your user credentials JSON. - If you DO NOT have user credentials: - Set the configuration **client** value to [downloaded client credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_client_installed.md).1. If the recipe has **auth** set to **service**: - Set the configuration **service** value to [downloaded service credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_service.md). ###Code from starthinker.util.configuration import Configuration CONFIG = Configuration( project="", client={}, service={}, user="/content/user.json", verbose=True ) ###Output _____no_output_____ ###Markdown 3. Enter Census Data Correlation Recipe Parameters 1. Pre-requisite is Census Normalize, run that at least once. 1. Specify JOIN, PASS, SUM, and CORRELATE columns to build the correlation query. 1. Define the DATASET and TABLE for the joinable source. Can be a view. 1. Choose the significance level. More significance usually means more NULL results, balance quantity and quality using this value. 1. Specify where to write the results. 1. IMPORTANT: If you use VIEWS, you will have to delete them manually if the recipe changes.Modify the values below for your use case, can be done multiple times, then click play. ###Code FIELDS = { 'auth': 'service', # Credentials used for writing data. 'join': '', # Name of column to join on, must match Census Geo_Id column. 'pass': [], # Comma seperated list of columns to pass through. 'sum': [], # Comma seperated list of columns to sum, optional. 'correlate': [], # Comma seperated list of percentage columns to correlate. 'from_dataset': '', # Existing BigQuery dataset. 'from_table': '', # Table to use as join data. 'significance': '80', # Select level of significance to test. 'to_dataset': '', # Existing BigQuery dataset. 'type': 'table', # Write Census_Percent as table or view. } print("Parameters Set To: %s" % FIELDS) ###Output _____no_output_____ ###Markdown 4. Execute Census Data CorrelationThis does NOT need to be modified unless you are changing the recipe, click play. ###Code from starthinker.util.configuration import execute from starthinker.util.recipe import json_set_fields TASKS = [ { 'census': { 'auth': 'user', 'correlate': { 'join': {'field': {'name': 'join', 'kind': 'string', 'order': 1, 'default': '', 'description': 'Name of column to join on, must match Census Geo_Id column.'}}, 'pass': {'field': {'name': 'pass', 'kind': 'string_list', 'order': 2, 'default': [], 'description': 'Comma seperated list of columns to pass through.'}}, 'sum': {'field': {'name': 'sum', 'kind': 'string_list', 'order': 3, 'default': [], 'description': 'Comma seperated list of columns to sum, optional.'}}, 'correlate': {'field': {'name': 'correlate', 'kind': 'string_list', 'order': 4, 'default': [], 'description': 'Comma seperated list of percentage columns to correlate.'}}, 'dataset': {'field': {'name': 'from_dataset', 'kind': 'string', 'order': 5, 'default': '', 'description': 'Existing BigQuery dataset.'}}, 'table': {'field': {'name': 'from_table', 'kind': 'string', 'order': 6, 'default': '', 'description': 'Table to use as join data.'}}, 'significance': {'field': {'name': 'significance', 'kind': 'choice', 'order': 7, 'default': '80', 'description': 'Select level of significance to test.', 'choices': ['80', '90', '98', '99', '99.5', '99.95']}} }, 'to': { 'dataset': {'field': {'name': 'to_dataset', 'kind': 'string', 'order': 9, 'default': '', 'description': 'Existing BigQuery dataset.'}}, 'type': {'field': {'name': 'type', 'kind': 'choice', 'order': 10, 'default': 'table', 'description': 'Write Census_Percent as table or view.', 'choices': ['table', 'view']}} } } } ] json_set_fields(TASKS, FIELDS) execute(CONFIG, TASKS, force=True) ###Output _____no_output_____ ###Markdown 1. Install DependenciesFirst install the libraries needed to execute recipes, this only needs to be done once, then click play. ###Code !pip install git+https://github.com/google/starthinker ###Output _____no_output_____ ###Markdown 2. Get Cloud Project IDTo run this recipe [requires a Google Cloud Project](https://github.com/google/starthinker/blob/master/tutorials/cloud_project.md), this only needs to be done once, then click play. ###Code CLOUD_PROJECT = 'PASTE PROJECT ID HERE' print("Cloud Project Set To: %s" % CLOUD_PROJECT) ###Output _____no_output_____ ###Markdown 3. Get Client CredentialsTo read and write to various endpoints requires [downloading client credentials](https://github.com/google/starthinker/blob/master/tutorials/cloud_client_installed.md), this only needs to be done once, then click play. ###Code CLIENT_CREDENTIALS = 'PASTE CREDENTIALS HERE' print("Client Credentials Set To: %s" % CLIENT_CREDENTIALS) ###Output _____no_output_____ ###Markdown 4. Enter Census Data Correlation ParametersCorrelate another table with US Census data. Expands a data set dimensions by finding population segments that correlate with the master table. 1. Pre-requisite is Census Normalize, run that at least once. 1. Specify JOIN, PASS, SUM, and CORRELATE columns to build the correlation query. 1. Define the DATASET and TABLE for the joinable source. Can be a view. 1. Choose the significance level. More significance usually means more NULL results, balance quantity and quality using this value. 1. Specify where to write the results. 1. IMPORTANT: If you use VIEWS, you will have to delete them manually if the recipe changes.Modify the values below for your use case, can be done multiple times, then click play. ###Code FIELDS = { 'auth': 'service', # Credentials used for writing data. 'join': '', # Name of column to join on, must match Census Geo_Id column. 'pass': [], # Comma seperated list of columns to pass through. 'sum': [], # Comma seperated list of columns to sum, optional. 'correlate': [], # Comma seperated list of percentage columns to correlate. 'from_dataset': '', # Existing BigQuery dataset. 'from_table': '', # Table to use as join data. 'significance': '80', # Select level of significance to test. 'to_dataset': '', # Existing BigQuery dataset. 'type': 'table', # Write Census_Percent as table or view. } print("Parameters Set To: %s" % FIELDS) ###Output _____no_output_____ ###Markdown 5. Execute Census Data CorrelationThis does NOT need to be modified unles you are changing the recipe, click play. ###Code from starthinker.util.project import project from starthinker.script.parse import json_set_fields USER_CREDENTIALS = '/content/user.json' TASKS = [ { 'census': { 'auth': 'user', 'correlate': { 'table': {'field': {'description': 'Table to use as join data.','name': 'from_table','order': 6,'default': '','kind': 'string'}}, 'dataset': {'field': {'description': 'Existing BigQuery dataset.','name': 'from_dataset','order': 5,'default': '','kind': 'string'}}, 'pass': {'field': {'description': 'Comma seperated list of columns to pass through.','name': 'pass','order': 2,'default': [],'kind': 'string_list'}}, 'correlate': {'field': {'description': 'Comma seperated list of percentage columns to correlate.','name': 'correlate','order': 4,'default': [],'kind': 'string_list'}}, 'join': {'field': {'description': 'Name of column to join on, must match Census Geo_Id column.','name': 'join','order': 1,'default': '','kind': 'string'}}, 'significance': {'field': {'kind': 'choice','order': 7,'choices': ['80','90','98','99','99.5','99.95'],'description': 'Select level of significance to test.','default': '80','name': 'significance'}}, 'sum': {'field': {'description': 'Comma seperated list of columns to sum, optional.','name': 'sum','order': 3,'default': [],'kind': 'string_list'}} }, 'to': { 'type': {'field': {'kind': 'choice','order': 10,'choices': ['table','view'],'description': 'Write Census_Percent as table or view.','default': 'table','name': 'type'}}, 'dataset': {'field': {'description': 'Existing BigQuery dataset.','name': 'to_dataset','order': 9,'default': '','kind': 'string'}} } } } ] json_set_fields(TASKS, FIELDS) project.initialize(_recipe={ 'tasks':TASKS }, _project=CLOUD_PROJECT, _user=USER_CREDENTIALS, _client=CLIENT_CREDENTIALS, _verbose=True, _force=True) project.execute(_force=True) ###Output _____no_output_____

python_ds.ipynb

###Markdown Python in Data Science*Prepared by:* **Jude Michael Teves** In this notebook, you will be introduced to the data science library trio: numpy, pandas, and matplotlib. These libraries power almost all data science tasks as they are the backbone of many libraries used in data science. We will be importing them in the following cell. ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt ###Output _____no_output_____ ###Markdown NumpyNumpy (Numerical Python) is an open-source library in Python for performing scientific computations. It lets us work with arrays and matrices in a more natural way unlike lists, wherein we have to loop through individual elements to perform a numerical operation.As a refresher, here are basic descriptions of arrays and matrices: - Arrays are simply a collection of values of same type indexed by integers--think of list - Matrices are defined to be multi-dimensional array indexed by rows, columns and dimensions--think of nested listsWhen doing mathematical operations, usage of Numpy library is highly recommended because it is designed with high performance in mind--Numpy is largely written in C which makes computations much faster than just using Python code. In addition, Numpy arrays are stored more efficiently than an equivalent data structure in Python such as lists and arrays. Numpy is a third-party module, which means it is not part of Python's suite of built-in libraries. Here are some important notes on numpy arrays: - all elements in a numpy array must be of the same type. - the size cannot be changed once construced. - supports “vectorized” operations such as element-wise addition and multiplication. Initializing an arrayWe simply plug in an iterable inside `np.array()` ###Code arr = np.array([1, 2, 3, 4]) arr ###Output _____no_output_____ ###Markdown We can also create a numpy array through `np.arange()`If only a single argument is passed--let's call this `n1`, it creates an array of size `n1` starting from 0 to `n1`-1. If two arguments (`n1` and `n2`) are passed, it creates an array starting from `n1` to `n2`-1. ###Code np.arange(5, dtype=float) np.arange(2, 5, dtype=float) ###Output _____no_output_____ ###Markdown Numpy Attributes Numpy has built-in attributes that we can use. Here are some of them: - ndarray.ndim - number of axes or dimensions of the array. - ndarray.shape - the dimension of the array--a tuple of integers indicating the size of the array in each dimension. - ndarray.dtype - the type of the elements in the array. Numpy provides its own `int16`, `int32`, `float64` data types, among others. - ndarray.itemsize - size in bytes of each element of the array. For example an array of elements of type `float64` has itemsize of $\frac{64}{8} = 8$ and `complex32` has item size of $\frac{32}{8} = 4$. ###Code print('Type: ',type(arr)) print('Shape: ',arr.shape) print('Dimension: ',arr.ndim) print('Itemsize: ',arr.itemsize) print('Size: ',arr.size) ###Output Type: <class 'numpy.ndarray'> Shape: (4,) Dimension: 1 Itemsize: 4 Size: 4 ###Markdown Accessing and Manipulating ArraysNumpy allows us to do manipulations on an array/matrix.**Indexing** and **Slicing**This is similar to how you index/slice a list. ###Code arr = np.arange(3, 10) arr arr[6] arr[:4] ###Output _____no_output_____ ###Markdown We can also indicate the number of steps by adding another colon `:` and an integer number after the slice syntax. ###Code arr[:4:2] ###Output _____no_output_____ ###Markdown Arithmetic OperationsWe can perform arithmetic operations using on Numpy matrices like in linear algebra. Be careful of the dimensions! Make sure that there is no mismatch for a particular operation that you will be using. ###Code arr1 = np.arange(9).reshape((3,3)) arr2 = np.ones(9).reshape((3,3)) arr1 + arr2 arr1 - arr2 arr1 * arr2 # note that this is an element-wise multiplication arr1 / arr2 # note that this is an element-wise division ###Output _____no_output_____ ###Markdown To do a proper matrix multiplication, we use the `np.dot` method. ###Code np.dot(arr1, arr2) ###Output _____no_output_____ ###Markdown Logical OperatorsWe have a numpy methods for doing the following logical operators: `or`, `and`, and `not`. ###Code np.logical_or([True, False, False], [True, True, False]) np.logical_and([True, False, False], [True, True, False]) np.logical_not([True, False]) ###Output _____no_output_____ ###Markdown Aggregation methodsWe can use methods like sum, max, min, and std. ###Code arr = np.arange(12).reshape((4,3)) arr arr.sum() ###Output _____no_output_____ ###Markdown We can also specify which dimension to use for the aggregation. ###Code arr.sum(axis=0) arr.sum(axis=1) arr.max() arr.max(axis=0) arr.max(axis=1) arr.min() arr.std() arr.std(axis=1) np.mean(arr, axis=0) ###Output _____no_output_____ ###Markdown PandasPandas is an easy-to-use, fast, flexible, and powerful open-source Python library for working with “relational” or “labeled” data. It aims to be the fundamental high-level building block for doing practical, real world data analysis in Python by offering data structures and operations for manipulating tables. And, like Numpy, a Pandas implementation is faster than a default Python ones, and it is a third-party module, which means it is not part of Python's suite of built-in libraries. Pandas is a very big topic and it has so many features that cannot be tacked in this module. You can do further studying by reading the official documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/dsintro.html. **Data Strucures**Pandas has 2 data structures: `Series` and `Dataframe`. These 2 give us many features that make it easy to do data analysis. SeriesPandas Series is a one-dimensional array-like object that has index and value just like NumPy and is capable of holding any data type. Creating SeriesYou can input a list, numpy array, and dictionary to create a Series. Here are some examples of showcasing those. ###Code s = pd.Series(np.random.randn(5), index=['a', 'b', 'c', 'd', 'e']) print(s) ###Output a -0.545619 b -0.961111 c -0.182544 d -1.258336 e 0.309230 dtype: float64 ###Markdown We can also create a Series from a dictionary. ###Code libs_dict = {'Library1': 'Numpy', 'Library2': 'Pandas', 'Library3': 'Matplotlib'} s = pd.Series(libs_dict) print(s) print(type(s)) s['Library2'] ###Output _____no_output_____ ###Markdown As you can see, when creating a Pandas Series, only the data (first argument) is mandatory here. The rest are optional; you can opt not to input the name or index. Editing SeriesEditing a Series is very similar to how you do it with `dict`s. ###Code libs_dict = {'Library1': 'Numpy', 'Library2': 'Pandas', 'Library3': 'Matplotlib'} s = pd.Series(libs_dict) print(s) s['Library2'] = 'Pandas 2.0' s['Library4'] = 'GeoPandas' print(s) s.pop('Library4') print(s) ###Output Library1 Numpy Library2 Pandas Library3 Matplotlib dtype: object Library1 Numpy Library2 Pandas 2.0 Library3 Matplotlib Library4 GeoPandas dtype: object Library1 Numpy Library2 Pandas 2.0 Library3 Matplotlib dtype: object ###Markdown DataframeDataframe is like spreadsheet or a SQL table. It is basically a 2-dimensional labelled data structure with columns of potentially different data types. To put it simply, `DataFrame` is a multi-column `Series` object. It is generally the most commonly used pandas object, and like `Series`, `DataFrame` accepts many different kinds of input: - Dict of 1D ndarrays, lists, dicts, or Series - 2-D numpy.ndarray - Structured or record ndarray - A `Series` - Another `DataFrame` Here are some examples of creating Dataframes using different data types and structures as inputs. Creating Dataframe using dict ###Code data = {'one' : pd.Series([1., 2., 3.], index=['a', 'b', 'c']), 'two' : pd.Series([1., 2., 3., 4.], index=['a', 'b', 'c', 'd'])} df = pd.DataFrame(data) print('Dataframe:\n', df) print('Type of Object:', type(df)) print('Type of elements:', type(df.values)) ###Output Dataframe: one two a 1.0 1.0 b 2.0 2.0 c 3.0 3.0 d NaN 4.0 Type of Object: <class 'pandas.core.frame.DataFrame'> Type of elements: <class 'numpy.ndarray'> ###Markdown Just like Series, you can access the following attributes: index, values and columns. ###Code print('Index: ', df.index) print('Columns: ', df.columns) print('Values of Column one: ', df['one'].values) print('Values of Column two: ', df['two'].values) ###Output Index: Index(['a', 'b', 'c', 'd'], dtype='object') Columns: Index(['one', 'two'], dtype='object') Values of Column one: [ 1. 2. 3. nan] Values of Column two: [1. 2. 3. 4.] ###Markdown Creating Dataframe using list of dict ###Code df2 = pd.DataFrame([{'a': 1, 'b': 2, 'c':3, 'd':None}, {'a': 2, 'b': 2, 'c': 3, 'd': 4}], index=['one', 'two']) print('Dataframe: \n',df2) # Ofcourse you can also transpose the result: print('Transposed Dataframe: \n',df2.T) ###Output Dataframe: a b c d one 1 2 3 NaN two 2 2 3 4.0 Transposed Dataframe: one two a 1.0 2.0 b 2.0 2.0 c 3.0 3.0 d NaN 4.0 ###Markdown Editing DataFrameAssigning a column that doesn’t exist will create a new column. If it exists, the assigned value will override the old one. ###Code df = pd.DataFrame(data) df['three'] = None print('Added third column: \n',df) # The del keyword can be used delete columns: del df['three'] print('\nDeleted third column: \n',df) # You can also use df.drop(). We shall see that later df.loc['a','one'] = 9000 print('\nEdited a value: \n',df) ###Output Added third column: one two three a 1.0 1.0 None b 2.0 2.0 None c 3.0 3.0 None d NaN 4.0 None Deleted third column: one two a 1.0 1.0 b 2.0 2.0 c 3.0 3.0 d NaN 4.0 Edited a value: one two a 9000.0 1.0 b 2.0 2.0 c 3.0 3.0 d NaN 4.0 ###Markdown **Using `.drop`** ###Code data = {'one' : pd.Series([1., 2., 3.], index=['a', 'b', 'c']), 'two' : pd.Series([1., 2., 3., 4.], index=['a', 'b', 'c', 'd'])} df = pd.DataFrame(data) df df.drop(['c', 'a']) ###Output _____no_output_____ ###Markdown IndexingThere are many ways to select and rearrange the data contained in a pandas object. Some indexing options can be seen in below table:|Indexing Type| Description||:---|:---||df[val] | Select single column or sequence of columns from the DataFrame. Special case con- veniences: boolean array (filter rows), slice (slice rows), or boolean DataFrame (set values based on some criterion).||df.ix[val] | Selects single row of subset of rows from the DataFrame.||df.ix[:, val] | Selects single column of subset of columns.||df.ix[val1, val2] | Select both rows and columns.||reindex method | Conform one or more axes to new indexes.||xs method | Select single row or column as a Series by label.||icol, irowmethods | Select single column or row, respectively, as a Series by integer location.||get_value, set_value methods | Select single value by row and column label.| Series indexing works similarly to a dict--we provide the key ###Code s s['Library2'] ###Output _____no_output_____ ###Markdown As for DataFrame, To slice and select only column one for rows 0 and 4 use the following. ###Code df # Slicing and selecting only column `one` for row 0 and row 4 df['one'][['a', 'd']] # Slicing df from row b to row 4 for column `one` df['one']['b':'d'] ###Output _____no_output_____ ###Markdown In the above cell, you will notice that slicing with labels behaves differently than normal Python slicing in that the endpoint is inclusive.For DataFrame label-indexing on the rows, there is a special indexing field loc, which enables us to select a subset of the rows and columns from a `DataFrame` with `numpy`-like notation plus axis labels. It is a less verbose way to do the reindexing, but we typically use this. ###Code df.loc[['a','c'],['one']] df.loc[['a','c'],['one', 'two']] ###Output _____no_output_____ ###Markdown FilteringWe can also filter by having a condition inside `loc`. ###Code df df.loc[df.one > 1] df.loc[df.two >= 3] ###Output _____no_output_____ ###Markdown SortingWe can sort items by doing the following. ###Code dt = pd.Series(np.random.randint(3, 10, size=7), index=['g','c','a','b','e','d','f']) print('Original Data: \n', dt, end="\n\n") print('Sorted by Index: \n',dt.sort_index()) ###Output Original Data: g 6 c 6 a 9 b 4 e 9 d 6 f 5 dtype: int32 Sorted by Index: a 9 b 4 c 6 d 6 e 9 f 5 g 6 dtype: int32 ###Markdown Using Numpy functions on DataFrameElement-wise numpy functions like log, exp, sqrt, ... and various other numpy functions can be used on DataFrame. ###Code np.random.seed(42) # ensures that we are getting consistent values df1 = pd.DataFrame(np.random.randn(10, 4), columns=['A', 'B', 'C', 'D']) df1 np.abs(df1) np.log(df1) ###Output C:\Users\Jude Michael Teves\AppData\Roaming\Python\Python37\site-packages\ipykernel_launcher.py:1: RuntimeWarning: invalid value encountered in log """Entry point for launching an IPython kernel. ###Markdown Reading / Loading Data ###Code df = pd.read_csv('https://raw.githubusercontent.com/Cyntwikip/data-repository/main/titanic.csv') # df = pd.read_csv('C:/Github/data-repository/titanic.csv') # to read local file instead df.head() ###Output _____no_output_____ ###Markdown Here are some datasets I have made available in my public data repository on Github:- Titanic: https://raw.githubusercontent.com/Cyntwikip/data-repository/main/titanic.csv - Illness Toy Dataset: https://raw.githubusercontent.com/Cyntwikip/data-repository/main/illness.csv Of course, you may use any dataset you wish to, whether it be offline (local) or online. We just used a dataset that is available online so that you can run this as is without the need to download a file. MatplotlibMatplotlib is the most used Python package for 2d graphics. It is simple to use and has almost all standard graphs/plots in it. This is a very big topic so we will just focus on the practical aspect of it by showing some code snippets for doing basic visualizations for commonly used data. Let's check the styles that we could use. ###Code plt.style.available ###Output _____no_output_____ ###Markdown Let's use the `seaborn-darkgrid` style. ###Code plt.style.use('seaborn-darkgrid') ###Output _____no_output_____ ###Markdown Line PlotFor sequential data like time, we can use a line plot. The following data points that we will be plotting are random generated, but for this example, just treat the axis as a temporal feature. ###Code np.random.seed(42) x = np.arange(10) y = np.random.randint(50, 100, size=10) plt.figure(figsize=(6, 4), dpi=100) plt.ylabel('value') plt.xlabel('time') plt.title('Line Plot') plt.plot(x, y) plt.show() ###Output _____no_output_____ ###Markdown Scatter plotWe can also do a scatter plot for the data above. ###Code np.random.seed(42) x = np.arange(10) y = np.random.randint(50, 100, size=10) plt.figure(figsize=(6, 4), dpi=100) plt.ylabel('value') plt.xlabel('time') plt.title('Scatter Plot') plt.scatter(x, y) plt.show() ###Output _____no_output_____ ###Markdown What if we have multiple categories in our data? In the following example, there are 3 categories. ###Code from sklearn import datasets # import some data to play with iris = datasets.load_iris() X = iris.data[:, :2] # we only take the first two features. y = iris.target plt.figure(figsize=(6, 4), dpi=100) plt.ylabel('sepal width') plt.xlabel('sepal length') plt.title('Scatter Plot') plt.scatter(X[:,0], X[:,1], c=y, cmap=plt.cm.Set1) plt.show() ###Output _____no_output_____ ###Markdown Bar graphBar graph is used for categorical data. ###Code x = ['Mei', 'Zhongli', 'Venti'] y = [5, 6, 4] plt.figure(figsize=(6, 4), dpi=100) plt.ylabel('height') plt.xlabel('person') plt.title('Height') plt.bar(x, y) plt.show() ###Output _____no_output_____ ###Markdown HistogramHistograms are typically used for showing the distribution of data. ###Code dist = np.random.normal(size=100) plt.figure(figsize=(6, 4), dpi=100) plt.hist(dist) plt.show() ###Output _____no_output_____

notebooks/People/People Making Choices.ipynb

###Markdown How People Decide what they want to do Directed graph approach Generally people want to do a number of different things. For this I'm going to create a schema for this in a graph language that allows me to designate how much a `pop` desires to take a certain action. This will be used later when determining AI decisions. **Note** this notebook actualy builds the desires into the graph, overwriting existing ontology. ###Code import sys import numpy as np import pandas as pd import altair as alt sys.path.append('..') import helpers.dbquery as db import helpers.functions as f import yaml, ssl, asyncio import nb_black ssl._create_default_https_context = ssl._create_unverified_context asyncio.set_event_loop_policy(asyncio.WindowsSelectorEventLoopPolicy()) import nest_asyncio # this is required for running in a Jupyter Notebook. nest_asyncio.apply() res = db.run_query("g.V().hasLabel('pop').has('username','userbill').valueMap()") pops = [db.clean_node(n) for n in res] pops[0] ###Output _____no_output_____ ###Markdown Each population wants to do everything to a degree, the amount of desire to do that thing is expressed by the edge weight. * Attack a population * Focus on improving literacy * Focus on improving industry Desires as Objects Desire with targets. Both factions and pops can have desire. Action is guided by desire based on the `max(desire.weight)`. `desire` is an edge, the type of that desire is a property of that edge, and the edge weight is the amount of desire. The target (`node2`) is the recipient. Examples: * faction wants trade with faction * pop wants war with another pop * pop wants faction to go to war with faction Desire without targets. Desires without targets must link to an objective. That objective can be it's own node. ###Code # # Drop the items, if they exist. # db.run_query("g.V().hasLabel('objective').has('username','notebook').drop()") # objectives_yaml = yaml.safe_load(open("desires.yaml"))['objectives'] # data = {"nodes":objectives_yaml,'edges':[]} # # Then Create the nodes and add them to the DB # db.upload_data(data,verbose=False) # After creating the nodes, pulling them into the notebook for reference res = db.run_query("g.V().hasLabel('objective').valueMap()") objectives = [db.clean_node(n) for n in res] # objectives ###Output _____no_output_____ ###Markdown population wants to improve industry populations want to improve industry when: * they are not wealty * they are at war ###Code # Marginal return on base attribute n = 2 ind_df = pd.DataFrame(np.sort([float(p['wealth']) for p in pops]),columns=['wealth']) ind_df['base'] = range(len(ind_df)) ind_df['desires_industry'] = ind_df['wealth'].apply(lambda x: ((x+1)**(1-n) - 1)/(1-n)) ind_df['desire_base'] = ind_df['base'].apply(lambda x: ((x+1)**(1-n) - 1)/(1-n)) alt.Chart(ind_df).mark_line().encode(x='base',y='desire_base').properties(title="Desire relative to the base attribute") alt.Chart(ind_df).mark_line().encode(x='wealth:N',y='desires_industry').properties(title="Desires wealth industry relative to industry") ###Output _____no_output_____ ###Markdown feeding that desire to the populations ###Code def get_desire(x): return np.round(((float(x)+1)**(1-n) - 1)/(1-n),3) edges = [] for p in pops: for o in objectives: edge = {'label':'desires', 'node1':p['objid'], 'node2':o['objid'], 'weight':get_desire(p[o['leadingAttribute']])} edges.append(edge) pd.DataFrame(edges) db.create_edge(edges[0]) db.upload_data({'nodes':[],'edges':edges},verbose=False) [p for p in pops if p['objtype']=='pop'] ###Output _____no_output_____

src/Equation_of_State_T_eq_0.ipynb

###Markdown Analysis of the Equation of State ###Code import numpy as np import matplotlib.pyplot as plt from graphenetools import gt import re,glob,os from scipy.signal import argrelextrema from scipy.optimize import brentq import multiprocessing import sys,importlib from dgutils import colors as colortools from collections import defaultdict import pickle from numpy import pi as π # Notebook display options %matplotlib inline %config InlineBackend.figure_format = 'svg' # plot style plot_style = {'notebook':'../include/notebook.mplstyle','aps':'../include/aps.mplstyle'} plt.style.reload_library() plt.style.use(plot_style['aps']) figsize = plt.rcParams['figure.figsize'] plt.rcParams['text.latex.preamble'] = f'\input{{{os.getcwd()}/../include/texheader}}' colors = plt.rcParams['axes.prop_cycle'].by_key()['color'] ###Output _____no_output_____ ###Markdown Do you want to process the full data set?Default is False. The full data set can be found here: [](https://doi.org/10.5281/zenodo.4553524)A minimal set of reduced (averaged and processed) data files is included with the repository `../data/QMC.tar.bz2`. We can extract if it hasn't already happened. ###Code reduce_data = False if not os.path.isdir('../data/QMC/'): ! tar xjf ../data/QMC.tar.bz2 ###Output _____no_output_____ ###Markdown Some helper and analysis functions ###Code import layerutils from layerutils import lab,vals,texformat,get_base_dir from pimcscripts import pimchelp ###Output _____no_output_____ ###Markdown Load QMC Data from Disk ###Code num_sites = [24] sim_params = {'T':0.0,'canonical':True,'τ':0.00313, 'β':0.5007} Lz = np.array([5.05,10.0]) pimcid = defaultdict(dict) par_map = defaultdict(dict) base_dir = defaultdict(dict) L,n,N,τ = defaultdict(dict),defaultdict(dict),defaultdict(dict),defaultdict(dict) N_ads = defaultdict(dict) simulations,pimcids = {},{} pigs_pimcids,pimc_pimcids = defaultdict(list),defaultdict(list) for cnum in num_sites: Nkey = lab(N=cnum) cbase_dir = get_base_dir(cnum,T=sim_params['T']) log_names = pimchelp.get_file_list_from_params(**sim_params,base_dir=cbase_dir) # We go through each file and automatically populate the simulation map for log in log_names: par_ = pimchelp.get_parameter_map(cbase_dir + log) cN = par_['Initial Number Particles'] cf = cN/cnum sim = lab(T=sim_params['T'],n=cf,Lz=par_['Container Length'],N=cnum) base_dir[Nkey][sim] = cbase_dir # sort the pimcids into two possible groups pimcid[Nkey][sim] = par_['PIMCID'] if sim_params['T'] > 0: pimc_pimcids[Nkey].append(par_['PIMCID']) else: pigs_pimcids[Nkey].append(par_['PIMCID']) par_map[Nkey][sim] = par_ # We add some short-hand variables for ease of referencing L[Nkey][sim] = par_map[Nkey][sim]['Container Dimensions'] n[Nkey][sim] = par_map[Nkey][sim]['Initial Density'] N[Nkey][sim] = par_map[Nkey][sim]['Initial Number Particles'] τ[Nkey][sim] = par_map[Nkey][sim]['Specified Imaginary Time Step'] simulations[Nkey] = list(pimcid[Nkey].keys()) pimcids[Nkey] = list(pimcid[Nkey].values()) ###Output _____no_output_____ ###Markdown Generate the graphene lattice ###Code sim = simulations[lab(N=24)][0] fix,ax = gt.plot_graphene_lattice_with_c_one_third(0.0,L[lab(N=24)][sim][:-1]) ###Output _____no_output_____ ###Markdown Reduce All Data Files ###Code if reduce_data: for cnum in num_sites[:]: print(f'=== N = {cnum} ===\n') reduce_command = f"parallel reduce-one.py -r T -i {{}} -s 0.8 --canonical {get_base_dir(cnum,T=sim_params['T'])} ::: {' '.join(pimcids[lab(N=cnum)])}" stream = os.popen(reduce_command) output = stream.read() print(output) ###Output _____no_output_____ ###Markdown Load the reduced estimators ###Code estimator = {} ρlin = {} for cnum in num_sites: cNkey = lab(N=cnum) for sim in simulations[cNkey]: ckey = lab(N=cnum,Lz=vals(sim)['Lz']) reduce_params = {'canonical':True,'reduce':'T', 'pimcid':pimcid[cNkey][sim],'base_dir':base_dir[cNkey][sim]} estimator[sim] = pimchelp.PIMCResults(pimchelp.get_reduce_name(**reduce_params,estimator='estimator')) ρlin[sim] = pimchelp.PIMCResults(pimchelp.get_reduce_name(**reduce_params,estimator='lineardensity')) filling = {} est = {} for cnum in num_sites: filling[lab(N=cnum)] = np.array([cn/cnum for cn in range(1,25)]) for cLz in Lz: est[lab(N=cnum,Lz=cLz)] = defaultdict(list) for cf in filling[lab(N=cnum)]: sim = lab(N=cnum,n=cf,T=0.0,Lz=cLz) for cest_name in estimator[sim].data.dtype.names: est[lab(N=cnum,Lz=cLz)][cest_name].append(estimator[sim].data[cest_name]) for cest_name in estimator[sim].headers: est[lab(N=cnum,Lz=cLz)][cest_name] = np.array(est[lab(N=cnum,Lz=cLz)][cest_name]) ###Output _____no_output_____ ###Markdown The Equation of State ###Code from mpl_toolkits.axes_grid1.inset_locator import inset_axes from fractions import Fraction shift = {} for cnum in num_sites: for cLz in Lz: key = lab(N=cnum,Lz=cLz) shift[key]= est[key]['E/N'][0] fig,ax = plt.subplots(figsize=(figsize[0],figsize[1]), constrained_layout=True) axins1 = inset_axes(ax, width="80%", height="70%", bbox_to_anchor=(.045, .2, .36, .78), bbox_transform=ax.transAxes) axins2 = inset_axes(ax, width="80%", height="70%", bbox_to_anchor=(.355, .2, .36, .78), bbox_transform=ax.transAxes) axins = [axins1,axins2] axins[0].set_xlabel(r'$\alabel{z}{\angstrom}$') axins[1].set_xlabel(r'$\alabel{z}{\angstrom}$') axins[0].set_ylabel(r'$\alabel{\rho(z)/N}{\angstrom^{-1}}$') params = {'mfc':'None', 'elinewidth':0.5, 'marker':'o', 'ms':5, 'lw':0.5, 'ls':'--','mew':0.75} for cnum in num_sites: for j,cLz in enumerate(Lz): for i,cf in enumerate([1/3,1]): sim = lab(N=cnum,T=0,n=cf,Lz=cLz) x,y,Δy = ρlin[sim].epdata(ρlin[sim].params[0]) axins[i].plot(x+0.5*L[lab(N=cnum)][sim][-1],y/N[lab(N=cnum)][sim], lw=0.75, color=colors[j]) axins[i].annotate(f'$f = {Fraction(cf).limit_denominator()}$', xy=(0.95,0.85),xytext=(0.95,0.85), xycoords='axes fraction', ha='right', va='bottom') axins[1].set_yticklabels([]) axins[0].set_yticklabels([]) for i in range(2): axins[i].set_xlim(0,8) for i,cLz in enumerate(Lz): ax.errorbar(filling[lab(N=24)],est[lab(N=24,Lz=cLz)]['E/N']-shift[lab(N=24,Lz=cLz)], yerr=est[lab(N=24,Lz=cLz)]['ΔE/N'],**params, label = f'$L_z = {cLz:.2f}\; \mathrm{{\AA}}$', color=colortools.get_alpha_hex(colors[i],0.5), mec=colors[i]) #ax.legend(loc=(0.6,0.4),ncol=1) ax.annotate("", xy=(1/3, 0.0), xycoords='data', zorder=-100, xytext=(0.4, 100), textcoords='data', arrowprops=dict(arrowstyle="-", connectionstyle="arc3", color='gray', ls=':',alpha=0.5,lw=0.5), ) ax.annotate("", xy=(1/3, 0.0), xycoords='data',zorder=-100, xytext=(0.09, 98), textcoords='data', arrowprops=dict(arrowstyle="-", connectionstyle="arc3", color='gray', ls=':', alpha=0.5,lw=0.5), ) data_val = est[lab(N=24,Lz=10)]['E/N'][-1]-shift[lab(N=24,Lz=10)] ax.annotate("", xy=(1, data_val), xycoords='data',zorder=-100, xytext=(0.72, 98), textcoords='data', arrowprops=dict(arrowstyle="-", connectionstyle="arc3", color='gray', ls=':', alpha=0.5,lw=0.5), ) data_val = est[lab(N=24,Lz=5.05)]['E/N'][-1]-shift[lab(N=24,Lz=5.05)] ax.annotate("", xy=(1, data_val), xycoords='data',zorder=-100, xytext=(0.72, 246), textcoords='data', arrowprops=dict(arrowstyle="-", connectionstyle="arc3", color='gray', ls=':', alpha=0.5,lw=0.5), ) cnum=24 loc=(0.19,0.1) ax.annotate(f'$N_\graphene = {cnum}$', xy=loc,xytext=loc, xycoords='axes fraction', ha='right', va='bottom') loc=(0.98,0.1) ax.annotate(r'$L_z = \SI{10}{\angstrom}$', xy=loc,xytext=loc, xycoords='axes fraction', ha='right', va='bottom') loc=(0.98,0.8) ax.annotate(r'$L_z = \SI{5.05}{\angstrom}$', xy=loc,xytext=loc, xycoords='axes fraction', ha='right', va='bottom') ax.set_xlabel('Filling Fraction $f = N/N_\graphene$') ax.set_ylabel(r'$\alabel{E/N-E_1}{\kelvin}$'); plt.savefig('../plots/EoS_Teq0.pdf',dpi=300) plt.savefig('../plots/EoS_Teq0.svg',dpi=300) ###Output _____no_output_____ ###Markdown How big is the raw offset between the curves? ###Code Δ = shift[lab(N=24,Lz=10)] - shift[lab(N=24,Lz=5.05)] print(f'Δ = {Δ:.2f} K') print(f'Relative Shift = {100*Δ/est[lab(N=24,Lz=cLz)]["E/N"][0]:.1f}%') ###Output Δ = -5.67 K Relative Shift = 4.6%

hopfiled/hopfileNeuralNetwork.ipynb

###Markdown hopfiled神经网络及其实现 小组成员：沈旭阳、谭力仁、温紫珺、邹子涵 汇报成员：沈旭阳 实验介绍 实验类别：hopfile神经网络；离散型；异步更新 Hopfield神经网络是一种非常典型的反馈型神经网络，除了与前馈神经系统相同的神经元之间的前馈连接，很明显还存在一种反馈连接。 Hopfield网络结构可以用以下示意图描述：  从示意图中可知，该神经网络结构具有以下三个特点： 1、神经元之间全连接，并且为单层神经网络。 2、每个神经元既是输入又是输出，导致得到的权重矩阵相对称，故可节约计算量。 3、在输入的激励下，其输出会产生不断的状态变化，这个反馈过程会一直反复进行。假如Hopfield神经网络是一个收敛的稳定网络，则这个反馈与迭代的计算过程所产生的变化越来越小，一旦达到了稳定的平衡状态，Hopfield网络就会输出一个稳定的恒值。 4、Hopfield网络可以储存一组平衡点，使得当给定网络一组初始状态时，网络通过自行运行而最终收敛于这个设计的平衡点上。当然，根据热力学上，平衡状态分为stable state和metastable state, 这两种状态在网络的收敛过程中都是非常可能的。 5、为递归型网络，t时刻的状态与t-1时刻的输出状态有关。之后的神经元更新过程也采用的是异步更新法（Asynchronous)。 python实现 导包 ###Code import numpy as np import random from PIL import Image import os import re import matplotlib.pyplot as plt from IPython.core.interactiveshell import InteractiveShell InteractiveShell.ast_node_interactivity = "all" ###Output _____no_output_____ ###Markdown 将图片转换为二值矩阵 函数参数为（file、size、threshold） 分别代表（图片文件、图片大小、2值化阈值） ###Code def readImg2array(file,size, threshold= 145): pilIN = Image.open(file).convert(mode="L") pilIN= pilIN.resize(size) imgArray = np.asarray(pilIN,dtype=np.uint8) x = np.zeros(imgArray.shape,dtype=np.float) x[imgArray > threshold] = 1 x[x==0] = -1 return x ###Output _____no_output_____ ###Markdown 二值矩阵转化为图片 函数参数为（矩阵、输出文件） 输出文件默认为空 ###Code def array2img(data, outFile = None): y = np.zeros(data.shape,dtype=np.uint8) y[data==1] = 255 y[data==-1] = 0 img = Image.fromarray(y,mode="L") if outFile is not None: img.save(outFile) return img ###Output _____no_output_____ ###Markdown 将矩阵转换为向量形式 ###Code def mat2vec(x): m = x.shape[0]*x.shape[1] tmp1 = np.zeros(m) c = 0 for i in range(x.shape[0]): for j in range(x.shape[1]): tmp1[c] = x[i,j] c +=1 return tmp1 ###Output _____no_output_____ ###Markdown 创建Hij即权重矩阵，依据hopfile特性，该矩阵为对称矩阵 ###Code def create_W_single_pattern(x): if len(x.shape) != 1: print ("该输入不是一个向量！") return else: w = np.zeros([len(x),len(x)]) for i in range(len(x)): for j in range(i,len(x)): if i == j: w[i,j] = 0 else: w[i,j] = x[i]*x[j] # 对称矩阵性质 w[j,i] = w[i,j] return w ###Output _____no_output_____ ###Markdown 建立hopfiled升级函数对神经元随机升级，采用异步更新，获取更新后的神经元向量以及系统能量。 ###Code def update_asynch(weight,vector,theta=0.5,times=100): # 初始化参数 energy_ = [] times_ = [] # 记录系统能量更新过程 energy_.append(energy(weight,vector)) # 记录迭代次数 times_.append(0) # 遍历迭代次数 for i in range(times): # 获取随机数，对随机神经元进行更新 length = len(vector) update_num = random.randint(0,length-1) # 对神经元更新 next_time_value = np.dot(weight[update_num][:],vector) - theta # sign激活函数，对更新值取符号 if next_time_value>=0: vector[update_num] = 1 if next_time_value<0: vector[update_num] = -1 # 记录迭代次数和系统能量变化 times_.append(i) energy_.append(energy(weight,vector)) return (vector,times_,energy_) ###Output _____no_output_____ ###Markdown 计算系统能量 ###Code def energy(weight,x,bias=0): energy = -x.dot(weight).dot(x.T)+sum(bias*x) return energy ###Output _____no_output_____ ###Markdown hopfiled主体实现 ###Code size_global =(80,80) threshold_global = 220 train_paths = [] train_path = "./training/" for i in os.listdir(train_path): if re.match(r'[0-9 a-z A-Z-_]*.jp[e]*g',i): train_paths.append(train_path+i) flag = 0 for path in train_paths: matrix_train = readImg2array(path,size = size_global,threshold=threshold_global) vector_train = mat2vec(matrix_train) plt.imshow(array2img(matrix_train)) plt.title("training picture") plt.show() if flag == 0: w_ = create_W_single_pattern(vector_train) flag = flag +1 else: w_ = w_ +create_W_single_pattern(vector_train) flag = flag +1 # 建立权值矩阵 w_ = w_/flag print(w_.shape) print(w_) test_paths = [] test_path = "./test/" for i in os.listdir(test_path): if re.match(r'[0-9 a-z A-Z-_]*.jp[e]*g',i): test_paths.append(test_path+i) num = 0 for path in test_paths: num = num+1 matrix_test = readImg2array(path,size = size_global,threshold=threshold_global) vector_test = mat2vec(matrix_test) plt.subplot(221) plt.imshow(array2img(matrix_test)) plt.title("test picture") oshape = matrix_test.shape aa = update_asynch(weight=w_,vector=vector_test,theta = 0.5 ,times=10000) vector_test_update = aa[0] matrix_test_update = vector_test_update.reshape(oshape) plt.subplot(222) plt.imshow(array2img(matrix_test_update)) plt.title("recall"+str(num)) #plt.show() plt.subplot(212) plt.plot(aa[1],aa[2]) plt.ylabel("energy") plt.xlabel("update times") plt.show() ###Output _____no_output_____

notebooks/04.Widget-libraries/04.02-ipympl.ipynb

###Markdown ipympl: The Matplotlib Jupyter Widget Backend https://github.com/matplotlib/ipymplEnabling interaction with matplotlib charts in the Jupyter notebook and JupyterLab- BSD-3-Clause**Installation:**```bashconda install -c conda-forge ipympl``` Enabling the `widget` backend. This requires ipympl. ipympl can be install via pip or conda. ###Code %matplotlib widget import numpy as np import matplotlib.pyplot as plt from ipywidgets import VBox, FloatSlider, IntSlider, Button ###Output _____no_output_____ ###Markdown When using the `widget` backend from ipympl, fig.canvas is a proper Jupyter interactive widget, which can be embedded in Layout classes like HBox and Vbox.One can bound figure attributes to other widget values. ###Code # Creating a new figure (1) fig = plt.figure() # Simple plot x = np.linspace(0,5,11) y = x ** 3 plt.plot(x,y, '-m'); ###Output _____no_output_____ ###Markdown Change the window title ###Code fig.canvas.set_window_title('My interactive widget-enabled plot') ###Output _____no_output_____ ###Markdown Remove toolbar, header and footer from the plot window ###Code fig.canvas.toolbar_visible = False fig.canvas.header_visible = False fig.canvas.footer_visible = False ###Output _____no_output_____ ###Markdown Disable canvas resizing ###Code fig.canvas.resizable = False ###Output _____no_output_____ ###Markdown Adding widget controls to our figure ###Code # Disabling internal matplotlib intaractive mode off (we use our own backend) plt.ioff() # Creating a simple slider widget slider = FloatSlider( value=1.0, min=0.02, max=2.0 ) # New figure object fig = plt.figure() plt.title('Plotting: y=sin({} * x)'.format(slider.value)) # 500 even-spaced data points on the x-axis between 0 and 20. x1 = np.linspace(0, 20, 500) # Applying and plotting the sin function for each data point lines = plt.plot(x1, np.sin(slider.value * x1)) # Callback function when our slider changes in value def update_lines(change): lines[0].set_data(x1, np.sin(change.new * x1)) fig.canvas.draw() fig.canvas.flush_events() plt.title('Plotting: y=sin({} * x)'.format(slider.value)) # Setting up an event listener for the slider value slider.observe(update_lines, names='value') # Render the slider and figure in a vertical box VBox([slider, fig.canvas]) ###Output _____no_output_____ ###Markdown 3D plots ###Code from mpl_toolkits.mplot3d import axes3d # Setting up a new, blank figure object fig = plt.figure() # Adding an axes to the figure ax = fig.add_subplot(111, projection='3d') # Grab some test data. X, Y, Z = axes3d.get_test_data(0.05) # Plot a basic wireframe. ax.plot_surface(X, Y, Z, rstride=10, cstride=10) # Display the plot fig.canvas ###Output _____no_output_____ ###Markdown Subplots ###Code # Static sample data np.random.seed(0) # Number of bins for the histogram n_bins = 10 x2 = np.random.randn(1000, 3) # a two-by-two plot grid (4 plots) fig3, axes = plt.subplots(nrows=2, ncols=2) ax0, ax1, ax2, ax3 = axes.flatten() # Setting up the colors and generating the top-left histogram colors = ['red', 'tan', 'lime'] ax0.hist(x2, n_bins, density=1, histtype='bar', color=colors, label=colors) ax0.legend(prop={'size': 10}) ax0.set_title('bars with legend') # Setting up the stacked bar ax1.hist(x2, n_bins, density=1, histtype='bar', stacked=True) ax1.set_title('stacked bar') # Setting up the bottom-left histogram ax2.hist(x2, n_bins, histtype='step', stacked=True, fill=False) ax2.set_title('stack step (unfilled)') # Make a multiple-histogram of data-sets with different length (bottom-right) x_multi = [np.random.randn(n) for n in [10000, 5000, 2000]] ax3.hist(x_multi, n_bins, histtype='bar') ax3.set_title('different sample sizes') # Display the plot fig3.tight_layout() fig3.canvas fig3.canvas.toolbar_position = 'right' fig3.canvas.toolbar_visible = False ###Output _____no_output_____ ###Markdown Exercise **This is a slightly challenging exercise!**Create a small app which generates and displays a simulation of a stock price (you can use the helper function) and has the following widgets:1. An interactive ipympl canvas with the toolbar on the left hand side2. A slider which selects the number of steps per simulation3. A button to ghenerate new data and update the plotThe plot should update whenever there is a change to the slider value, or the button is clicked. ###Code # Helper function def generate_timeseries(steps): return (np.arange(1,steps + 1,1), 100 + np.random.normal(0,1,steps).cumsum()) # Starting data x_data, y_data = generate_timeseries(100) # Code goes here fig = plt.figure() lines = plt.plot(x_data, y_data) s1 = IntSlider(description='Steps', min=50, value=100, max=150) b = Button(description='Generate Data') def update_plot(change=None): x_data, y_data = generate_timeseries(s1.value) lines[0].set_data(x_data, y_data) lines[0].axes.set_ylim(min(y_data) - 1, max(y_data) + 1) lines[0].axes.set_xlim(min(x_data) - 1, max(x_data) + 1) fig.canvas.draw() fig.canvas.flush_events() # Setting up an event listener for the slider value s1.observe(update_plot, 'value') # Set up event listener for the button b.on_click(update_plot) # Rendering slider and figure and a vertical box VBox([s1, b, fig.canvas]) ###Output _____no_output_____ ###Markdown ipympl: The Matplotlib Jupyter Widget Backend https://github.com/matplotlib/ipymplEnabling interaction with matplotlib charts in the Jupyter notebook and JupyterLab- BSD-3-Clause**Installation:**```bashconda install -c conda-forge ipympl``` Enabling the `widget` backend. This requires ipympl. ipympl can be install via pip or conda. ###Code %matplotlib widget import numpy as np import matplotlib.pyplot as plt from ipywidgets import VBox, FloatSlider, IntSlider, Button ###Output _____no_output_____ ###Markdown When using the `widget` backend from ipympl, fig.canvas is a proper Jupyter interactive widget, which can be embedded in Layout classes like HBox and Vbox.One can bound figure attributes to other widget values. ###Code # Creating a new figure (1) fig = plt.figure() # Simple plot x = np.linspace(0,5,11) y = x ** 3 plt.plot(x,y, '-m'); ###Output _____no_output_____ ###Markdown Change the window title ###Code fig.canvas.set_window_title('My interactive widget-enabled plot') ###Output _____no_output_____ ###Markdown Remove toolbar, header and footer from the plot window ###Code fig.canvas.toolbar_visible = False fig.canvas.header_visible = False fig.canvas.footer_visible = False ###Output _____no_output_____ ###Markdown Disable canvas resizing ###Code fig.canvas.resizable = False ###Output _____no_output_____ ###Markdown Adding widget controls to our figure ###Code # Disabling internal matplotlib intaractive mode off (we use our own backend) plt.ioff() # Creating a simple slider widget slider = FloatSlider( value=1.0, min=0.02, max=2.0 ) # New figure object fig = plt.figure() plt.title('Plotting: y=sin({} * x)'.format(slider.value)) # 500 even-spaced data points on the x-axis between 0 and 20. x1 = np.linspace(0, 20, 500) # Applying and plotting the sin function for each data point lines = plt.plot(x1, np.sin(slider.value * x1)) # Callback function when our slider changes in value def update_lines(change): lines[0].set_data(x1, np.sin(change.new * x1)) fig.canvas.draw() fig.canvas.flush_events() plt.title('Plotting: y=sin({} * x)'.format(slider.value)) # Setting up an event listener for the slider value slider.observe(update_lines, names='value') # Render the slider and figure in a vertical box VBox([slider, fig.canvas]) ###Output _____no_output_____ ###Markdown 3D plots ###Code from mpl_toolkits.mplot3d import axes3d # Setting up a new, blank figure object fig = plt.figure() # Adding an axes to the figure ax = fig.add_subplot(111, projection='3d') # Grab some test data. X, Y, Z = axes3d.get_test_data(0.05) # Plot a basic wireframe. ax.plot_surface(X, Y, Z, rstride=10, cstride=10) # Display the plot fig.canvas ###Output _____no_output_____ ###Markdown Subplots ###Code # Static sample data np.random.seed(0) # Number of bins for the histogram n_bins = 10 x2 = np.random.randn(1000, 3) # a two-by-two plot grid (4 plots) fig3, axes = plt.subplots(nrows=2, ncols=2) ax0, ax1, ax2, ax3 = axes.flatten() # Setting up the colors and generating the top-left histogram colors = ['red', 'tan', 'lime'] ax0.hist(x2, n_bins, density=1, histtype='bar', color=colors, label=colors) ax0.legend(prop={'size': 10}) ax0.set_title('bars with legend') # Setting up the stacked bar ax1.hist(x2, n_bins, density=1, histtype='bar', stacked=True) ax1.set_title('stacked bar') # Setting up the bottom-left histogram ax2.hist(x2, n_bins, histtype='step', stacked=True, fill=False) ax2.set_title('stack step (unfilled)') # Make a multiple-histogram of data-sets with different length (bottom-right) x_multi = [np.random.randn(n) for n in [10000, 5000, 2000]] ax3.hist(x_multi, n_bins, histtype='bar') ax3.set_title('different sample sizes') # Display the plot fig3.tight_layout() fig3.canvas fig3.canvas.toolbar_position = 'right' fig3.canvas.toolbar_visible = False ###Output _____no_output_____ ###Markdown Exercise **This is a slightly challenging exercise!**Create a small app which generates and displays a simulation of a stock price (you can use the helper function) and has the following widgets:1. An interactive ipympl canvas with the toolbar on the left hand side2. A slider which selects the number of steps per simulation3. A button to ghenerate new data and update the plotThe plot should update whenever there is a change to the slider value, or the button is clicked. ###Code # Helper function def generate_timeseries(steps): return (np.arange(1,steps + 1,1), 100 + np.random.normal(0,1,steps).cumsum()) # Starting data x_data, y_data = generate_timeseries(100) # Code goes here fig = plt.figure() lines = plt.plot(x_data, y_data) s1 = IntSlider(description='Steps', min=50, value=100, max=150) b = Button(description='Generate Data') def update_plot(change=None): x_data, y_data = generate_timeseries(s1.value) lines[0].set_data(x_data, y_data) lines[0].axes.set_ylim(min(y_data) - 1, max(y_data) + 1) lines[0].axes.set_xlim(min(x_data) - 1, max(x_data) + 1) fig.canvas.draw() fig.canvas.flush_events() # Setting up an event listener for the slider value s1.observe(update_plot, 'value') # Set up event listener for the button b.on_click(update_plot) # Rendering slider and figure and a vertical box VBox([s1, b, fig.canvas]) ###Output _____no_output_____

docs/bokeh/bokeh-server.ipynb

###Markdown Bokeh-ServerDie Architektur von Bokeh ist so, dass übergeordnete *Modellobjekte*, also Darstellungen wie Plots, Bereiche, Achsen, Glyphen usw.) in Python erstellt und dann in ein JSON-Format konvertiert werden, das von der Client-Bibliothek `BokehJS` verwendet wird. Mit Hilfe des Bokeh-Servers können die *Modellobjekte* in Python und im Browser miteinander synchronisiert werden, wodurch mächtige Funktionen geschaffen werden:* Browser-Events führen zu serverseitigen Python-Berechnungen oder -Abfragen* Automatische Push-Aktualisierung des Browser-UI (z.B. Widgets oder Plots)* Periodische, Timeout- und asynchronen Callbacks für Streaming-UpdatesDiese Funktion zur Synchronisierung zwischen serverseitigem Python und dem Browser ist der Hauptzweck des Bokeh-Servers.Es ist auch möglich, Bokeh-Anwendungen zu definieren, indem ein Standard-Python-Skript erstellt wird. In diesem Fall ist es nicht erforderlich, eine Funktion wie `modify_doc` zu erstellen. Normalerweise erstellt das Skript einfach alle Bokeh-Kontingente und fügt es mit einer Zeile dem Dokument hinzu:```curdoc().add_root(layout)```Um das Beispiel unten auszuprobieren, kopiert den Code in eine Datei `hello.py` und führt dann Folgendes aus:```pipenv run bokeh serve --show hello.py``` ###Code from bokeh.io import curdoc from bokeh.layouts import column from bokeh.models.widgets import TextInput, Button, Paragraph # create some widgets button = Button(label="Say Hi") input = TextInput(value="Pythonistas") output = Paragraph() # add a callback to a widget def update(): output.text = "Hello, " + input.value + "!" button.on_click(update) # create a layout for everything layout = column(button, input, output) # add the layout to curdoc curdoc().add_root(layout) ###Output _____no_output_____

2-Data-Analysis/1-Numpy/2-Numpy Array Indexing.ipynb

###Markdown NumPy Indexing und SelectionIn dieser Lektion werden wir diskutieren, wie man Elemente oder Gruppen von Elementen aus einem Array auswählt. ###Code import numpy as np # Ein Beispielarray erstellen arr = np.arange(0,11) # Anzeigen arr ###Output _____no_output_____ ###Markdown Indexing und Selection mit KlammernDer einfachste Weg um ein oder mehrere Element(e) aus einem Array auszuwählen sieht dem bei einer Liste sehr ähnlich: ###Code # Wert mit seinem Index erhalten arr[8] # Erhalte die Werte in einem Bereich arr[1:5] # Erhalte die Werte in einem Bereich arr[0:5] ###Output _____no_output_____ ###Markdown BroadcastingNumPy Arrays unterscheiden sich von normalen Python Listen durch ihre Fähigkeit des [Broadcasting](https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html). ###Code # Einen Wert durch einen Index-Bereich festlegen (Broadcasting) arr[0:5]=100 # Anzeigen arr # Das Array zurücksetzen. Warum das nötig ist sehen wir gleich arr = np.arange(0,11) # Anzeigen arr # Ein Stück des Arrays wählen stueck_des_arr = arr[0:6] # Anzeigen stueck_des_arr # Das Stück bearbeiten stueck_des_arr[:]=99 # Das Stück erneut anzeigen stueck_des_arr ###Output _____no_output_____ ###Markdown Achtet darauf, wie diese Änderung auch im originalen Array auftaucht! ###Code arr ###Output _____no_output_____ ###Markdown Die Daten wurden hier nicht kopiert. Das erzeugte Teilstück ist eine Betrachtung des originalen Arrays. Das vermeidet Speicherprobleme. ###Code # Um eine Kopie zu erzeugen, müssen wir das explizit anweisen arr_kopie = arr.copy() arr_kopie ###Output _____no_output_____ ###Markdown Indexing in 2D Arrays (Matrizen)Das allgemeine Format ist arr_2d[row][col] oder arr_2d[row,col]. Ich empfehle normalerweise die Komma-Notation für mehr Klarheit. ###Code arr_2d = np.array(([5,10,15],[20,25,30],[35,40,45])) # Anzeigen arr_2d # Die Reihe indexieren arr_2d[1] # Das Format ist arr_2d[row][col] oder arr_2d[row,col] # Einzelne Elemente auswählen arr_2d[1][0] # Einzelne Elemente auswählen arr_2d[1,0] # 2D Array Stücke auswählen # Form (2,2) von oben rechts arr_2d[:2,1:] # Form untere Reihe arr_2d[2] # Form untere Reihe arr_2d[2,:] ###Output _____no_output_____ ###Markdown Raffiniertes IndexingRaffiniertes Indexing erlaubt es uns ganze Reihen oder Spalten entgegen ihrer Reihenfolge zu wählen. Um das zu verdeutlichen erstellen wir zunächst ein NumPy Array: ###Code # Eine Matrix erstellen arr2d = np.zeros((10,10)) # Länge des Array arr_laenge = arr2d.shape[1] # Das Array erstellen for i in range(arr_laenge): arr2d[i] = i arr2d ###Output _____no_output_____ ###Markdown Raffiniertes Indexing erlaubt uns nun folgendes: ###Code arr2d[[2,4,6,8]] # Und das in jeder Reihenfolge arr2d[[6,4,8,2]] ###Output _____no_output_____ ###Markdown Mehr Hilfe beim IndexingIndexing in einer 2D Matrix kann anfangs etwas verwirrend sein. Bei Google Bilder findet man nützliche Bilder, die einem dabei helfen. Bspw. das folgende: SelectionLass uns jetzt noch kurz anschauen, wie wir Klammern nutzen können, um eine Selection basieren auf Vergleichsoperatoren durchzuführen. ###Code arr = np.arange(1,11) arr arr > 4 bool_arr = arr>4 bool_arr arr[bool_arr] arr[arr>2] x=2 arr[arr>x] ###Output _____no_output_____

queue_imbalance/svm/svm_rbf.ipynb

###Markdown SVM with rbf kernelThe goal of this notebook is to find the best parameters for polynomial kernel. We also want to check if the parameters depend on stock.We will use [sklearn.svm](http://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.htmlsklearn.svm.SVC) library to perform calculations. We want to pick the best parameters for **SVC**:* C (default 1.0)* gamma (default 1/number_of_features, so 1 in our case)Kernel function looks like this: $\exp(-\gamma \|x-x'\|^2)$. $\gamma$ is specified by keyword **gamma**, must be greater than 0. ###Code %matplotlib inline import pandas as pd import matplotlib.pyplot as plt import matplotlib.dates as md from statsmodels.distributions.empirical_distribution import ECDF import numpy as np import seaborn as sns from sklearn.metrics import roc_auc_score from sklearn.metrics import roc_curve from sklearn.metrics import classification_report from sklearn import svm import warnings from lob_data_utils import lob sns.set_style('whitegrid') warnings.filterwarnings('ignore') ###Output _____no_output_____ ###Markdown DataWe use data from 5 stocks (from dates 2013-09-01 - 2013-11-16) for which logistic regression yielded the best results.We selected 3 subsets for each stock:* training set (60% of data)* test set (20% of data)* cross-validation set (20% of data) ###Code stocks = ['10795', '12098', '11618', '1243', '11234'] dfs = {} dfs_cv = {} dfs_test = {} for s in stocks: df, df_cv, df_test = lob.load_prepared_data(s, cv=True) dfs[s] = df dfs_cv[s] = df_cv dfs_test[s] = df_test dfs[stocks[0]].head(5) def svm_classification(d, kernel, gamma='auto', C=1.0): clf = svm.SVC(kernel=kernel, gamma=gamma, C=C) X = d['queue_imbalance'].values.reshape(-1, 1) y = d['mid_price_indicator'].values.reshape(-1, 1) clf.fit(X, y) return clf ###Output _____no_output_____ ###Markdown MethodologyWe will use at first naive approach to grasp how each of the parameter influences the ROC area score and what values make sense, when the other parameters are set to defaults.After that we will try to get the best combination of the parameters. C parameterThe C parameter has influence over margin picked by SVM:* for large values of **C** SVM will choose a smaller-margin hyperplane, which means that more data points will be classified correctly* for small values of **C** SVM will choose a bigger-margin hyperplane, so there may be more misclassificationsAt first we tried parameters: [0.0001, 0.001, 0.01, 0.1, 1, 10, 1000], but after first calculations it seems that it wasn't enough, so a few more values were introduced or removed. ###Code cs = [0.08, 0.09, 0.1, 0.12, 1, 1.25, 1.9, 2, 6.4, 6.5, 6.6, 7, 7.1, 107, 108, 108.5] # 0.06, 0.07 # 6.3, 6.7 # 7.2, 7.5, 8, 9 # 109, 110, 111 df_css = {} ax = plt.subplot() ax.set_xscale("log", basex=10) for s in stocks: df_cs = pd.DataFrame(index=cs) df_cs['roc'] = np.zeros(len(df_cs)) for c in cs: reg_svm = svm_classification(dfs[s], 'rbf', C=c) prediction = reg_svm.predict(dfs_cv[s]['queue_imbalance'].values.reshape(-1, 1)) score = roc_auc_score(dfs_cv[s]['mid_price_indicator'], prediction) df_cs.loc[c] = score plt.plot(df_cs, linestyle='--', label=s, marker='x', alpha=0.5) df_css[s] = df_cs plt.legend() ###Output _____no_output_____ ###Markdown Best values of C parameterThere is no rule, how to set this parameter. ###Code for s in stocks: idx = df_css[s]['roc'].idxmax() print('For {} the best is {}'.format(s, idx)) ###Output For 10795 the best is 0.09 For 12098 the best is 107.0 For 11618 the best is 7.0 For 1243 the best is 0.1 For 11234 the best is 6.4 ###Markdown Influence of C parameterThe score difference between SVM with the worst choice of parameter **C** and the best choice one is shown on the output below. For scoring method we used *roc_area*. ###Code for s in stocks: err_max = df_css[s]['roc'].max() err_min = df_css[s]['roc'].min() print('For {} the diff between best and worst {}'.format(s, err_max - err_min)) ###Output For 10795 the diff between best and worst 0.004800787014264674 For 12098 the diff between best and worst 0.004854368932038833 For 11618 the diff between best and worst 0.0021372549019607057 For 1243 the diff between best and worst 0.005039215686274523 For 11234 the diff between best and worst 0.003030303030302939 ###Markdown GammaGamma is a parameter which has influence over decision region - the bigger it is, the bigger influence every single row of data has. When gamma is low the decision region is very broad. When gamma is high it can even create islands of decision-boundaries around data points. ###Code gammas = [0.0008, 0.001, 0.09, 0.15, 0.2, 0.3, 0.4, 0.45, 0.5, 0.6, 100.5, 101, 101.5] # 0.1 # 102 # 1, 10, 99 df_gammas = {} ax = plt.subplot() ax.set_xscale("log", basex=10) for s in stocks: df_gamma = pd.DataFrame(index=gammas) df_gamma['roc'] = np.zeros(len(df_gamma)) for g in gammas: reg_svm = svm_classification(dfs[s], 'rbf', gamma=g) pred_svm_out_of_sample = reg_svm.predict(dfs_cv[s]['queue_imbalance'].values.reshape(-1, 1)) logit_roc_auc = roc_auc_score(dfs_cv[s]['mid_price_indicator'], pred_svm_out_of_sample) df_gamma.loc[g] = logit_roc_auc plt.plot(df_gamma, linestyle='--', label=s, marker='x', alpha=0.7) df_gammas[s] = df_gamma plt.legend() ###Output _____no_output_____ ###Markdown Best values of gammaThere is no rule, how to set this parameter. ###Code for s in stocks: idx = df_gammas[s]['roc'].idxmax() print('For {} the best is {}'.format(s, idx)) ###Output For 10795 the best is 100.5 For 12098 the best is 0.3 For 11618 the best is 0.2 For 1243 the best is 0.5 For 11234 the best is 0.5 ###Markdown Influence of gammaThe score difference between SVM with the worst choice of **gamma** and the best choice one is shown on the output below. For scoring method we used *roc_area*. For all stocks the error difference is small - less than 0.04. ###Code for s in stocks: err_max = df_gammas[s]['roc'].max() err_min = df_gammas[s]['roc'].min() print('For {} the diff between best and worst {}'.format(s, err_max - err_min)) ###Output For 10795 the diff between best and worst 0.11365469749139212 For 12098 the diff between best and worst 0.03974698440717861 For 11618 the diff between best and worst 0.027764705882352914 For 1243 the diff between best and worst 0.033627450980392215 For 11234 the diff between best and worst 0.09537118760419727 ###Markdown ResultsWe compare results of the SVMs with the best choices of parameters against the logistic regression and SVM with defaults.We will use two approaches for choosing parameters:* naive - for each stock we will just pick the best values we found in the previous section* grid - we will caluclate roc_area error for every combination of parameters used in previous section (computionally heavy).We could also use GridSearchCV from sklearn library, but the issue with it is supplying the cross-validation set (it has to be continous in time). In the future we need to implement the method for that. Naive approachWe pick the best **C** parameter and the best **gamma** separately from the results of [section above](Methodology), which were obtained using cross-validation set. ###Code df_results = pd.DataFrame(index=stocks) df_results['logistic'] = np.zeros(len(stocks)) df_results['rbf-naive'] = np.zeros(len(stocks)) df_results['gamma-naive'] = np.zeros(len(stocks)) df_results['c-naive'] = np.zeros(len(stocks)) df_results['rbf-default'] = np.zeros(len(stocks)) plt.subplot(121) for s in stocks: reg_svm = svm_classification(dfs[s], 'rbf', C=df_css[s]['roc'].idxmax(), gamma=df_gammas[s]['roc'].idxmax()) roc_score = lob.plot_roc(df_test, reg_svm, stock=s, title='ROC for test set with the naive') df_results['rbf-naive'][s] = roc_score df_results['gamma-naive'][s] = df_gammas[s]['roc'].idxmax() df_results['c-naive'][s] = df_css[s]['roc'].idxmax() colors = ['b', 'g', 'r', 'c', 'm', 'y', 'k', 'w'] plt.subplot(122) for s in stocks: reg_svm = svm_classification(dfs[s], 'rbf') roc_score = lob.plot_roc(df_test, reg_svm, stock=s, title='ROC for test set with the defaults') df_results['rbf-default'][s] = roc_score reg_log = lob.logistic_regression(dfs[s], 0, len(dfs[s])) roc_score = lob.plot_roc(df_test, reg_log, stock=s, title='ROC for test set with logistic', c=colors[stocks.index(s)], linestyle='--') df_results['logistic'][s] = roc_score plt.subplots_adjust(left=0, wspace=0.1, top=1, right=2) df_results ###Output _____no_output_____ ###Markdown Grid approachWe iterate over all combinations of parameters **C** and **gamma**.This approach works usually better, but not for all cases. ###Code df_params = {} for s in stocks: print(s) params = [] for c in cs: for g in gammas: reg_svm = svm_classification(dfs[s], 'rbf', C=c, gamma=g) prediction = reg_svm.predict(dfs_cv[s]['queue_imbalance'].values.reshape(-1, 1)) score = roc_auc_score(dfs_cv[s]['mid_price_indicator'], prediction) params.append({'score': score, 'gamma': g, 'c': c}) df_params[s] = pd.DataFrame(params) for s in stocks: df_g = df_params[s].pivot(index='c', columns='gamma', values='score') sns.heatmap(df_g) plt.title('Best params for ' + s) plt.figure() ###Output _____no_output_____ ###Markdown Best parameters for grid approach ###Code for s in stocks: print(s, df_params[s].iloc[df_params[s]['score'].idxmax()]) df_results['rbf-grid'] = np.zeros(len(stocks)) df_results['c-grid'] = np.zeros(len(stocks)) df_results['gamma-grid'] = np.zeros(len(stocks)) plt.subplot(121) for s in stocks: best_idx = df_params[s]['score'].idxmax() reg_svm = svm_classification(dfs[s], 'rbf', C=df_params[s].iloc[best_idx]['c'], gamma=df_params[s].iloc[best_idx]['gamma']) roc_score = lob.plot_roc(df_test, reg_svm, stock=s, title='ROC for test set with the best params') df_results['rbf-grid'][s] = roc_score df_results['gamma-grid'][s] = df_params[s].iloc[best_idx]['gamma'] df_results['c-grid'][s] = df_params[s].iloc[best_idx]['c'] plt.subplot(122) for s in stocks: reg_svm = svm_classification(dfs[s], 'rbf') prediction = reg_svm.predict(dfs_test[s]['queue_imbalance'].values.reshape(-1, 1)) roc_score = lob.plot_roc(df_test, reg_svm, stock=s, title='ROC for test set with defaults') df_results['rbf-default'][s] = roc_score plt.subplots_adjust(left=0, wspace=0.1, top=1, right=2) plt.subplot(121) for s in stocks: best_idx = df_params[s]['score'].idxmax() reg_svm = svm_classification(dfs[s], 'rbf', C=df_params[s].iloc[best_idx]['c'], gamma=df_params[s].iloc[best_idx]['gamma']) roc_score = lob.plot_roc(df_test, reg_svm, stock=s, title='ROC for test set with the best params') df_results['rbf-grid'][s] = roc_score plt.subplot(122) for s in stocks: reg_log = lob.logistic_regression(dfs[s], 0, len(dfs[s])) roc_score = lob.plot_roc(df_test, reg_log, stock=s, title='ROC for test set with the best params') df_results['logistic'][s] = roc_score plt.subplots_adjust(left=0, wspace=0.1, top=1, right=2) df_results[['logistic', 'rbf-naive', 'rbf-default', 'rbf-grid']] df_results ###Output _____no_output_____

content/ch-algorithms/quantum-fourier-transform.ipynb

###Markdown Quantum Fourier Transform In this tutorial, we introduce the quantum fourier transform (QFT), derive the circuit, and implement it using Qiskit. We show how to run QFT on a simulator and a five qubit device. Contents1. [Introduction](introduction)2. [Example 1: 1-qubit QFT](example1)3. [The Quantum Fourier transform](qfteqn)4. [The circuit that implements QFT](circuit)5. [Example 2: 3-qubit QFT](example1)6. [A note about the form of the QFT circuit](formnote)7. [Qiskit Implementation](implementation) - [Running QFT on a simulator](implementationsim) - [Running QFT on a real quantum device](implementationdev)8. [Problems](problems)9. [References](references) 1. Introduction The Fourier transform occurs in many different versions throughout classical computing, in areas ranging from signal processing to data compression to complexity theory. The quantum Fourier transform (QFT) is the quantum implementation of the discrete Fourier transform over the amplitudes of a wavefunction. It is part of many quantum algorithms, most notably Shor's factoring algorithm and quantum phase estimation. The discrete Fourier transform acts on a vector $(x_0, ..., x_{N-1})$ and maps it to the vector $(y_0, ..., y_{N-1})$ according to the formula$$y_k = \frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}x_j\omega_N^{jk}$$where $\omega_N^{jk} = e^{2\pi i \frac{jk}{N}}$.Similarly, the quantum Fourier transform acts on a quantum state $\sum_{i=0}^{N-1} x_i \vert i \rangle$ and maps it to the quantum state $\sum_{i=0}^{N-1} y_i \vert i \rangle$ according to the formula$$y_k = \frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}x_j\omega_N^{jk}$$with $\omega_N^{jk}$ defined as above. Note that only the amplitudes of the state were affected by this transformation.This can also be expressed as the map:$$\vert x \rangle \mapsto \frac{1}{\sqrt{N}}\sum_{y=0}^{N-1}\omega_N^{xy} \vert y \rangle$$Or the unitary matrix:$$ U_{QFT} = \frac{1}{\sqrt{N}} \sum_{x=0}^{N-1} \sum_{y=0}^{N-1} \omega_N^{xy} \vert y \rangle \langle x \vert$$ 2. Example 1: 1-qubit QFT Consider how the QFT operator as defined above acts on a single qubit state $\vert\psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle$. In this case, $x_0 = \alpha$, $x_1 = \beta$, and $N = 2$. Then,$$y_0 = \frac{1}{\sqrt{2}}\left( \alpha \exp\left(2\pi i\frac{0\times0}{2}\right) + \beta \exp\left(2\pi i\frac{1\times0}{2}\right) \right) = \frac{1}{\sqrt{2}}\left(\alpha + \beta\right)$$and$$y_1 = \frac{1}{\sqrt{2}}\left( \alpha \exp\left(2\pi i\frac{0\times1}{2}\right) + \beta \exp\left(2\pi i\frac{1\times1}{2}\right) \right) = \frac{1}{\sqrt{2}}\left(\alpha - \beta\right)$$such that the final result is the state $$U_{QFT}\vert\psi\rangle = \frac{1}{\sqrt{2}}(\alpha + \beta) \vert 0 \rangle + \frac{1}{\sqrt{2}}(\alpha - \beta) \vert 1 \rangle$$This operation is exactly the result of applying the Hadamard operator ($H$) on the qubit:$$H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$$If we apply the $H$ operator to the state $\vert\psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle$, we obtain the new state:$$\frac{1}{\sqrt{2}}(\alpha + \beta) \vert 0 \rangle + \frac{1}{\sqrt{2}}(\alpha - \beta) \vert 1 \rangle \equiv \tilde{\alpha}\vert 0 \rangle + \tilde{\beta}\vert 1 \rangle$$Notice how the Hadamard gate performs the discrete Fourier transform for $N = 2$ on the amplitudes of the state. 3. The Quantum Fourier transform So what does the quantum Fourier transform look like for larger $N$? Let's derive a circuit for $N=2^n$, $QFT_N$ acting on the state $\vert x \rangle = \vert x_1\ldots x_n \rangle$ where $x_1$ is the most significant bit.\begin{aligned}QFT_N\vert x \rangle & = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1}\omega_N^{xy} \vert y \rangle \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} e^{2 \pi i xy / 2^n} \vert y \rangle ~\text{since}\: \omega_N^{xy} = e^{2\pi i \frac{xy}{N}} \:\text{and}\: N = 2^n \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} e^{2 \pi i \left(\sum_{k=1}^n y_k/2^k\right) x} \vert y_1 \ldots y_n \rangle \:\text{rewriting in fractional binary notation}\: y = y_1\ldots y_n, y/2^n = \sum_{k=1}^n y_k/2^k \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} \prod_{k=1}^n e^{2 \pi i x y_k/2^k } \vert y_1 \ldots y_n \rangle \:\text{after expanding the exponential of a sum to a product of exponentials} \\& = \frac{1}{\sqrt{N}} \bigotimes_{k=1}^n \left(\vert0\rangle + e^{2 \pi i x /2^k } \vert1\rangle \right) \:\text{after rearranging the sum and products, and expanding} \sum_{y=0}^{N-1} = \sum_{y_1=0}^{1}\sum_{y_2=0}^{1}\ldots\sum_{y_n=0}^{1} \\& = \frac{1}{\sqrt{N}}\left(\vert0\rangle + e^{\frac{2\pi i}{2}x} \vert1\rangle\right) \otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^2}x} \vert1\rangle\right) \otimes \ldots\otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^{n-1}}x} \vert1\rangle\right) \otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^n}x} \vert1\rangle\right) \end{aligned} 4. The circuit that implements QFT The circuit that implements QFT makes use of two gates. The first one is a single-qubit Hadamard gate, $H$, that you already know. From the discussion in [Example 1](example1) above, you have already seen that the action of $H$ on the single-qubit state $\vert x_k\rangle$ is$$H\vert x_k \rangle = \vert0\rangle + \exp\left(\frac{2\pi i}{2}x_k\right)\vert1\rangle$$The second is a two-qubit controlled rotation $CROT_k$ given in block-diagonal form as $$CROT_k = \left[\begin{matrix}I&0\\0&UROT_k\\\end{matrix}\right]$$where $$UROT_k = \left[\begin{matrix}1&0\\0&\exp\left(\frac{2\pi i}{2^k}\right)\\\end{matrix}\right]$$The action of $CROT_k$ on the two-qubit state $\vert x_jx_k\rangle$ where the first qubit is the control and the second is the target is given by$$CROT_k\vert x_j0\rangle = \vert x_j0\rangle$$and$$CROT_k\vert x_j1\rangle = \exp\left( \frac{2\pi i}{2^k}x_j \right)\vert x_j1\rangle$$Given these two gates, a circuit that implements [an n-qubit QFT](qfteqn) is shown below.The circuit operates as follows. We start with an n-qubit input state $\vert x_1x_2\ldots x_n\rangle$. After the first Hadamard gate on qubit 1, the state is transformed from the input state to $$H_1\vert x_1x_2\ldots x_n\rangle = \frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the $CROT_2$ gate on qubit 1 controlled by qubit 2, the state is transformed to$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the application of the last $CROT_n$ gate on qubit 1 controlled by qubit $n$, the state becomes$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x_n + \frac{2\pi i}{2^{n-1}}x_{n-1} + \ldots + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$Noting that $$x = 2^{n-1}x_1 + 2^{n-2}x_2 + \ldots + 2^1x_{n-1} + 2^0x_n$$we can write the above state as $$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x \right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the application of a similar sequence of gates for qubits $2\ldots n$, we find the final state to be$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x \right)\vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{n-1}}x \right)\vert1\rangle\right]\otimes\ldots\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{2}}x \right)\vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{1}}x \right)\vert1\rangle\right]$$which is exactly the QFT of the input state as derived above with the caveat that the order of the qubits is reversed in the output state. 5. Example 2: 3-qubit QFT The steps to creating the circuit for $\vert y_1y_2y_3\rangle = QFT_8\vert x_1x_2x_3\rangle$ would be: Apply a Hadamard gate to $\vert x_3 \rangle$$$\psi_1 = \vert x_1\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a $CROT_2$ gate to $\vert x_3\rangle$ depending on $\vert x_2\rangle$$$\psi_2 = \vert x_1\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a $CROT_3$ gate to $\vert x_3\rangle$ depending on $\vert x_1\rangle$$$\psi_3 = \vert x_1\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a Hadamard gate to $\vert x_2 \rangle$$$\psi_4 = \vert x_1\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a $CROT_2$ gate to $\vert x_2\rangle$ depending on $\vert x_1\rangle$$$\psi_5 = \vert x_1\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_1 + \frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a Hadamard gate to $\vert x_1\rangle$$$\psi_6 = \frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_1\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_1 + \frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Keep in mind the reverse order of the output state relative to the desired QFT. Therefore, measure the bits in reverse order, that is $y_3 = x_1, y_2 = x_2, y_1 = x_3$. 6. A note about the form of the QFT circuit The example above demonstrates a very useful form of the QFT for $N=2^n$. Note that only the last qubit depends on the values of all the other input qubits and each further bit depends less and less on the input qubits. This becomes important in physical implementations of the QFT, where nearest-neighbor couplings are easier to achieve than distant couplings between qubits. 7. Qiskit ImplementationIn Qiskit, the implementation of the $CROT$ gate used in the discussion above is a controlled phase rotation gate. This gate is defined in [OpenQASM](https://github.com/QISKit/openqasm) as$$CU_1(\theta) =\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\theta}\end{bmatrix}$$Hence, the mapping from the $CROT_k$ gate in the discussion above into the $CU_1$ gate is found from the equation$$\theta = 2\pi/2^k = \pi/2^{k-1}$$It is instructive to write out the relevant code for the 3-qubit case before generalizing to the $n$-qubit case. In Qiskit, it is:```qft3 = QuantumCircuit(3, 3)qft3.h(0)qft3.cu1(math.pi/2.0, 1, 0) CROT_2 from qubit 1 to qubit 0qft3.cu1(math.pi/4.0, 2, 0) CROT_3 from qubit 2 to qubit 0qft3.h(q[1])qft3.cu1(math.pi/2.0, 2, 1) CROT_2 from qubit 2 to qubit 1qft3.h(2)```Following the above example, the case for $n$ qubits can be generalized as:```def qft(circ, n): """n-qubit QFT on the qubits in circ.""" for j in range(n): circ.h(j) for k in range(j+1,n): circ.cu1(math.pi/float(2**(k-j)), k, j)``` We will now implement the three-qubit QFT as discussed above. We first create a state whose QFT is known. The output after a QFT is applied to this special state is $\vert001\rangle$. ###Code import numpy as np pi = np.pi # importing Qiskit from qiskit import BasicAer, IBMQ from qiskit import QuantumCircuit, execute from qiskit.providers.ibmq import least_busy from qiskit.tools.monitor import job_monitor from qiskit.visualization import plot_histogram ###Output _____no_output_____ ###Markdown First let's define the QFT function, as well as a function that creates a state from which a QFT will return 001: ###Code def input_state(circ, n): """special n-qubit input state for QFT that produces output 1.""" for j in range(n): circ.h(j) circ.u1(-pi/float(2**(j)), j) def qft(circ, n): """n-qubit QFT on the qubits in circ.""" for j in range(n): circ.h(j) for k in range(j+1,n): circ.cu1(pi/float(2**(k-j)), k, j) circ.barrier() swap_registers(circ, n) def swap_registers(circ, n): for j in range(int(np.floor(n/2.))): circ.swap(j, n-j-1) return circ ###Output _____no_output_____ ###Markdown Let's now implement a QFT on a prepared three qubit input state that should return $001$: ###Code n = 3 qft_circuit = QuantumCircuit(n) # first, prepare the state that should return 001 and draw that circuit input_state(qft_circuit, n) qft_circuit.draw(output='mpl') # next, do a qft on the prepared state and draw the entire circuit qft_circuit.barrier() qft(qft_circuit, n) qft_circuit.measure_all() qft_circuit.draw(output='mpl') ###Output _____no_output_____ ###Markdown 7a. Running QFT on a simulator ###Code # run on local simulator backend = BasicAer.get_backend("qasm_simulator") simulate = execute(qft_circuit, backend=backend, shots=1024).result() simulate.get_counts() ###Output _____no_output_____ ###Markdown We indeed see that the outcome is always $001$ when we execute the code on the simulator. Note the reversed order of the output value $100$ compared to the expected value $001$. We expected this as well, since the output register contains the reversed QFT values. 7b. Running QFT on a real quantum device We then see how the same circuit can be executed on real-device backends. ###Code # Load our saved IBMQ accounts and get the least busy backend device with less than or equal to n qubits IBMQ.load_account() provider = IBMQ.get_provider(hub='ibm-q') backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= n and not x.configuration().simulator and x.status().operational==True)) print("least busy backend: ", backend) shots = 2048 job_exp = execute(qft_circuit, backend=backend, shots=shots) job_monitor(job_exp) results = job_exp.result() plot_histogram(results.get_counts()) ###Output _____no_output_____ ###Markdown We see that the highest probability outcome is still $100$ on a real device. Recall again that the output of the QFT circuit has the qubits in reverse order. 8. Problems 1. The [above implementation](implementation) of QFT was tested by using a special input state for which QFT(input state) = 001. Implement an input state for which QFT(input state) = 100.2. The [above implementation](implementation) of QFT was tested by using a special input state for which QFT(input state) = 001. Implement an input state for which QFT(input state) = 101. 9. References 1. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences (Cambridge University Press, Cambridge, 2000). ###Code import qiskit qiskit.__qiskit_version__ ###Output _____no_output_____ ###Markdown Quantum Fourier Transform In this tutorial, we introduce the quantum fourier transform (QFT), derive the circuit, and implement it using Qiskit. We show how to run QFT on a simulator and a five qubit device. Contents1. [Introduction](introduction)2. [Intuition](intuition) 2.1 [Counting in the Fourier Basis](counting-fourier) 3. [Example 1: 1-qubit QFT](example1)4. [The Quantum Fourier transform](qfteqn)5. [The Circuit that Implements the QFT](circuit)6. [Example 2: 3-qubit QFT](example2)7. [Some Notes About the Form of the QFT Circuit](formnote)8. [Qiskit Implementation](implementation) 8.1 [Example on 3 Qubits](threeqft) 8.2 [General QFT Function](generalqft) 8.3 [Running QFT on a Real Quantum Device](implementationdev) 9. [Problems](problems)10. [References](references) 1. Introduction The Fourier transform occurs in many different versions throughout classical computing, in areas ranging from signal processing to data compression to complexity theory. The quantum Fourier transform (QFT) is the quantum implementation of the discrete Fourier transform over the amplitudes of a wavefunction. It is part of many quantum algorithms, most notably Shor's factoring algorithm and quantum phase estimation. The discrete Fourier transform acts on a vector $(x_0, ..., x_{N-1})$ and maps it to the vector $(y_0, ..., y_{N-1})$ according to the formula$$y_k = \frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}x_j\omega_N^{jk}$$where $\omega_N^{jk} = e^{2\pi i \frac{jk}{N}}$.Similarly, the quantum Fourier transform acts on a quantum state $\vert X\rangle = \sum_{j=0}^{N-1} x_j \vert j \rangle$ and maps it to the quantum state $\vert Y\rangle = \sum_{k=0}^{N-1} y_k \vert k \rangle$ according to the formula$$y_k = \frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}x_j\omega_N^{jk}$$with $\omega_N^{jk}$ defined as above. Note that only the amplitudes of the state were affected by this transformation.This can also be expressed as the map:$$\vert j \rangle \mapsto \frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}\omega_N^{jk} \vert k \rangle$$Or the unitary matrix:$$ U_{QFT} = \frac{1}{\sqrt{N}} \sum_{j=0}^{N-1} \sum_{k=0}^{N-1} \omega_N^{jk} \vert k \rangle \langle j \vert$$ 2. Intuition The quantum Fourier transform (QFT) transforms between two bases, the computational (Z) basis, and the Fourier basis. The H-gate is the single-qubit QFT, and it transforms between the Z-basis states $|0\rangle$ and $|1\rangle$ to the X-basis states $|{+}\rangle$ and $|{-}\rangle$. In the same way, all multi-qubit states in the computational basis have corresponding states in the Fourier basis. The QFT is simply the function that transforms between these bases.$$|\text{State in Computational Basis}\rangle \quad \xrightarrow[]{\text{QFT}} \quad |\text{State in Fourier Basis}\rangle$$$$\text{QFT}|x\rangle = |\widetilde{x}\rangle$$(We often note states in the Fourier basis using the tilde (~)). 2.1 Counting in the Fourier basis: In the computational basis, we store numbers in binary using the states $|0\rangle$ and $|1\rangle$:Note the frequency with which the different qubits change; the leftmost qubit flips with every increment in the number, the next with every 2 increments, the third with every 4 increments, and so on. In the Fourier basis, we store numbers using different rotations around the Z-axis:The number we want to store dictates the angle at which each qubit is rotated around the Z-axis. In the state $|\widetilde{0}\rangle$, all qubits are in the state $|{+}\rangle$. As seen in the example above, to encode the state $|\widetilde{5}\rangle$ on 4 qubits, we rotated the leftmost qubit by $\tfrac{5}{2^n} = \tfrac{5}{16}$ full turns ($\tfrac{5}{16}\times 2\pi$ radians). The next qubit is turned double this ($\tfrac{10}{16}\times 2\pi$ radians, or $10/16$ full turns), this angle is then doubled for the qubit after, and so on. Again, note the frequency with which each qubit changes. The leftmost qubit (`qubit 0`) in this case has the lowest frequency, and the rightmost the highest. 3. Example 1: 1-qubit QFT Consider how the QFT operator as defined above acts on a single qubit state $\vert\psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle$. In this case, $x_0 = \alpha$, $x_1 = \beta$, and $N = 2$. Then,$$y_0 = \frac{1}{\sqrt{2}}\left( \alpha \exp\left(2\pi i\frac{0\times0}{2}\right) + \beta \exp\left(2\pi i\frac{1\times0}{2}\right) \right) = \frac{1}{\sqrt{2}}\left(\alpha + \beta\right)$$and$$y_1 = \frac{1}{\sqrt{2}}\left( \alpha \exp\left(2\pi i\frac{0\times1}{2}\right) + \beta \exp\left(2\pi i\frac{1\times1}{2}\right) \right) = \frac{1}{\sqrt{2}}\left(\alpha - \beta\right)$$such that the final result is the state $$U_{QFT}\vert\psi\rangle = \frac{1}{\sqrt{2}}(\alpha + \beta) \vert 0 \rangle + \frac{1}{\sqrt{2}}(\alpha - \beta) \vert 1 \rangle$$This operation is exactly the result of applying the Hadamard operator ($H$) on the qubit:$$H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$$If we apply the $H$ operator to the state $\vert\psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle$, we obtain the new state:$$\frac{1}{\sqrt{2}}(\alpha + \beta) \vert 0 \rangle + \frac{1}{\sqrt{2}}(\alpha - \beta) \vert 1 \rangle \equiv \tilde{\alpha}\vert 0 \rangle + \tilde{\beta}\vert 1 \rangle$$Notice how the Hadamard gate performs the discrete Fourier transform for $N = 2$ on the amplitudes of the state. 4. The Quantum Fourier transform So what does the quantum Fourier transform look like for larger $N$? Let's derive a transformation for $N=2^n$, $QFT_N$ acting on the state $\vert x \rangle = \vert x_1\ldots x_n \rangle$ where $x_1$ is the most significant bit. This maths is here for those that find it useful, if you struggle with it then don’t worry; as long as you understand the intuition in section 2 then you can continue straight to the next section.$$\begin{aligned}QFT_N\vert x \rangle & = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1}\omega_N^{xy} \vert y \rangle \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} e^{2 \pi i xy / 2^n} \vert y \rangle ~\text{since}\: \omega_N^{xy} = e^{2\pi i \frac{xy}{N}} \:\text{and}\: N = 2^n \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} e^{2 \pi i \left(\sum_{k=1}^n y_k/2^k\right) x} \vert y_1 \ldots y_n \rangle \:\text{rewriting in fractional binary notation}\: y = y_1\ldots y_n, y/2^n = \sum_{k=1}^n y_k/2^k \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} \prod_{k=1}^n e^{2 \pi i x y_k/2^k } \vert y_1 \ldots y_n \rangle \:\text{after expanding the exponential of a sum to a product of exponentials} \\& = \frac{1}{\sqrt{N}} \bigotimes_{k=1}^n \left(\vert0\rangle + e^{2 \pi i x /2^k } \vert1\rangle \right) \:\text{after rearranging the sum and products, and expanding} \sum_{y=0}^{N-1} = \sum_{y_1=0}^{1}\sum_{y_2=0}^{1}\ldots\sum_{y_n=0}^{1} \\& = \frac{1}{\sqrt{N}}\left(\vert0\rangle + e^{\frac{2\pi i}{2}x} \vert1\rangle\right) \otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^2}x} \vert1\rangle\right) \otimes \ldots\otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^{n-1}}x} \vert1\rangle\right) \otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^n}x} \vert1\rangle\right) \end{aligned}$$This is a mathematical description of the animation we saw in the intuition section: 5. The Circuit that Implements the QFT The circuit that implements QFT makes use of two gates. The first one is a single-qubit Hadamard gate, $H$, that you already know. From the discussion in [Example 1](example1) above, you have already seen that the action of $H$ on the single-qubit state $\vert x_k\rangle$ is$$H\vert x_k \rangle = \frac{1}{\sqrt{2}}\left(\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_k\right)\vert1\rangle\right)$$The second is a two-qubit controlled rotation $CROT_k$ given in block-diagonal form as $$CROT_k = \left[\begin{matrix}I&0\\0&UROT_k\\\end{matrix}\right]$$where $$UROT_k = \left[\begin{matrix}1&0\\0&\exp\left(\frac{2\pi i}{2^k}\right)\\\end{matrix}\right]$$The action of $CROT_k$ on a two-qubit state $\vert x_l x_j\rangle$ where the first qubit is the control and the second is the target is given by$$CROT_k\vert 0x_j\rangle = \vert 0x_j\rangle$$and$$CROT_k\vert 1x_j\rangle = \exp\left( \frac{2\pi i}{2^k}x_j \right)\vert 1x_j\rangle$$Given these two gates, a circuit that implements [an n-qubit QFT](qfteqn) is shown below.The circuit operates as follows. We start with an n-qubit input state $\vert x_1x_2\ldots x_n\rangle$. After the first Hadamard gate on qubit 1, the state is transformed from the input state to $$H_1\vert x_1x_2\ldots x_n\rangle = \frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the $UROT_2$ gate on qubit 1 controlled by qubit 2, the state is transformed to$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the application of the last $UROT_n$ gate on qubit 1 controlled by qubit $n$, the state becomes$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x_n + \frac{2\pi i}{2^{n-1}}x_{n-1} + \ldots + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$Noting that $$x = 2^{n-1}x_1 + 2^{n-2}x_2 + \ldots + 2^1x_{n-1} + 2^0x_n$$we can write the above state as $$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x \right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the application of a similar sequence of gates for qubits $2\ldots n$, we find the final state to be:$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x \right)\vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{n-1}}x \right)\vert1\rangle\right]\otimes\ldots\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{2}}x \right)\vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{1}}x \right)\vert1\rangle\right]$$which is exactly the QFT of the input state as derived above with the caveat that the order of the qubits is reversed in the output state. 6. Example 2: 3-qubit QFT The steps to creating the circuit for $\vert y_3y_2y_1\rangle = QFT_8\vert x_3x_2x_1\rangle$ would be: Apply a Hadamard gate to $\vert x_1 \rangle$$$|\psi_1\rangle = \vert x_3\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_1\right) \vert1\rangle\right]$$ Apply a $UROT_2$ gate to $\vert x_1\rangle$ depending on $\vert x_2\rangle$$$|\psi_2\rangle = \vert x_3\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right) \vert1\rangle\right]$$ Apply a $UROT_3$ gate to $\vert x_1\rangle$ depending on $\vert x_3\rangle$$$|\psi_3\rangle = \vert x_3\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_3 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right) \vert1\rangle\right]$$ Apply a Hadamard gate to $\vert x_2 \rangle$$$|\psi_4\rangle = \vert x_3\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_3 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right) \vert1\rangle\right]$$ Apply a $UROT_2$ gate to $\vert x_2\rangle$ depending on $\vert x_3\rangle$$$|\psi_5\rangle = \vert x_3\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_3 + \frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_3 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right) \vert1\rangle\right]$$ Apply a Hadamard gate to $\vert x_3\rangle$$$|\psi_6\rangle = \frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_3\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_3 + \frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_3 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right) \vert1\rangle\right]$$ Keep in mind the reverse order of the output state relative to the desired QFT. Therefore, we must reverse the order of the qubits (in this case swap $y_1$ and $y_3$). 7. Some Notes About the Form of the QFT Circuit The example above demonstrates a very useful form of the QFT for $N=2^n$. Note that only the last qubit depends on the values of all the other input qubits and each further bit depends less and less on the input qubits. This becomes important in physical implementations of the QFT, where nearest-neighbor couplings are easier to achieve than distant couplings between qubits.Additionally, as the QFT circuit becomes large, an increasing amount of time is spent doing increasingly slight rotations. It turns out that we can ignore rotations below a certain threshold and still get decent results, this is known as the approximate QFT. This is also important in physical implementations, as reducing the number of operations can greatly reduce decoherence and potential gate errors. 8. Qiskit ImplementationIn Qiskit, the implementation of the $CROT$ gate used in the discussion above is a controlled phase rotation gate. This gate is defined in [OpenQASM](https://github.com/QISKit/openqasm) as$$CP(\theta) =\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\theta}\end{bmatrix}$$Hence, the mapping from the $CROT_k$ gate in the discussion above into the $CP$ gate is found from the equation$$\theta = 2\pi/2^k = \pi/2^{k-1}$$ 8.1 Example on 3 Qubits ###Code import numpy as np from numpy import pi # importing Qiskit from qiskit import QuantumCircuit, transpile, assemble, Aer, IBMQ from qiskit.providers.ibmq import least_busy from qiskit.tools.monitor import job_monitor from qiskit.visualization import plot_histogram, plot_bloch_multivector ###Output _____no_output_____ ###Markdown It is useful to work out the relevant code for the 3-qubit case before generalizing to the $n$-qubit case. First, we must define our quantum circuit: ###Code qc = QuantumCircuit(3) ###Output _____no_output_____ ###Markdown **Note**: Remember that Qiskit's least significant bit has the lowest index (0), thus the circuit will be mirrored through the horizontal in relation to the image in section 5. First, we apply a H-gate to qubit 2 : ###Code qc.h(2) qc.draw() ###Output _____no_output_____ ###Markdown Next, we want to turn this an extra quarter turn if qubit 1 is in the state $|1\rangle$: ###Code qc.cp(pi/2, 1, 2) # CROT from qubit 1 to qubit 2 qc.draw() ###Output _____no_output_____ ###Markdown And another eighth turn if the least significant qubit (0) is $|1\rangle$: ###Code qc.cp(pi/4, 0, 2) # CROT from qubit 2 to qubit 0 qc.draw() ###Output _____no_output_____ ###Markdown With that qubit taken care of, we can now ignore it and repeat the process, using the same logic for qubits 0 and 1: ###Code qc.h(1) qc.cp(pi/2, 0, 1) # CROT from qubit 0 to qubit 1 qc.h(0) qc.draw() ###Output _____no_output_____ ###Markdown Finally we must swap the qubits 0 and 2 to complete the QFT: ###Code qc.swap(0,2) qc.draw() ###Output _____no_output_____ ###Markdown 8.2 General QFT Function We will now create a general circuit for the QFT in Qiskit. Creating large general circuits like this is really where Qiskit shines. It is easier to build a circuit that implements the QFT with the qubits upside down, then swap them afterwards; we will start off by creating the function that rotates our qubits correctly. Let’s start as we did with the 3 qubit example, by correctly rotating the most significant qubit (the qubit with the highest index): ###Code def qft_rotations(circuit, n): if n == 0: # Exit function if circuit is empty return circuit n -= 1 # Indexes start from 0 circuit.h(n) # Apply the H-gate to the most significant qubit for qubit in range(n): # For each less significant qubit, we need to do a # smaller-angled controlled rotation: circuit.cp(pi/2**(n-qubit), qubit, n) ###Output _____no_output_____ ###Markdown Let’s see how this looks: ###Code qc = QuantumCircuit(4) qft_rotations(qc,4) qc.draw() ###Output _____no_output_____ ###Markdown We can use the widget below to see how this circuit scales with the number of qubits in our circuit: ###Code from qiskit_textbook.widgets import scalable_circuit scalable_circuit(qft_rotations) ###Output _____no_output_____ ###Markdown Great! This is the first part of our QFT. Now we have correctly rotated the most significant qubit, we need to correctly rotate the second most significant qubit. Then we must deal with the third most significant, and so on. But why write more code? When we get to the end of our `qft_rotations()` function, we can use the same code to repeat the process on the next `n-1` qubits: ###Code def qft_rotations(circuit, n): """Performs qft on the first n qubits in circuit (without swaps)""" if n == 0: return circuit n -= 1 circuit.h(n) for qubit in range(n): circuit.cp(pi/2**(n-qubit), qubit, n) # At the end of our function, we call the same function again on # the next qubits (we reduced n by one earlier in the function) qft_rotations(circuit, n) # Let's see how it looks: qc = QuantumCircuit(4) qft_rotations(qc,4) qc.draw() ###Output _____no_output_____ ###Markdown That was easy! Process in which a function calls itself directly or indirectly is called _recursion._ It can greatly simplify code. We can again see how this scales using the widget below: ###Code scalable_circuit(qft_rotations) ###Output _____no_output_____ ###Markdown Finally, we need to add the swaps at the end of the QFT function to match the definition of the QFT. We will combine this into the final function `qft()`: ###Code def swap_registers(circuit, n): for qubit in range(n//2): circuit.swap(qubit, n-qubit-1) return circuit def qft(circuit, n): """QFT on the first n qubits in circuit""" qft_rotations(circuit, n) swap_registers(circuit, n) return circuit # Let's see how it looks: qc = QuantumCircuit(4) qft(qc,4) qc.draw() ###Output _____no_output_____ ###Markdown This is the generalised circuit for the quantum Fourier transform. We can again see how this scales using the widget below: ###Code scalable_circuit(qft) ###Output _____no_output_____ ###Markdown We now want to demonstrate this circuit works correctly. To do this we must first encode a number in the computational basis. We can see the number 5 in binary is `101`: ###Code bin(5) ###Output _____no_output_____ ###Markdown (The `0b` just reminds us this is a binary number). Let's encode this into our qubits: ###Code # Create the circuit qc = QuantumCircuit(3) # Encode the state 5 qc.x(0) qc.x(2) qc.draw() ###Output _____no_output_____ ###Markdown And let's check the qubit's states using the aer simulator: ###Code sim = Aer.get_backend("aer_simulator") qc_init = qc.copy() qc_init.save_statevector() statevector = sim.run(qc_init).result().get_statevector() plot_bloch_multivector(statevector) ###Output _____no_output_____ ###Markdown Finally, let's use our QFT function and view the final state of our qubits: ###Code qft(qc,3) qc.draw() qc.save_statevector() statevector = sim.run(qc).result().get_statevector() plot_bloch_multivector(statevector) ###Output _____no_output_____ ###Markdown We can see out QFT function has worked correctly. Compared the state $|\widetilde{0}\rangle = |{+}{+}{+}\rangle$, Qubit 0 has been rotated by $\tfrac{5}{8}$ of a full turn, qubit 1 by $\tfrac{10}{8}$ full turns (equivalent to $\tfrac{1}{4}$ of a full turn), and qubit 2 by $\tfrac{20}{8}$ full turns (equivalent to $\tfrac{1}{2}$ of a full turn). 8.3 Running QFT on a Real Quantum Device If we tried running the circuit at the end of section 8.2 on a real device, the results would be completely random, since all qubits are in equal superposition of $|0\rangle$ and $|1\rangle$. If we want to demonstrate and investigate the QFT working on real hardware, we can instead create the state $|\widetilde{5}\rangle$ seen at the end of section 8.2, run the QFT in reverse, and verify the output is the state $|5\rangle$ as expected. Firstly, let’s use Qiskit to easily reverse our QFT operation: ###Code def inverse_qft(circuit, n): """Does the inverse QFT on the first n qubits in circuit""" # First we create a QFT circuit of the correct size: qft_circ = qft(QuantumCircuit(n), n) # Then we take the inverse of this circuit invqft_circ = qft_circ.inverse() # And add it to the first n qubits in our existing circuit circuit.append(invqft_circ, circuit.qubits[:n]) return circuit.decompose() # .decompose() allows us to see the individual gates ###Output _____no_output_____ ###Markdown Now let's put our qubits in the state $|\widetilde{5}\rangle$: ###Code nqubits = 3 number = 5 qc = QuantumCircuit(nqubits) for qubit in range(nqubits): qc.h(qubit) qc.p(number*pi/4,0) qc.p(number*pi/2,1) qc.p(number*pi,2) qc.draw() ###Output _____no_output_____ ###Markdown And we can see this does indeed result in the Fourier state $|\widetilde{5}\rangle$: ###Code qc_init = qc.copy() qc_init.save_statevector() sim = Aer.get_backend("aer_simulator") statevector = sim.run(qc_init).result().get_statevector() plot_bloch_multivector(statevector) ###Output _____no_output_____ ###Markdown Finally, let's apply our inverse QFT: ###Code qc = inverse_qft(qc, nqubits) qc.measure_all() qc.draw() # Load our saved IBMQ accounts and get the least busy backend device with less than or equal to nqubits IBMQ.load_account() provider = IBMQ.get_provider(hub='ibm-q') backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= nqubits and not x.configuration().simulator and x.status().operational==True)) print("least busy backend: ", backend) shots = 2048 transpiled_qc = transpile(qc, backend, optimization_level=3) job = backend.run(transpiled_qc, shots=shots) job_monitor(job) counts = job.result().get_counts() plot_histogram(counts) ###Output _____no_output_____ ###Markdown We (hopefully) see that the highest probability outcome is $101$. 9. Problems 1. The [above implementation](implementationdev) of QFT was tested by preparing the Fourier state $|\widetilde{5}\rangle$ for which $\text{QFT}^{\dagger}|\widetilde{5}\rangle = |101\rangle$. Try to find the state $|a\rangle$ such that $\text{QFT}^{\dagger}|a\rangle = |100\rangle$.2. Find the state $|b\rangle$ such that $\text{QFT}^{\dagger}|b\rangle = |011\rangle$.3. Try to write the QFT function without recursion. Use Qiskit's unitary simulator to verify your results. 10. References 1. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences (Cambridge University Press, Cambridge, 2000). ###Code import qiskit.tools.jupyter %qiskit_version_table ###Output _____no_output_____ ###Markdown Quantum Fourier Transform In this tutorial, we introduce the quantum fourier transform (QFT), derive the circuit, and implement it using Qiskit. We show how to run QFT on a simulator and a five qubit device. Contents1. [Introduction](introduction)2. [Example 1: 1-qubit QFT](example1)3. [The Quantum Fourier transform](qfteqn)4. [The circuit that implements QFT](circuit)5. [Example 2: 3-qubit QFT](example1)6. [A note about the form of the QFT circuit](formnote)7. [Qiskit Implementation](implementation) - [Running QFT on a simulator](implementationsim) - [Running QFT on a real quantum device](implementationdev)8. [Problems](problems)9. [References](references) 1. Introduction The Fourier transform occurs in many different versions throughout classical computing, in areas ranging from signal processing to data compression to complexity theory. The quantum Fourier transform (QFT) is the quantum implementation of the discrete Fourier transform over the amplitudes of a wavefunction. It is part of many quantum algorithms, most notably Shor's factoring algorithm and quantum phase estimation. The discrete Fourier transform acts on a vector $(x_0, ..., x_{N-1})$ and maps it to the vector $(y_0, ..., y_{N-1})$ according to the formula$$y_k = \frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}x_j\omega_N^{jk}$$where $\omega_N^{jk} = e^{2\pi i \frac{jk}{N}}$.Similarly, the quantum Fourier transform acts on a quantum state $\sum_{i=0}^{N-1} x_i \vert i \rangle$ and maps it to the quantum state $\sum_{i=0}^{N-1} y_i \vert i \rangle$ according to the formula$$y_k = \frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}x_j\omega_N^{jk}$$with $\omega_N^{jk}$ defined as above. Note that only the amplitudes of the state were affected by this transformation.This can also be expressed as the map:$$\vert x \rangle \mapsto \frac{1}{\sqrt{N}}\sum_{y=0}^{N-1}\omega_N^{xy} \vert y \rangle$$Or the unitary matrix:$$ U_{QFT} = \frac{1}{\sqrt{N}} \sum_{x=0}^{N-1} \sum_{y=0}^{N-1} \omega_N^{xy} \vert y \rangle \langle x \vert$$ 2. Example 1: 1-qubit QFT Consider how the QFT operator as defined above acts on a single qubit state $\vert\psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle$. In this case, $x_0 = \alpha$, $x_1 = \beta$, and $N = 2$. Then,$$y_0 = \frac{1}{\sqrt{2}}\left( \alpha \exp\left(2\pi i\frac{0\times0}{2}\right) + \beta \exp\left(2\pi i\frac{1\times0}{2}\right) \right) = \frac{1}{\sqrt{2}}\left(\alpha + \beta\right)$$and$$y_1 = \frac{1}{\sqrt{2}}\left( \alpha \exp\left(2\pi i\frac{0\times1}{2}\right) + \beta \exp\left(2\pi i\frac{1\times1}{2}\right) \right) = \frac{1}{\sqrt{2}}\left(\alpha - \beta\right)$$such that the final result is the state $$U_{QFT}\vert\psi\rangle = \frac{1}{\sqrt{2}}(\alpha + \beta) \vert 0 \rangle + \frac{1}{\sqrt{2}}(\alpha - \beta) \vert 1 \rangle$$This operation is exactly the result of applying the Hadamard operator ($H$) on the qubit:$$H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$$If we apply the $H$ operator to the state $\vert\psi\rangle = \alpha \vert 0 \rangle + \beta \vert 1 \rangle$, we obtain the new state:$$\frac{1}{\sqrt{2}}(\alpha + \beta) \vert 0 \rangle + \frac{1}{\sqrt{2}}(\alpha - \beta) \vert 1 \rangle \equiv \tilde{\alpha}\vert 0 \rangle + \tilde{\beta}\vert 1 \rangle$$Notice how the Hadamard gate performs the discrete Fourier transform for $N = 2$ on the amplitudes of the state. 3. The Quantum Fourier transform So what does the quantum Fourier transform look like for larger $N$? Let's derive a circuit for $N=2^n$, $QFT_N$ acting on the state $\vert x \rangle = \vert x_1\ldots x_n \rangle$ where $x_1$ is the most significant bit.\begin{aligned}QFT_N\vert x \rangle & = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1}\omega_N^{xy} \vert y \rangle \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} e^{2 \pi i xy / 2^n} \vert y \rangle ~\text{since}\: \omega_N^{xy} = e^{2\pi i \frac{xy}{N}} \:\text{and}\: N = 2^n \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} e^{2 \pi i \left(\sum_{k=1}^n y_k/2^k\right) x} \vert y_1 \ldots y_n \rangle \:\text{rewriting in fractional binary notation}\: y = y_1\ldots y_n, y/2^n = \sum_{k=1}^n y_k/2^k \\& = \frac{1}{\sqrt{N}} \sum_{y=0}^{N-1} \prod_{k=1}^n e^{2 \pi i x y_k/2^k } \vert y_1 \ldots y_n \rangle \:\text{after expanding the exponential of a sum to a product of exponentials} \\& = \frac{1}{\sqrt{N}} \bigotimes_{k=1}^n \left(\vert0\rangle + e^{2 \pi i x /2^k } \vert1\rangle \right) \:\text{after rearranging the sum and products, and expanding} \sum_{y=0}^{N-1} = \sum_{y_1=0}^{1}\sum_{y_2=0}^{1}\ldots\sum_{y_n=0}^{1} \\& = \frac{1}{\sqrt{N}}\left(\vert0\rangle + e^{\frac{2\pi i}{2}x} \vert1\rangle\right) \otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^2}x} \vert1\rangle\right) \otimes \ldots\otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^{n-1}}x} \vert1\rangle\right) \otimes\left(\vert0\rangle + e^{\frac{2\pi i}{2^n}x} \vert1\rangle\right) \end{aligned} 4. The circuit that implements QFT The circuit that implements QFT makes use of two gates. The first one is a single-qubit Hadamard gate, $H$, that you already know. From the discussion in [Example 1](example1) above, you have already seen that the action of $H$ on the single-qubit state $\vert x_k\rangle$ is$$H\vert x_k \rangle = \vert0\rangle + \exp\left(\frac{2\pi i}{2}x_k\right)\vert1\rangle$$The second is a two-qubit controlled rotation $CROT_k$ given in block-diagonal form as $$CROT_k = \left[\begin{matrix}I&0\\0&UROT_k\\\end{matrix}\right]$$where $$UROT_k = \left[\begin{matrix}1&0\\0&\exp\left(\frac{2\pi i}{2^k}\right)\\\end{matrix}\right]$$The action of $CROT_k$ on the two-qubit state $\vert x_jx_k\rangle$ where the first qubit is the control and the second is the target is given by$$CROT_k\vert x_j0\rangle = \vert x_j0\rangle$$and$$CROT_k\vert x_j1\rangle = \exp\left( \frac{2\pi i}{2^k}x_j \right)\vert x_j1\rangle$$Given these two gates, a circuit that implements [an n-qubit QFT](qfteqn) is shown below.The circuit operates as follows. We start with an n-qubit input state $\vert x_1x_2\ldots x_n\rangle$. After the first Hadamard gate on qubit 1, the state is transformed from the input state to $$H_1\vert x_1x_2\ldots x_n\rangle = \frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the $CROT_2$ gate on qubit 1 controlled by qubit 2, the state is transformed to$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the application of the last $CROT_n$ gate on qubit 1 controlled by qubit $n$, the state becomes$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x_n + \frac{2\pi i}{2^{n-1}}x_{n-1} + \ldots + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_1\right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$Noting that $$x = 2^{n-1}x_1 + 2^{n-2}x_2 + \ldots + 2^1x_{n-1} + 2^0x_n$$we can write the above state as $$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x \right)\vert1\rangle\right]\otimes\vert x_2x_3\ldots x_n\rangle$$ After the application of a similar sequence of gates for qubits $2\ldots n$, we find the final state to be$$\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^n}x \right)\vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{n-1}}x \right)\vert1\rangle\right]\otimes\ldots\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{2}}x \right)\vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^{1}}x \right)\vert1\rangle\right]$$which is exactly the QFT of the input state as derived above with the caveat that the order of the qubits is reversed in the output state. 5. Example 2: 3-qubit QFT The steps to creating the circuit for $\vert y_1y_2y_3\rangle = QFT_8\vert x_1x_2x_3\rangle$ would be: Apply a Hadamard gate to $\vert x_3 \rangle$$$\psi_1 = \vert x_1\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a $CROT_2$ gate to $\vert x_3\rangle$ depending on $\vert x_2\rangle$$$\psi_2 = \vert x_1\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a $CROT_3$ gate to $\vert x_3\rangle$ depending on $\vert x_1\rangle$$$\psi_3 = \vert x_1\rangle\otimes\vert x_2\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a Hadamard gate to $\vert x_2 \rangle$$$\psi_4 = \vert x_1\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a $CROT_2$ gate to $\vert x_2\rangle$ depending on $\vert x_1\rangle$$$\psi_5 = \vert x_1\rangle\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_1 + \frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Apply a Hadamard gate to $\vert x_1\rangle$$$\psi_6 = \frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2}x_1\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^2}x_1 + \frac{2\pi i}{2}x_2\right) \vert1\rangle\right]\otimes\frac{1}{\sqrt{2}}\left[\vert0\rangle + \exp\left(\frac{2\pi i}{2^3}x_1 + \frac{2\pi i}{2^2}x_2 + \frac{2\pi i}{2}x_3\right) \vert1\rangle\right]$$ Keep in mind the reverse order of the output state relative to the desired QFT. Therefore, measure the bits in reverse order, that is $y_3 = x_1, y_2 = x_2, y_1 = y_3$. 6. A note about the form of the QFT circuit The example above demonstrates a very useful form of the QFT for $N=2^n$. Note that only the last qubit depends on the values of all the other input qubits and each further bit depends less and less on the input qubits. This becomes important in physical implementations of the QFT, where nearest-neighbor couplings are easier to achieve than distant couplings between qubits. 7. Qiskit ImplementationIn Qiskit, the implementation of the $CROT$ gate used in the discussion above is a controlled phase rotation gate. This gate is defined in [OpenQASM](https://github.com/QISKit/openqasm) as$$CU_1(\theta) =\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\theta}\end{bmatrix}$$Hence, the mapping from the $CROT_k$ gate in the discussion above into the $CU_1$ gate is found from the equation$$\theta = 2\pi/2^k = \pi/2^{k-1}$$It is instructive to write out the relevant code for the 3-qubit case before generalizing to the $n$-qubit case. In Qiskit, it is:```q = QuantumRegister(3)c = ClassicalRegister(3)qft3 = QuantumCircuit(q, c)qft3.h(q[0])qft3.cu1(math.pi/2.0, q[1], q[0]) CROT_2 from q[1] to q[0]qft3.cu1(math.pi/4.0, q[2], q[0]) CROT_3 from q[2] to q[0]qft3.h(q[1])qft3.cu1(math.pi/2.0, q[2], q[1]) CROT_2 from q[2] to q[1]qft3.h(q[2])```Following the above example, the case for $n$ qubits can be generalized as:```def qft(circ, q, n): """n-qubit QFT on q in circ.""" for j in range(n): circ.h(q[j]) for k in range(j+1,n): circ.cu1(math.pi/float(2**(k-j)), q[k], q[j])``` We will now implement the three-qubit QFT as discussed above. We first create a state whose QFT is known. The output after a QFT is applied to this special state is $\vert001\rangle$. ###Code import math # importing Qiskit from qiskit import Aer, IBMQ from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, execute from qiskit.providers.ibmq import least_busy from qiskit.tools.monitor import job_monitor from qiskit.tools.visualization import plot_histogram IBMQ.load_account() ###Output _____no_output_____ ###Markdown First let's define the QFT function, as well as a function that creates a state from which a QFT will return 001: ###Code def input_state(circ, q, n): """n-qubit input state for QFT that produces output 1.""" for j in range(n): circ.h(q[j]) circ.u1(-math.pi/float(2**(j)), q[j]) def qft(circ, q, n): """n-qubit QFT on q in circ.""" for j in range(n): circ.h(q[j]) for k in range(j+1,n): circ.cu1(math.pi/float(2**(k-j)), q[k], q[j]) circ.barrier() ###Output _____no_output_____ ###Markdown Let's now implement a QFT on a prepared three qubit input state that should return $001$: ###Code q = QuantumRegister(3, 'x') c = ClassicalRegister(3, 'c') qft3 = QuantumCircuit(q, c) # first, prepare the state that should return 001 and draw that circuit input_state(qft3, q, 3) qft3.draw(output='mpl') # next, do a qft on the prepared state and draw the entire circuit qft(qft3, q, 3) for i in range(3): qft3.measure(q[i], c[i]) qft3.draw(output='mpl') ###Output _____no_output_____ ###Markdown 7a. Running QFT on a simulator ###Code # run on local simulator backend = Aer.get_backend("qasm_simulator") simulate = execute(qft3, backend=backend, shots=1024).result() simulate.get_counts() ###Output _____no_output_____ ###Markdown We indeed see that the outcome is always $001$ when we execute the code on the simulator. 7b. Running QFT on a real quantum device We then see how the same circuit can be executed on real-device backends. ###Code # Use the IBMQ Vigo device with 5 qubits provider = IBMQ.get_provider(hub='ibm-q') backend = provider.get_backend('ibmq_vigo') shots = 2048 job_exp = execute(qft3, backend=backend, shots=shots) job_monitor(job_exp) results = job_exp.result() plot_histogram(results.get_counts()) ###Output _____no_output_____ ###Markdown We see that the highest probability outcome is still $001$ when we execute the code on a real device. 8. Problems 1. The [above implementation](implementation) of QFT was tested by using a special input state for which QFT(input state) = 001. Implement an input state for which QFT(input state) = 100.2. The [above implementation](implementation) of QFT was tested by using a special input state for which QFT(input state) = 001. Implement an input state for which QFT(input state) = 101. 9. References 1. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences (Cambridge University Press, Cambridge, 2000). ###Code import qiskit qiskit.__qiskit_version__ ###Output _____no_output_____

notebooks/kmeans_mnmg_demo.ipynb

###Markdown K-Means Multi-Node Multi-GPU (MNMG) DemoK-Means multi-Node multi-GPU implementation leverages Dask to spread data and computations across multiple workers. cuML uses One Process Per GPU (OPG) layout, which maps a single Dask worker to each GPU.The main difference between cuML's MNMG implementation of k-means and the single-GPU is that the fit can be performed in parallel for each iteration, sharing only the centroids between iterations. The MNMG version also provides the same scalable k-means++ initialization algorithm as the single-GPU version.Unlike the single-GPU implementation, The MNMG k-means API requires a Dask cuDF Dataframe as input. `predict()` and `transform()` also return a Dask cuDF Dataframe. The Dask cuDF Dataframe API is very similar to the Dask DataFrame API, but underlying Dataframes are cuDF, rather than Pandas.For information about cuDF, refer to the [cuDF documentation](https://docs.rapids.ai/api/cudf/stable).For additional information on cuML's k-means implementation: https://docs.rapids.ai/api/cuml/stable/api.htmlcuml.dask.cluster.KMeans. Imports ###Code from cuml.dask.cluster.kmeans import KMeans as cuKMeans from cuml.dask.common import to_dask_df from cuml.dask.datasets import make_blobs from cuml.metrics import adjusted_rand_score from dask.distributed import Client, wait from dask_cuda import LocalCUDACluster from dask_ml.cluster import KMeans as skKMeans ###Output _____no_output_____ ###Markdown Start Dask ClusterWe can use the `LocalCUDACluster` to start a Dask cluster on a single machine with one worker mapped to each GPU. This is called one-process-per-GPU (OPG). ###Code cluster = LocalCUDACluster(threads_per_worker=1) client = Client(cluster) ###Output _____no_output_____ ###Markdown Define Parameters ###Code n_samples = 1000000 n_features = 2 n_total_partitions = len(list(client.has_what().keys())) ###Output _____no_output_____ ###Markdown Generate Data DeviceWe can generate a dask_cudf.DataFrame of synthetic data for multiple clusters using `cuml.dask.datasets.make_blobs`. ###Code X_cudf, Y_cudf = make_blobs(n_samples, n_features, centers = 5, n_parts = n_total_partitions, cluster_std=0.1, verbose=True) ###Output _____no_output_____ ###Markdown HostWe use `cuml.dask.common.to_dask_df` to convert a dask_cuml.DataFrame using device memory into a dask.DataFrame containing Pandas in host memory. ###Code wait(X_cudf) X_df = to_dask_df(X_cudf) ###Output _____no_output_____ ###Markdown Scikit-learn model Fit and predictSince a scikit-learn equivalent to the multi-node multi-GPU K-means in cuML doesn't exist, we will use Dask-ML's implementation for comparison. ###Code %%time kmeans_sk = skKMeans(init="k-means||", n_clusters=5, n_jobs=-1, random_state=100) kmeans_sk.fit(X_df) %%time labels_sk = kmeans_sk.predict(X_df).compute() ###Output _____no_output_____ ###Markdown cuML Model Fit and predict ###Code %%time kmeans_cuml = cuKMeans(init="k-means||", n_clusters=5, random_state=100) kmeans_cuml.fit(X_cudf) %%time labels_cuml = kmeans_cuml.predict(X_cudf).compute() ###Output _____no_output_____ ###Markdown Compare Results ###Code score = adjusted_rand_score(labels_sk, labels_cuml.to_pandas().values) passed = score == 1.0 print('compare kmeans: cuml vs sklearn labels_ are ' + ('equal' if passed else 'NOT equal')) ###Output _____no_output_____ ###Markdown K-Means Multi-Node Multi-GPU (MNMG) DemoK-Means multi-Node multi-GPU implementation leverages Dask to spread data and computations across multiple workers. cuML uses One Process Per GPU (OPG) layout, which maps a single Dask worker to each GPU.The main difference between cuML's MNMG implementation of k-means and the single-GPU is that the fit can be performed in parallel for each iteration, sharing only the centroids between iterations. The MNMG version also provides the same scalable k-means++ initialization algorithm as the single-GPU version.Unlike the single-GPU implementation, The MNMG k-means API requires a Dask Dataframe or Array as input. `predict()` and `transform()` return the same type as input. The Dask cuDF Dataframe API is very similar to the Dask DataFrame API, but underlying Dataframes are cuDF, rather than Pandas. Dask cuPy arrays are also available.For information about cuDF, refer to the [cuDF documentation](https://docs.rapids.ai/api/cudf/stable).For additional information on cuML's k-means implementation: https://docs.rapids.ai/api/cuml/stable/api.htmlcuml.dask.cluster.KMeans. Imports ###Code from cuml.dask.cluster.kmeans import KMeans as cuKMeans from cuml.dask.common import to_dask_df from cuml.dask.datasets import make_blobs from cuml.metrics import adjusted_rand_score from dask.distributed import Client, wait from dask_cuda import LocalCUDACluster from dask_ml.cluster import KMeans as skKMeans import cupy as cp ###Output _____no_output_____ ###Markdown Start Dask ClusterWe can use the `LocalCUDACluster` to start a Dask cluster on a single machine with one worker mapped to each GPU. This is called one-process-per-GPU (OPG). ###Code cluster = LocalCUDACluster(threads_per_worker=1) client = Client(cluster) ###Output _____no_output_____ ###Markdown Define Parameters ###Code n_samples = 1000000 n_features = 2 n_total_partitions = len(list(client.has_what().keys())) ###Output _____no_output_____ ###Markdown Generate Data DeviceWe can generate a Dask cuPY Array of synthetic data for multiple clusters using `cuml.dask.datasets.make_blobs`. ###Code X_dca, Y_dca = make_blobs(n_samples, n_features, centers = 5, n_parts = n_total_partitions, cluster_std=0.1, verbose=True) ###Output _____no_output_____ ###Markdown HostWe collect the Dask cuPy Array on a single node as a cuPy array. Then we transfer the cuPy array from device to host memory into a Numpy array. ###Code X_cp = X_dca.compute() X_np = cp.asnumpy(X_cp) del X_cp ###Output _____no_output_____ ###Markdown Scikit-learn model Fit and predictSince a scikit-learn equivalent to the multi-node multi-GPU K-means in cuML doesn't exist, we will use Dask-ML's implementation for comparison. ###Code %%time kmeans_sk = skKMeans(init="k-means||", n_clusters=5, n_jobs=-1, random_state=100) kmeans_sk.fit(X_np) %%time labels_sk = kmeans_sk.predict(X_np).compute() ###Output _____no_output_____ ###Markdown cuML Model Fit and predict ###Code %%time kmeans_cuml = cuKMeans(init="k-means||", n_clusters=5, random_state=100) kmeans_cuml.fit(X_dca) %%time labels_cuml = kmeans_cuml.predict(X_dca).compute() ###Output _____no_output_____ ###Markdown Compare Results ###Code score = adjusted_rand_score(labels_sk, labels_cuml) passed = score == 1.0 print('compare kmeans: cuml vs sklearn labels_ are ' + ('equal' if passed else 'NOT equal')) ###Output _____no_output_____

notebooks/Transfer_Learning_Demo.ipynb

###Markdown > **How to run this notebook (command-line)?**1. Install the `ReinventCommunity` environment:`conda env create -f environment.yml`2. Activate the environment:`conda activate ReinventCommunity`3. Execute `jupyter`:`jupyter notebook`4. Copy the link to a browser `REINVENT 3.0`: transfer learning mode demo The *transfer learning* mode can be used for either 1. Initial training of the Agent - where a newly built agent is trained from scratch while iterating through sufficiently large datasets over many epochs 2. Focusing of pre-trained Agent - where an already pre-trained agent is introduced to a small dataset for a small number of epochs.In this notebook we are going to illustrate the second scenario. The small dataset can consist of a few hundred molecules that normally share same features/scaffolds. The purpose of `Focusing` is to "learn" the common patterns/scaffolds in the structures. The `Focused` Agent will start producing with higher probablility the molecules with the common scaffolds. The `Focused` Agent can be used directly for *reinforcement learning* thus having as a starting point the small chemical space it has been focused on. ###Code # load dependencies import os import re import json import tempfile # --------- change these path variables as required reinvent_dir = os.path.expanduser("~/Desktop/reinventcli") reinvent_env = os.path.expanduser("~/miniconda3/envs/reinvent.v3.0") output_dir = os.path.expanduser("~/Desktop/REINVENT_transfer_learning_demo") # --------- do not change # get the notebook's root path try: ipynb_path except NameError: ipynb_path = os.getcwd() # if required, generate a folder to store the results try: os.mkdir(output_dir) except FileExistsError: pass ###Output _____no_output_____ ###Markdown Setting up the configuration`REINVENT` has an entry point that loads a specified `JSON` file on startup. `JSON` is a low-level data format that allows to specify a fairly large number of parameters in a cascading fashion very quickly. The parameters are structured into *blocks* which can in turn contain blocks or simple values, such as *True* or *False*, strings and numbers. In this tutorial, we will go through the different blocks step-by-step, explaining their purpose and potential values for given parameters. Note, that while we will write out the configuration as a `JSON` file in the end, in `python` we handle the same information as a simple `dict`. ###Code # initialize the dictionary configuration = { "version": 3, # we are going to use REINVENT's newest release "run_type": "transfer_learning" # other run types: "scoring", "validation", # "transfer_learning", # "reinforcement_learning" and # "create_model" } # add block to specify whether to run locally or not and # where to store the results and logging configuration["logging"] = { "sender": "http://127.0.0.1", # only relevant if "recipient" is set to "remote" "recipient": "local", # either to local logging or use a remote REST-interface "logging_path": os.path.join(output_dir, "progress.log"), # where the run's output is stored "job_name": "Transfer Learning demo", # set an arbitrary job name for identification "job_id": "demo" # only relevant if "recipient" is set to "remote" } ###Output _____no_output_____ ###Markdown We will need to specify a path to an agent (parameter `model_path`), which can be a prior or trained agent. For the purpose of this notebook, we will use a prior shipped with the `REINVENT 3.0` repository. The code block below will define the settings for `adaptive_lr_config` property of the configuration. These parameters are defining the behavior of the learning rate. Note that the mode is set to `"constant"`. We recommend the default values as they dont play significant role for the purpose of focusing the agent. ###Code adaptive_lr_config = { "mode": "constant", # other modes: "exponential", "adaptive", "constant" "gamma": 0.8, "step": 1, "start": 5E-4, "min": 1E-5, "threshold": 1E-4, "average_steps": 4, "patience": 8, "restart_value": 1E-5, "sample_size": 10000, "restart_times": 0 } output_model_path = os.path.join(output_dir, "focused.agent") \ # The final focused agent will be named "focused.agent" # The intermediate steps will be named "focused.agent.1", "focused.agent.2", "focused.agent.3" and etc. # add the "parameters" block configuration["parameters"] = { "input_model_path": os.path.join(ipynb_path, # path to prior or trained agent "models", "random.prior.new"), "output_model_path": output_model_path, # location to store the focused agent "input_smiles_path": os.path.join(ipynb_path, # path to input smiles "data", # this is a dummy dataset consisting only of celecoxib "smiles.smi"), "save_every_n_epochs": 1, # how often to save the focused Agent. Here it's stored after each epoch "batch_size": 128, # batch size the input data "num_epochs": 10, # number of epochs to focus the agent for "standardize": True, # the input may contain SMILES strings that are invalid according to the agent # this atempts to clean up the input dataset "randomize": True, # this triggers data augmentation which is quite important for small datasets "adaptive_lr_config": adaptive_lr_config # setting the learning rate behavior } # write the configuration file to the disc configuration_JSON_path = os.path.join(output_dir, "transfer_learning_config.json") with open(configuration_JSON_path, 'w') as f: json.dump(configuration, f, indent=4, sort_keys=True) ###Output _____no_output_____ ###Markdown Run `REINVENT`Now it is time to execute `REINVENT` locally. The command-line execution looks like this:``` activate envionmentconda activate reinvent.v3.0 execute REINVENTpython /input.py .json``` ###Code %%capture captured_err_stream --no-stderr # execute REINVENT from the command-line !{reinvent_env}/bin/python {reinvent_dir}/input.py {configuration_JSON_path} # print the output to a file, just to have it for documentation with open(os.path.join(output_dir, "run.err"), 'w') as file: file.write(captured_err_stream.stdout) ###Output _____no_output_____ ###Markdown > **How to run this notebook (command-line)?**1. Install the `ReinventCommunity` environment:`conda env create -f environment.yml`2. Activate the environment:`conda activate ReinventCommunity`3. Execute `jupyter`:`jupyter notebook`4. Copy the link to a browser `REINVENT 3.0`: transfer learning mode demo The *transfer learning* mode can be used for either 1. Initial training of the Agent - where a newly built agent is trained from scratch while iterating through sufficiently large datasets over many epochs 2. Focusing of pre-trained Agent - where an already pre-trained agent is introduced to a small dataset for a small number of epochs.In this notebook we are going to illustrate the second scenario. The small dataset can consist of a few hundred molecules that normally share same features/scaffolds. The purpose of `Focusing` is to "learn" the common patterns/scaffolds in the structures. The `Focused` Agent will start producing with higher probablility the molecules with the common scaffolds. The `Focused` Agent can be used directly for *reinforcement learning* thus having as a starting point the small chemical space it has been focused on. ###Code # load dependencies import os import re import json import tempfile # --------- change these path variables as required reinvent_dir = os.path.expanduser("~/Desktop/Reinvent") reinvent_env = os.path.expanduser("~/miniconda3/envs/reinvent.v3.0") output_dir = os.path.expanduser("~/Desktop/REINVENT_transfer_learning_demo") # --------- do not change # get the notebook's root path try: ipynb_path except NameError: ipynb_path = os.getcwd() # if required, generate a folder to store the results try: os.mkdir(output_dir) except FileExistsError: pass ###Output _____no_output_____ ###Markdown Setting up the configuration`REINVENT` has an entry point that loads a specified `JSON` file on startup. `JSON` is a low-level data format that allows to specify a fairly large number of parameters in a cascading fashion very quickly. The parameters are structured into *blocks* which can in turn contain blocks or simple values, such as *True* or *False*, strings and numbers. In this tutorial, we will go through the different blocks step-by-step, explaining their purpose and potential values for given parameters. Note, that while we will write out the configuration as a `JSON` file in the end, in `python` we handle the same information as a simple `dict`. ###Code # initialize the dictionary configuration = { "version": 3, # we are going to use REINVENT's newest release "run_type": "transfer_learning" # other run types: "scoring", "validation", # "transfer_learning", # "reinforcement_learning" and # "create_model" } # add block to specify whether to run locally or not and # where to store the results and logging configuration["logging"] = { "sender": "http://127.0.0.1", # only relevant if "recipient" is set to "remote" "recipient": "local", # either to local logging or use a remote REST-interface "logging_path": os.path.join(output_dir, "progress.log"), # where the run's output is stored "job_name": "Transfer Learning demo", # set an arbitrary job name for identification "job_id": "demo" # only relevant if "recipient" is set to "remote" } ###Output _____no_output_____ ###Markdown We will need to specify a path to an agent (parameter `model_path`), which can be a prior or trained agent. For the purpose of this notebook, we will use a prior shipped with the `REINVENT 3.0` repository. The code block below will define the settings for `adaptive_lr_config` property of the configuration. These parameters are defining the behavior of the learning rate. Note that the mode is set to `"constant"`. We recommend the default values as they dont play significant role for the purpose of focusing the agent. ###Code adaptive_lr_config = { "mode": "constant", # other modes: "exponential", "adaptive", "constant" "gamma": 0.8, "step": 1, "start": 5E-4, "min": 1E-5, "threshold": 1E-4, "average_steps": 4, "patience": 8, "restart_value": 1E-5, "sample_size": 10000, "restart_times": 0 } output_model_path = os.path.join(output_dir, "focused.agent") \ # The final focused agent will be named "focused.agent" # The intermediate steps will be named "focused.agent.1", "focused.agent.2", "focused.agent.3" and etc. # add the "parameters" block configuration["parameters"] = { "input_model_path": os.path.join(ipynb_path, # path to prior or trained agent "models", "random.prior.new"), "output_model_path": output_model_path, # location to store the focused agent "input_smiles_path": os.path.join(ipynb_path, # path to input smiles "data", # this is a dummy dataset consisting only of celecoxib "smiles.smi"), "save_every_n_epochs": 1, # how often to save the focused Agent. Here it's stored after each epoch "batch_size": 128, # batch size the input data "num_epochs": 10, # number of epochs to focus the agent for "standardize": True, # the input may contain SMILES strings that are invalid according to the agent # this atempts to clean up the input dataset "randomize": True, # this triggers data augmentation which is quite important for small datasets "adaptive_lr_config": adaptive_lr_config # setting the learning rate behavior } # write the configuration file to the disc configuration_JSON_path = os.path.join(output_dir, "transfer_learning_config.json") with open(configuration_JSON_path, 'w') as f: json.dump(configuration, f, indent=4, sort_keys=True) ###Output _____no_output_____ ###Markdown Run `REINVENT`Now it is time to execute `REINVENT` locally. The command-line execution looks like this:``` activate envionmentconda activate reinvent.v3.0 execute REINVENTpython /input.py .json``` ###Code %%capture captured_err_stream --no-stderr # execute REINVENT from the command-line !{reinvent_env}/bin/python {reinvent_dir}/input.py {configuration_JSON_path} # print the output to a file, just to have it for documentation with open(os.path.join(output_dir, "run.err"), 'w') as file: file.write(captured_err_stream.stdout) ###Output _____no_output_____ ###Markdown > **How to run this notebook (command-line)?**1. Install the `reinvent_shared.v2.1` environment:`conda env create -f reinvent_shared.yml`2. Activate the environment:`conda activate reinvent_shared.v2.1`3. Execute `jupyter`:`jupyter notebook`4. Copy the link to a browser `REINVENT 2.0`: transfer learning mode demo The *transfer learning* mode can be used for either 1. Initial training of the Agent - where a newly built agent is trained from scratch while iterating through sufficiently large datasets over many epochs 2. Focusing of pre-trained Agent - where an already pre-trained agent is introduced to a small dataset for a small number of epochs.In this notebook we are going to illustrate the second scenario. The small dataset can consist of a few hundred molecules that normally share same features/scaffolds. The purpose of `Focusing` is to "learn" the common patterns/scaffolds in the structures. The `Focused` Agent will start producing with higher probablility the molecules with the common scaffolds. The `Focused` Agent can be used directly for *reinforcement learning* thus having as a starting point the small chemical space it has been focused on. ###Code # load dependencies import os import re import json import tempfile # --------- change these path variables as required reinvent_dir = os.path.expanduser("~/Desktop/Projects/Publications/2020/2020-04_REINVENT_2.0/Reinvent") reinvent_env = os.path.expanduser("~/miniconda3/envs/reinvent_shared.v2.1") output_dir = os.path.expanduser("~/Desktop/REINVENT_transfer_learning_demo") # --------- do not change # get the notebook's root path try: ipynb_path except NameError: ipynb_path = os.getcwd() # if required, generate a folder to store the results try: os.mkdir(output_dir) except FileExistsError: pass ###Output _____no_output_____ ###Markdown Setting up the configuration`REINVENT` has an entry point that loads a specified `JSON` file on startup. `JSON` is a low-level data format that allows to specify a fairly large number of parameters in a cascading fashion very quickly. The parameters are structured into *blocks* which can in turn contain blocks or simple values, such as *True* or *False*, strings and numbers. In this tutorial, we will go through the different blocks step-by-step, explaining their purpose and potential values for given parameters. Note, that while we will write out the configuration as a `JSON` file in the end, in `python` we handle the same information as a simple `dict`. ###Code # initialize the dictionary configuration = { "version": 2, # we are going to use REINVENT's newest release "run_type": "transfer_learning" # other run types: "scoring", "validation", # "transfer_learning", # "reinforcement_learning" and # "create_model" } # add block to specify whether to run locally or not and # where to store the results and logging configuration["logging"] = { "sender": "http://127.0.0.1", # only relevant if "recipient" is set to "remote" "recipient": "local", # either to local logging or use a remote REST-interface "logging_path": os.path.join(output_dir, "progress.log"), # where the run's output is stored "job_name": "Transfer Learning demo", # set an arbitrary job name for identification "job_id": "demo" # only relevant if "recipient" is set to "remote" } ###Output _____no_output_____ ###Markdown We will need to specify a path to an agent (parameter `model_path`), which can be a prior or trained agent. For the purpose of this notebook, we will use a prior shipped with the `REINVENT 2.0` repository. The code block below will define the settings for `adaptive_lr_config` property of the configuration. These parameters are defining the behavior of the learning rate. Note that the mode is set to `"constant"`. We recommend the default values as they dont play significant role for the purpose of focusing the agent. ###Code adaptive_lr_config = { "mode": "constant", # other modes: "exponential", "adaptive", "constant" "gamma": 0.8, "step": 1, "start": 5E-4, "min": 1E-5, "threshold": 1E-4, "average_steps": 4, "patience": 8, "restart_value": 1E-5, "sample_size": 10000, "restart_times": 0 } output_model_path = os.path.join(output_dir, "focused.agent") \ # The final focused agent will be named "focused.agent" # The intermediate steps will be named "focused.agent.1", "focused.agent.2", "focused.agent.3" and etc. # add the "parameters" block configuration["parameters"] = { "input_model_path": os.path.join(reinvent_dir, # path to prior or trained agent "data", "augmented.prior"), "output_model_path": output_model_path, # location to store the focused agent "input_smiles_path": os.path.join(reinvent_dir, # path to input smiles "data", # this is a dummy dataset consisting only of celecoxib "smiles.smi"), "save_every_n_epochs": 1, # how often to save the focused Agent. Here its stored after each epoch "batch_size": 128, # batch size the input data "num_epochs": 10, # number of epochs to focus the agent for "standardize": True, # the input may contain SMILES strings that are invalid according to the agent # this atempts to clean up the input dataset "randomize": True, # this triggers data augmentation which is quite important for small datasets "adaptive_lr_config": adaptive_lr_config # setting the learning rate behavior } # write the configuration file to the disc configuration_JSON_path = os.path.join(output_dir, "transfer_learning_config.json") with open(configuration_JSON_path, 'w') as f: json.dump(configuration, f, indent=4, sort_keys=True) ###Output _____no_output_____ ###Markdown Run `REINVENT`Now it is time to execute `REINVENT` locally. The command-line execution looks like this:``` activate envionmentconda activate reinvent_shared.v2.1 execute REINVENTpython /input.py .json``` ###Code %%capture captured_err_stream --no-stderr # execute REINVENT from the command-line !python {reinvent_dir}/input.py {configuration_JSON_path} # print the output to a file, just to have it for documentation with open(os.path.join(output_dir, "run.err"), 'w') as file: file.write(captured_err_stream.stdout) ###Output _____no_output_____ ###Markdown > **How to run this notebook (command-line)?**1. Install the `ReinventCommunity` environment:`conda env create -f environment.yml`2. Activate the environment:`conda activate ReinventCommunity`3. Execute `jupyter`:`jupyter notebook`4. Copy the link to a browser `REINVENT 3.0`: transfer learning mode demo The *transfer learning* mode can be used for either 1. Initial training of the Agent - where a newly built agent is trained from scratch while iterating through sufficiently large datasets over many epochs 2. Focusing of pre-trained Agent - where an already pre-trained agent is introduced to a small dataset for a small number of epochs.In this notebook we are going to illustrate the second scenario. The small dataset can consist of a few hundred molecules that normally share same features/scaffolds. The purpose of `Focusing` is to "learn" the common patterns/scaffolds in the structures. The `Focused` Agent will start producing with higher probablility the molecules with the common scaffolds. The `Focused` Agent can be used directly for *reinforcement learning* thus having as a starting point the small chemical space it has been focused on. ###Code # load dependencies import os import re import json import tempfile # --------- change these path variables as required reinvent_dir = os.path.expanduser("~/Desktop/Projects/Publications/2020/2020-04_REINVENT_2.0/Reinvent") reinvent_env = os.path.expanduser("~/miniconda3/envs/reinvent_shared.v2.1") output_dir = os.path.expanduser("~/Desktop/REINVENT_transfer_learning_demo") # --------- do not change # get the notebook's root path try: ipynb_path except NameError: ipynb_path = os.getcwd() # if required, generate a folder to store the results try: os.mkdir(output_dir) except FileExistsError: pass ###Output _____no_output_____ ###Markdown Setting up the configuration`REINVENT` has an entry point that loads a specified `JSON` file on startup. `JSON` is a low-level data format that allows to specify a fairly large number of parameters in a cascading fashion very quickly. The parameters are structured into *blocks* which can in turn contain blocks or simple values, such as *True* or *False*, strings and numbers. In this tutorial, we will go through the different blocks step-by-step, explaining their purpose and potential values for given parameters. Note, that while we will write out the configuration as a `JSON` file in the end, in `python` we handle the same information as a simple `dict`. ###Code # initialize the dictionary configuration = { "version": 3, # we are going to use REINVENT's newest release "run_type": "transfer_learning" # other run types: "scoring", "validation", # "transfer_learning", # "reinforcement_learning" and # "create_model" } # add block to specify whether to run locally or not and # where to store the results and logging configuration["logging"] = { "sender": "http://127.0.0.1", # only relevant if "recipient" is set to "remote" "recipient": "local", # either to local logging or use a remote REST-interface "logging_path": os.path.join(output_dir, "progress.log"), # where the run's output is stored "job_name": "Transfer Learning demo", # set an arbitrary job name for identification "job_id": "demo" # only relevant if "recipient" is set to "remote" } ###Output _____no_output_____ ###Markdown We will need to specify a path to an agent (parameter `model_path`), which can be a prior or trained agent. For the purpose of this notebook, we will use a prior shipped with the `REINVENT 3.0` repository. The code block below will define the settings for `adaptive_lr_config` property of the configuration. These parameters are defining the behavior of the learning rate. Note that the mode is set to `"constant"`. We recommend the default values as they dont play significant role for the purpose of focusing the agent. ###Code adaptive_lr_config = { "mode": "constant", # other modes: "exponential", "adaptive", "constant" "gamma": 0.8, "step": 1, "start": 5E-4, "min": 1E-5, "threshold": 1E-4, "average_steps": 4, "patience": 8, "restart_value": 1E-5, "sample_size": 10000, "restart_times": 0 } output_model_path = os.path.join(output_dir, "focused.agent") \ # The final focused agent will be named "focused.agent" # The intermediate steps will be named "focused.agent.1", "focused.agent.2", "focused.agent.3" and etc. # add the "parameters" block configuration["parameters"] = { "input_model_path": os.path.join(ipynb_path, # path to prior or trained agent "models", "augmented.prior"), "output_model_path": output_model_path, # location to store the focused agent "input_smiles_path": os.path.join(ipynb_path, # path to input smiles "data", # this is a dummy dataset consisting only of celecoxib "smiles.smi"), "save_every_n_epochs": 1, # how often to save the focused Agent. Here its stored after each epoch "batch_size": 128, # batch size the input data "num_epochs": 10, # number of epochs to focus the agent for "standardize": True, # the input may contain SMILES strings that are invalid according to the agent # this atempts to clean up the input dataset "randomize": True, # this triggers data augmentation which is quite important for small datasets "adaptive_lr_config": adaptive_lr_config # setting the learning rate behavior } # write the configuration file to the disc configuration_JSON_path = os.path.join(output_dir, "transfer_learning_config.json") with open(configuration_JSON_path, 'w') as f: json.dump(configuration, f, indent=4, sort_keys=True) ###Output _____no_output_____ ###Markdown Run `REINVENT`Now it is time to execute `REINVENT` locally. The command-line execution looks like this:``` activate envionmentconda activate reinvent.v3.0 execute REINVENTpython /input.py .json``` ###Code %%capture captured_err_stream --no-stderr # execute REINVENT from the command-line !python {reinvent_dir}/input.py {configuration_JSON_path} # print the output to a file, just to have it for documentation with open(os.path.join(output_dir, "run.err"), 'w') as file: file.write(captured_err_stream.stdout) ###Output _____no_output_____ ###Markdown > **How to run this notebook (command-line)?**1. Install the `ReinventCommunity` environment:`conda env create -f environment.yml`2. Activate the environment:`conda activate ReinventCommunity`3. Execute `jupyter`:`jupyter notebook`4. Copy the link to a browser `REINVENT 2.0`: transfer learning mode demo The *transfer learning* mode can be used for either 1. Initial training of the Agent - where a newly built agent is trained from scratch while iterating through sufficiently large datasets over many epochs 2. Focusing of pre-trained Agent - where an already pre-trained agent is introduced to a small dataset for a small number of epochs.In this notebook we are going to illustrate the second scenario. The small dataset can consist of a few hundred molecules that normally share same features/scaffolds. The purpose of `Focusing` is to "learn" the common patterns/scaffolds in the structures. The `Focused` Agent will start producing with higher probablility the molecules with the common scaffolds. The `Focused` Agent can be used directly for *reinforcement learning* thus having as a starting point the small chemical space it has been focused on. ###Code # load dependencies import os import re import json import tempfile # --------- change these path variables as required reinvent_dir = os.path.expanduser("~/Desktop/Projects/Publications/2020/2020-04_REINVENT_2.0/Reinvent") reinvent_env = os.path.expanduser("~/miniconda3/envs/reinvent_shared.v2.1") output_dir = os.path.expanduser("~/Desktop/REINVENT_transfer_learning_demo") # --------- do not change # get the notebook's root path try: ipynb_path except NameError: ipynb_path = os.getcwd() # if required, generate a folder to store the results try: os.mkdir(output_dir) except FileExistsError: pass ###Output _____no_output_____ ###Markdown Setting up the configuration`REINVENT` has an entry point that loads a specified `JSON` file on startup. `JSON` is a low-level data format that allows to specify a fairly large number of parameters in a cascading fashion very quickly. The parameters are structured into *blocks* which can in turn contain blocks or simple values, such as *True* or *False*, strings and numbers. In this tutorial, we will go through the different blocks step-by-step, explaining their purpose and potential values for given parameters. Note, that while we will write out the configuration as a `JSON` file in the end, in `python` we handle the same information as a simple `dict`. ###Code # initialize the dictionary configuration = { "version": 2, # we are going to use REINVENT's newest release "run_type": "transfer_learning" # other run types: "scoring", "validation", # "transfer_learning", # "reinforcement_learning" and # "create_model" } # add block to specify whether to run locally or not and # where to store the results and logging configuration["logging"] = { "sender": "http://127.0.0.1", # only relevant if "recipient" is set to "remote" "recipient": "local", # either to local logging or use a remote REST-interface "logging_path": os.path.join(output_dir, "progress.log"), # where the run's output is stored "job_name": "Transfer Learning demo", # set an arbitrary job name for identification "job_id": "demo" # only relevant if "recipient" is set to "remote" } ###Output _____no_output_____ ###Markdown We will need to specify a path to an agent (parameter `model_path`), which can be a prior or trained agent. For the purpose of this notebook, we will use a prior shipped with the `REINVENT 2.0` repository. The code block below will define the settings for `adaptive_lr_config` property of the configuration. These parameters are defining the behavior of the learning rate. Note that the mode is set to `"constant"`. We recommend the default values as they dont play significant role for the purpose of focusing the agent. ###Code adaptive_lr_config = { "mode": "constant", # other modes: "exponential", "adaptive", "constant" "gamma": 0.8, "step": 1, "start": 5E-4, "min": 1E-5, "threshold": 1E-4, "average_steps": 4, "patience": 8, "restart_value": 1E-5, "sample_size": 10000, "restart_times": 0 } output_model_path = os.path.join(output_dir, "focused.agent") \ # The final focused agent will be named "focused.agent" # The intermediate steps will be named "focused.agent.1", "focused.agent.2", "focused.agent.3" and etc. # add the "parameters" block configuration["parameters"] = { "input_model_path": os.path.join(reinvent_dir, # path to prior or trained agent "data", "augmented.prior"), "output_model_path": output_model_path, # location to store the focused agent "input_smiles_path": os.path.join(reinvent_dir, # path to input smiles "data", # this is a dummy dataset consisting only of celecoxib "smiles.smi"), "save_every_n_epochs": 1, # how often to save the focused Agent. Here its stored after each epoch "batch_size": 128, # batch size the input data "num_epochs": 10, # number of epochs to focus the agent for "standardize": True, # the input may contain SMILES strings that are invalid according to the agent # this atempts to clean up the input dataset "randomize": True, # this triggers data augmentation which is quite important for small datasets "adaptive_lr_config": adaptive_lr_config # setting the learning rate behavior } # write the configuration file to the disc configuration_JSON_path = os.path.join(output_dir, "transfer_learning_config.json") with open(configuration_JSON_path, 'w') as f: json.dump(configuration, f, indent=4, sort_keys=True) ###Output _____no_output_____ ###Markdown Run `REINVENT`Now it is time to execute `REINVENT` locally. The command-line execution looks like this:``` activate envionmentconda activate reinvent_shared.v2.1 execute REINVENTpython /input.py .json``` ###Code %%capture captured_err_stream --no-stderr # execute REINVENT from the command-line !python {reinvent_dir}/input.py {configuration_JSON_path} # print the output to a file, just to have it for documentation with open(os.path.join(output_dir, "run.err"), 'w') as file: file.write(captured_err_stream.stdout) ###Output _____no_output_____

Assignment1/1_notmnist.ipynb

###Markdown Deep Learning=============Assignment 1------------The objective of this assignment is to learn about simple data curation practices, and familiarize you with some of the data we'll be reusing later.This notebook uses the [notMNIST](http://yaroslavvb.blogspot.com/2011/09/notmnist-dataset.html) dataset to be used with python experiments. This dataset is designed to look like the classic [MNIST](http://yann.lecun.com/exdb/mnist/) dataset, while looking a little more like real data: it's a harder task, and the data is a lot less 'clean' than MNIST. ###Code # These are all the modules we'll be using later. Make sure you can import them # before proceeding further. from __future__ import print_function import imageio import matplotlib.pyplot as plt import numpy as np import os import sys import tarfile from IPython.display import display, Image from sklearn.linear_model import LogisticRegression from six.moves.urllib.request import urlretrieve from six.moves import cPickle as pickle # Config the matplotlib backend as plotting inline in IPython %matplotlib inline ###Output _____no_output_____ ###Markdown First, we'll download the dataset to our local machine. The data consists of characters rendered in a variety of fonts on a 28x28 image. The labels are limited to 'A' through 'J' (10 classes). The training set has about 500k and the testset 19000 labeled examples. Given these sizes, it should be possible to train models quickly on any machine. ###Code url = 'https://commondatastorage.googleapis.com/books1000/' last_percent_reported = None data_root = '.' # Change me to store data elsewhere def download_progress_hook(count, blockSize, totalSize): """A hook to report the progress of a download. This is mostly intended for users with slow internet connections. Reports every 5% change in download progress. """ global last_percent_reported percent = int(count * blockSize * 100 / totalSize) if last_percent_reported != percent: if percent % 5 == 0: sys.stdout.write("%s%%" % percent) sys.stdout.flush() else: sys.stdout.write(".") sys.stdout.flush() last_percent_reported = percent def maybe_download(filename, expected_bytes, force=False): """Download a file if not present, and make sure it's the right size.""" dest_filename = os.path.join(data_root, filename) if force or not os.path.exists(dest_filename): print('Attempting to download:', filename) filename, _ = urlretrieve(url + filename, dest_filename, reporthook=download_progress_hook) print('\nDownload Complete!') statinfo = os.stat(dest_filename) if statinfo.st_size == expected_bytes: print('Found and verified', dest_filename) else: raise Exception( 'Failed to verify ' + dest_filename + '. Can you get to it with a browser?') return dest_filename train_filename = maybe_download('notMNIST_large.tar.gz', 247336696) test_filename = maybe_download('notMNIST_small.tar.gz', 8458043) ###Output Found and verified ./notMNIST_large.tar.gz Found and verified ./notMNIST_small.tar.gz ###Markdown Extract the dataset from the compressed .tar.gz file.This should give you a set of directories, labeled A through J. ###Code num_classes = 10 np.random.seed(133) def maybe_extract(filename, force=False): root = os.path.splitext(os.path.splitext(filename)[0])[0] # remove .tar.gz if os.path.isdir(root) and not force: # You may override by setting force=True. print('%s already present - Skipping extraction of %s.' % (root, filename)) else: print('Extracting data for %s. This may take a while. Please wait.' % root) tar = tarfile.open(filename) sys.stdout.flush() tar.extractall(data_root) tar.close() data_folders = [ os.path.join(root, d) for d in sorted(os.listdir(root)) if os.path.isdir(os.path.join(root, d))] if len(data_folders) != num_classes: raise Exception( 'Expected %d folders, one per class. Found %d instead.' % ( num_classes, len(data_folders))) print(data_folders) return data_folders train_folders = maybe_extract(train_filename) test_folders = maybe_extract(test_filename) ###Output ./notMNIST_large already present - Skipping extraction of ./notMNIST_large.tar.gz. ['./notMNIST_large/A', './notMNIST_large/B', './notMNIST_large/C', './notMNIST_large/D', './notMNIST_large/E', './notMNIST_large/F', './notMNIST_large/G', './notMNIST_large/H', './notMNIST_large/I', './notMNIST_large/J'] ./notMNIST_small already present - Skipping extraction of ./notMNIST_small.tar.gz. ['./notMNIST_small/A', './notMNIST_small/B', './notMNIST_small/C', './notMNIST_small/D', './notMNIST_small/E', './notMNIST_small/F', './notMNIST_small/G', './notMNIST_small/H', './notMNIST_small/I', './notMNIST_small/J'] ###Markdown ---Problem 1---------Let's take a peek at some of the data to make sure it looks sensible. Each exemplar should be an image of a character A through J rendered in a different font. Display a sample of the images that we just downloaded. Hint: you can use the package IPython.display.--- ###Code import random #Image(filename='test.png') #Taken from https://stackoverflow.com/questions/36006136/how-to-display-images-in-a-row-with-ipython-display/38556650 from matplotlib.pyplot import figure, imshow, axis from matplotlib.image import imread def showImagesHorizontally(list_of_files): fig = figure() number_of_files = len(list_of_files) for i in range(number_of_files): a=fig.add_subplot(1,number_of_files,i+1) # nrows, ncols, index. So, add a subplot at that position. image = imread(list_of_files[i]) # apparently you can read a list of files as one image? imshow(image,cmap='Greys_r') # show image as grey # imshow(image) # yup, looks odd if you don't use the cmap axis('off') # turn off axis lines and labels. #END COPIED CODE FROM https://stackoverflow.com/questions/36006136/how-to-display-images-in-a-row-with-ipython-display/38556650 exemplars_per_folder = 10 #note that the images are scaled to exemplars_by_folder = [] for folder in test_folders: filenames = os.listdir(folder) folder_exemplars = [] for i in range(0, exemplars_per_folder): file_choice = random.choice(filenames) path_to_chosen_file = os.path.join(folder, file_choice) folder_exemplars.append(path_to_chosen_file) exemplars_by_folder.append(folder_exemplars) for folder in exemplars_by_folder: # using code from https://stackoverflow.com/questions/36006136/how-to-display-images-in-a-row-with-ipython-display/38556650 showImagesHorizontally(folder) # the way I did it at first: # for exemplar in folder: # display(Image(exemplar)) ###Output _____no_output_____ ###Markdown Now let's load the data in a more manageable format. Since, depending on your computer setup you might not be able to fit it all in memory, we'll load each class into a separate dataset, store them on disk and curate them independently. Later we'll merge them into a single dataset of manageable size.We'll convert the entire dataset into a 3D array (image index, x, y) of floating point values, normalized to have approximately zero mean and standard deviation ~0.5 to make training easier down the road. A few images might not be readable, we'll just skip them. ###Code image_size = 28 # Pixel width and height. pixel_depth = 255.0 # Number of levels per pixel. def load_letter(folder, min_num_images): """Load the data for a single letter label.""" image_files = os.listdir(folder) dataset = np.ndarray(shape=(len(image_files), image_size, image_size), dtype=np.float32) print(folder) num_images = 0 for image in image_files: image_file = os.path.join(folder, image) try: image_data = (imageio.imread(image_file).astype(float) - pixel_depth / 2) / pixel_depth if image_data.shape != (image_size, image_size): raise Exception('Unexpected image shape: %s' % str(image_data.shape)) dataset[num_images, :, :] = image_data num_images = num_images + 1 except (IOError, ValueError) as e: print('Could not read:', image_file, ':', e, '- it\'s ok, skipping.') dataset = dataset[0:num_images, :, :] if num_images < min_num_images: raise Exception('Many fewer images than expected: %d < %d' % (num_images, min_num_images)) print('Full dataset tensor:', dataset.shape) print('Mean:', np.mean(dataset)) print('Standard deviation:', np.std(dataset)) return dataset def maybe_pickle(data_folders, min_num_images_per_class, force=False): dataset_names = [] for folder in data_folders: set_filename = folder + '.pickle' dataset_names.append(set_filename) if os.path.exists(set_filename) and not force: # You may override by setting force=True. print('%s already present - Skipping pickling.' % set_filename) else: print('Pickling %s.' % set_filename) dataset = load_letter(folder, min_num_images_per_class) try: with open(set_filename, 'wb') as f: pickle.dump(dataset, f, pickle.HIGHEST_PROTOCOL) except Exception as e: print('Unable to save data to', set_filename, ':', e) return dataset_names train_datasets = maybe_pickle(train_folders, 45000) test_datasets = maybe_pickle(test_folders, 1800) ###Output ./notMNIST_large/A.pickle already present - Skipping pickling. ./notMNIST_large/B.pickle already present - Skipping pickling. ./notMNIST_large/C.pickle already present - Skipping pickling. ./notMNIST_large/D.pickle already present - Skipping pickling. ./notMNIST_large/E.pickle already present - Skipping pickling. ./notMNIST_large/F.pickle already present - Skipping pickling. ./notMNIST_large/G.pickle already present - Skipping pickling. ./notMNIST_large/H.pickle already present - Skipping pickling. ./notMNIST_large/I.pickle already present - Skipping pickling. ./notMNIST_large/J.pickle already present - Skipping pickling. ./notMNIST_small/A.pickle already present - Skipping pickling. ./notMNIST_small/B.pickle already present - Skipping pickling. ./notMNIST_small/C.pickle already present - Skipping pickling. ./notMNIST_small/D.pickle already present - Skipping pickling. ./notMNIST_small/E.pickle already present - Skipping pickling. ./notMNIST_small/F.pickle already present - Skipping pickling. ./notMNIST_small/G.pickle already present - Skipping pickling. ./notMNIST_small/H.pickle already present - Skipping pickling. ./notMNIST_small/I.pickle already present - Skipping pickling. ./notMNIST_small/J.pickle already present - Skipping pickling. ###Markdown ---Problem 2---------Let's verify that the data still looks good. Displaying a sample of the labels and images from the ndarray. Hint: you can use matplotlib.pyplot.--- ###Code #Colin Leong's solution to Problem 2. # unpickling takes forever so I'm breaking it out into its own cell def load_pickled_dataset(name_of_pickle_file): pkl_file = open(name_of_pickle_file, 'rb') data = pickle.load(pkl_file) return data def unpickle_datasets(datasets): unpickled_datasets = [] for dataset in datasets: print("unpickling dataset {}...".format(dataset)) data = load_pickled_dataset(dataset) unpickled_datasets.append(data) return unpickled_datasets unpickled_train = unpickle_datasets(train_datasets) unpickled_test = unpickle_datasets(test_datasets) #Problem 2 solution, part 2: pick at random from unpickled data, and display. def show_images(list_of_images): fig = figure() number_of_images = len(list_of_images) for i in range(number_of_images): a=fig.add_subplot(1,number_of_images,i+1) # nrows, ncols, index. So, add a subplot at that position. image = list_of_images[i] imshow(image,cmap='Greys_r') # show image as grey axis('off') # turn off axis lines and labels. plt.show() def get_one_sample_from_each_dataset(datasets): samples = [] for dataset in datasets: pic = random.choice(dataset) samples.append(pic) return samples train_samples = get_one_sample_from_each_dataset(unpickled_train) test_samples = get_one_sample_from_each_dataset(unpickled_train) # print(train_samples) show_images(train_samples) show_images(test_samples) ###Output _____no_output_____ ###Markdown ---Problem 3---------Another check: we expect the data to be balanced across classes. Verify that.--- ###Code # how the heck do I do that. def get_some_exemplars(unpickled_class_dataset, number=5): exemplars = [] for i in range(0,number): exemplars.append(random.choice(unpickled_class_dataset)) return exemplars def get_dataset_stats(unpickled_datasets, name): for index, class_dataset in enumerate(unpickled_datasets): class_exemplars = get_some_exemplars(class_dataset) print("Getting examples for {0}, class #{1}".format(name, index)) print("Some examples of this class:") show_images(class_exemplars) print("for this class we have {0} data items\n\n".format(len(class_dataset))) get_dataset_stats(unpickled_train, "train data") get_dataset_stats(unpickled_test, "test data") ###Output Getting examples for train data, class #0 Some examples of this class: ###Markdown Merge and prune the training data as needed. Depending on your computer setup, you might not be able to fit it all in memory, and you can tune `train_size` as needed. The labels will be stored into a separate array of integers 0 through 9.Also create a validation dataset for hyperparameter tuning. ###Code def make_arrays(nb_rows, img_size): if nb_rows: dataset = np.ndarray((nb_rows, img_size, img_size), dtype=np.float32) labels = np.ndarray(nb_rows, dtype=np.int32) else: dataset, labels = None, None return dataset, labels def merge_datasets(pickle_files, train_size, valid_size=0): num_classes = len(pickle_files) valid_dataset, valid_labels = make_arrays(valid_size, image_size) train_dataset, train_labels = make_arrays(train_size, image_size) vsize_per_class = valid_size // num_classes tsize_per_class = train_size // num_classes start_v, start_t = 0, 0 end_v, end_t = vsize_per_class, tsize_per_class end_l = vsize_per_class+tsize_per_class for label, pickle_file in enumerate(pickle_files): try: with open(pickle_file, 'rb') as f: letter_set = pickle.load(f) # let's shuffle the letters to have random validation and training set np.random.shuffle(letter_set) if valid_dataset is not None: valid_letter = letter_set[:vsize_per_class, :, :] valid_dataset[start_v:end_v, :, :] = valid_letter valid_labels[start_v:end_v] = label start_v += vsize_per_class end_v += vsize_per_class train_letter = letter_set[vsize_per_class:end_l, :, :] train_dataset[start_t:end_t, :, :] = train_letter train_labels[start_t:end_t] = label start_t += tsize_per_class end_t += tsize_per_class except Exception as e: print('Unable to process data from', pickle_file, ':', e) raise return valid_dataset, valid_labels, train_dataset, train_labels train_size = 200000 valid_size = 10000 test_size = 10000 valid_dataset, valid_labels, train_dataset, train_labels = merge_datasets( train_datasets, train_size, valid_size) _, _, test_dataset, test_labels = merge_datasets(test_datasets, test_size) print('Training:', train_dataset.shape, train_labels.shape) print('Validation:', valid_dataset.shape, valid_labels.shape) print('Testing:', test_dataset.shape, test_labels.shape) ###Output Training: (200000, 28, 28) (200000,) Validation: (10000, 28, 28) (10000,) Testing: (10000, 28, 28) (10000,) ###Markdown Next, we'll randomize the data. It's important to have the labels well shuffled for the training and test distributions to match. ###Code def randomize(dataset, labels): permutation = np.random.permutation(labels.shape[0]) shuffled_dataset = dataset[permutation,:,:] shuffled_labels = labels[permutation] return shuffled_dataset, shuffled_labels train_dataset, train_labels = randomize(train_dataset, train_labels) test_dataset, test_labels = randomize(test_dataset, test_labels) valid_dataset, valid_labels = randomize(valid_dataset, valid_labels) ###Output _____no_output_____ ###Markdown ---Problem 4---------Convince yourself that the data is still good after shuffling!--- ###Code #problem 4 solution: label_to_char = {0:'a',1:'b',2:'c',3:'d',4:'e',5:'f',6:'g',7:'h',8:'i',9:'j'} def labels_to_chars(labels): label_chars =[] for label in labels: label_char = label_to_char[label] label_chars.append(label_char) return label_chars def get_matching_items_randomly_from_two_lists(first, second, num_tuples=5): #assuming the length is the same... max_index = len(first)-1 #solution adapted from https://stackoverflow.com/questions/19485641/python-random-sample-of-two-arrays-but-matching-indices idx = np.random.choice(np.arange(len(first)), num_tuples, replace=False) # print("picking {0} random items using idx {1}".format(num_tuples, idx)) # print(type(idx)) first_samples = first[idx] second_samples = second[idx] return first_samples, second_samples def check_after_shuffle(dataset_name, dataset_to_check, labels_to_check, num_samples=15): imgs, labels = get_matching_items_randomly_from_two_lists(dataset_to_check, labels_to_check,num_samples) label_chars = labels_to_chars(labels) print("sample {0} labels:{1}".format(dataset_name,label_chars)) show_images(imgs) num_samples = 12 check_after_shuffle("train", train_dataset, train_labels, num_samples) check_after_shuffle("val", valid_dataset, valid_labels, num_samples) check_after_shuffle("test", test_dataset, test_labels, num_samples) ###Output sample train labels:['i', 'd', 'i', 'd', 'i', 'i', 'f', 'd', 'b', 'g', 'c', 'i'] ###Markdown Finally, let's save the data for later reuse: ###Code pickle_file = os.path.join(data_root, 'notMNIST.pickle') try: f = open(pickle_file, 'wb') save = { 'train_dataset': train_dataset, 'train_labels': train_labels, 'valid_dataset': valid_dataset, 'valid_labels': valid_labels, 'test_dataset': test_dataset, 'test_labels': test_labels, } pickle.dump(save, f, pickle.HIGHEST_PROTOCOL) f.close() except Exception as e: print('Unable to save data to', pickle_file, ':', e) raise statinfo = os.stat(pickle_file) print('Compressed pickle size:', statinfo.st_size) ###Output Compressed pickle size: 690800441 ###Markdown ---Problem 5---------By construction, this dataset might contain a lot of overlapping samples, including training data that's also contained in the validation and test set! Overlap between training and test can skew the results if you expect to use your model in an environment where there is never an overlap, but are actually ok if you expect to see training samples recur when you use it.Measure how much overlap there is between training, validation and test samples.Optional questions:- What about near duplicates between datasets? (images that are almost identical)- Create a sanitized validation and test set, and compare your accuracy on those in subsequent assignments.--- ###Code # train_dataset = test_dataset # valid_dataset = test_dataset # Checking overlap: how the heck would I do this? Check filenames? Hashing? def generate_hashes(list_of_numpy_arrays): list_of_numpy_arrays.flags.writeable=False hashes=[hash(item.data) for item in list_of_numpy_arrays] return hashes def check_within_dataset(hashes, hashes_set, name): hashes_len = len(hashes) set_len = len(hashes_set) diff = hashes_len-set_len print("within {0} dataset, there are {1} items, but only {2} unique items, which works out to {3} items that are repeats".format(name, hashes_len, set_len, diff)) return diff def check_intersections(set1, set2, name1, name2): intersections=set1.intersection(set2) print("between {0} and {1} there are {2} unique items that are in both at least once".format(name1,name2,len(intersections))) return intersections train_hashes = generate_hashes(train_dataset) valid_hashes = generate_hashes(valid_dataset) test_hashes = generate_hashes(test_dataset) # train_hashes = [1, 2, 3] # valid_hashes = [1, 2, 3] # test_hashes = [1, 2, 3, 3] train_hashes_set=set(train_hashes) train_repeats = check_within_dataset(train_hashes,train_hashes_set, "train") valid_hashes_set = set(valid_hashes) valid_repeats = check_within_dataset(valid_hashes,valid_hashes_set, "valid") test_hashes_set=set(test_hashes) test_repeats = check_within_dataset(test_hashes,test_hashes_set, "test") repeats_within_datasets = train_repeats + valid_repeats + test_repeats print("Total repeats within datasets: {}".format(repeats_within_datasets)) train_val_intersections = check_intersections(train_hashes_set, valid_hashes_set, "train", "valid") train_test_intersections = check_intersections(train_hashes_set, test_hashes_set, "train", "valid") val_test_intersections = check_intersections(valid_hashes_set, test_hashes_set, "valid", "test") intersected_train_items = train_val_intersections.union(train_test_intersections) intersected_valid_items = train_val_intersections.union(val_test_intersections) intersected_test_items = train_test_intersections.union(val_test_intersections) print("Number of unique items in {} that can be found in other sets: {}".format("train",len(intersected_train_items))) print("Number of unique items in {} that can be found in other sets: {}".format("valid",len(intersected_valid_items))) print("Number of unique items in {} that can be found in other sets: {}".format("test",len(intersected_test_items))) all_hashes = train_hashes+valid_hashes+test_hashes all_hashes_set = set(all_hashes) all_repeats = check_within_dataset(all_hashes, all_hashes_set, "all") repeats_percent = float(all_repeats)/float(len(all_hashes)) * 100 items_only_in_train = train_hashes_set - valid_hashes_set - test_hashes_set items_only_in_valid = valid_hashes_set - train_hashes_set - test_hashes_set items_only_in_test = test_hashes_set - train_hashes_set - valid_hashes_set print("There are {} items that only exist in train".format(len(items_only_in_train))) print("There are {} items that only exist in valid".format(len(items_only_in_valid))) print("There are {} items that only exist in test".format(len(items_only_in_test))) set([1, 2, 3]) - set([2]) - set([3]) print("Total percentage of repeat items in all datasets is about {:.2f} %".format(repeats_percent)) print("Total number of repeat items in all datasets is {}".format(all_repeats)) repeats_due_to_overlap = all_repeats - repeats_within_datasets overlap_percent = float(repeats_due_to_overlap)/float(len(all_hashes)) *100 print("We previously found that repeats within datasets totaled to {}".format(repeats_within_datasets)) print("Repeats due to overlap is therefore {0}. \nOut of {1} total items, that gives an overlap percentage of {2:.2f}%".format(repeats_due_to_overlap, len(all_hashes), overlap_percent)) ###Output within train dataset, there are 200000 items, but only 187350 unique items, which works out to 12650 items that are repeats within valid dataset, there are 10000 items, but only 9863 unique items, which works out to 137 items that are repeats within test dataset, there are 10000 items, but only 9802 unique items, which works out to 198 items that are repeats Total repeats within datasets: 12985 between train and valid there are 1003 unique items that are in both at least once between train and valid there are 1174 unique items that are in both at least once between valid and test there are 72 unique items that are in both at least once Number of unique items in train that can be found in other sets: 2153 Number of unique items in valid that can be found in other sets: 1051 Number of unique items in test that can be found in other sets: 1222 within all dataset, there are 220000 items, but only 204790 unique items, which works out to 15210 items that are repeats There are 185197 items that only exist in train There are 8812 items that only exist in valid There are 8580 items that only exist in test Total percentage of repeat items in all datasets is about 6.91 % Total number of repeat items in all datasets is 15210 We previously found that repeats within datasets totaled to 12985 Repeats due to overlap is therefore 2225. Out of 220000 total items, that gives an overlap percentage of 1.01% ###Markdown ---Problem 6---------Let's get an idea of what an off-the-shelf classifier can give you on this data. It's always good to check that there is something to learn, and that it's a problem that is not so trivial that a canned solution solves it.Train a simple model on this data using 50, 100, 1000 and 5000 training samples. Hint: you can use the LogisticRegression model from sklearn.linear_model.Optional question: train an off-the-shelf model on all the data!--- ###Code #Training time. def reshape_to_sklearn_format(dataset): num_items, nx, ny = dataset.shape return dataset.reshape(num_items, nx*ny) default_settings_classifier = LogisticRegression() num_to_train_with = 500 #num_to_train_with = len(train_dataset) #sample_data_for_training, sample_labels_for_training = train_dataset[:num_to_train_with], train_labels[:num_to_train_with] sample_data_for_training, sample_labels_for_training = get_matching_items_randomly_from_two_lists(train_dataset, train_labels, num_to_train_with) num_to_test_with = 1010 sample_data_for_testing, sample_labels_for_testing = get_matching_items_randomly_from_two_lists(train_dataset, train_labels, num_to_test_with) # Gotta reshape, according to https://stackoverflow.com/questions/34972142/sklearn-logistic-regression-valueerror-found-array-with-dim-3-estimator-expec # Basically we want the 28x28 images flattened out. sample_data_for_training = reshape_to_sklearn_format(sample_data_for_training) sample_data_for_testing = reshape_to_sklearn_format(sample_data_for_testing) default_settings_classifier.fit(sample_data_for_training, sample_labels_for_training) df_score = default_settings_classifier.score(sample_data_for_testing, sample_labels_for_testing) # Settings lifted from # http://scikit-learn.org/stable/auto_examples/linear_model/plot_sparse_logistic_regression_mnist.html # without understanding fancy_settings_classifier = LogisticRegression(C=50. / num_to_train_with, multi_class='multinomial', penalty='l1', solver='saga', tol=0.1) fancy_settings_classifier.fit(sample_data_for_training, sample_labels_for_training) fs_score = fancy_settings_classifier.score(sample_data_for_testing, sample_labels_for_testing) fancy_settings_classifier_l2 = LogisticRegression(C=50. / num_to_train_with, multi_class='multinomial', penalty='l2', solver='saga', tol=0.1) fancy_settings_classifier_l2.fit(sample_data_for_training, sample_labels_for_training) fs_l2_score = fancy_settings_classifier_l2.score(sample_data_for_testing, sample_labels_for_testing) print("Score for classifier with default settings: {}".format(df_score)) print("Score for classifier with fancy settings and l1: {}".format(fs_score)) print("Score for classifier with fancy settings and l2: {}".format(fs_l2_score)) solver_list = ['newton-cg', 'lbfgs', 'sag', 'saga'] for choice in solver_list: print("trying solver {}".format(choice))) classifier = LogisticRegression(solver=choice, penalty='l2') classifier.fit(sample_data_for_training, sample_labels_for_training) classifier.score(sample_data_for_testing, sample_labels_for_testing) print("Score for classifier using solver {0}: {1}".format(choice, df_score)) ###Output Score for classifier with default settings: 0.774257425743 Score for classifier with fancy settings: 0.70396039604 Score for classifier with fancy settings and l2: 0.805940594059 Score for classifier using solver newton-cg: 0.774257425743 Score for classifier using solver lbfgs: 0.774257425743 Score for classifier using solver sag: 0.774257425743 Score for classifier using solver saga: 0.774257425743 ###Markdown Deep Learning=============Assignment 1------------The objective of this assignment is to learn about simple data curation practices, and familiarize you with some of the data we'll be reusing later.This notebook uses the [notMNIST](http://yaroslavvb.blogspot.com/2011/09/notmnist-dataset.html) dataset to be used with python experiments. This dataset is designed to look like the classic [MNIST](http://yann.lecun.com/exdb/mnist/) dataset, while looking a little more like real data: it's a harder task, and the data is a lot less 'clean' than MNIST. ###Code # These are all the modules we'll be using later. Make sure you can import them # before proceeding further. from __future__ import print_function import matplotlib.pyplot as plt import numpy as np import os import sys import tarfile from IPython.display import display, Image from scipy import ndimage from sklearn.linear_model import LogisticRegression from six.moves.urllib.request import urlretrieve from six.moves import cPickle as pickle # Config the matlotlib backend as plotting inline in IPython %matplotlib inline ###Output _____no_output_____ ###Markdown First, we'll download the dataset to our local machine. The data consists of characters rendered in a variety of fonts on a 28x28 image. The labels are limited to 'A' through 'J' (10 classes). The training set has about 500k and the testset 19000 labelled examples. Given these sizes, it should be possible to train models quickly on any machine. ###Code url = 'http://commondatastorage.googleapis.com/books1000/' last_percent_reported = None def download_progress_hook(count, blockSize, totalSize): """A hook to report the progress of a download. This is mostly intended for users with slow internet connections. Reports every 1% change in download progress. """ global last_percent_reported percent = int(count * blockSize * 100 / totalSize) if last_percent_reported != percent: if percent % 5 == 0: sys.stdout.write("%s%%" % percent) sys.stdout.flush() else: sys.stdout.write(".") sys.stdout.flush() last_percent_reported = percent def maybe_download(filename, expected_bytes, force=False): """Download a file if not present, and make sure it's the right size.""" if force or not os.path.exists(filename): print('Attempting to download:', filename) filename, _ = urlretrieve(url + filename, filename, reporthook=download_progress_hook) print('\nDownload Complete!') statinfo = os.stat(filename) if statinfo.st_size == expected_bytes: print('Found and verified', filename) else: raise Exception( 'Failed to verify ' + filename + '. Can you get to it with a browser?') return filename train_filename = maybe_download('notMNIST_large.tar.gz', 247336696) test_filename = maybe_download('notMNIST_small.tar.gz', 8458043) ###Output Attempting to download: notMNIST_large.tar.gz 0%....5%....10%....15%....20%....25%....30%....35%....40%....45%....50%....55%....60%....65%....70%....75%....80%....85%....90%....95%....100% Download Complete! Found and verified notMNIST_large.tar.gz Attempting to download: notMNIST_small.tar.gz 0%....5%....10%....15%....20%....25%....30%....35%....40%....45%....50%....55%....60%....65%....70%....75%....80%....85%....90%....95%....100% Download Complete! Found and verified notMNIST_small.tar.gz ###Markdown Extract the dataset from the compressed .tar.gz file.This should give you a set of directories, labelled A through J. ###Code num_classes = 10 np.random.seed(133) def maybe_extract(filename, force=False): root = os.path.splitext(os.path.splitext(filename)[0])[0] # remove .tar.gz if os.path.isdir(root) and not force: # You may override by setting force=True. print('%s already present - Skipping extraction of %s.' % (root, filename)) else: print('Extracting data for %s. This may take a while. Please wait.' % root) tar = tarfile.open(filename) sys.stdout.flush() tar.extractall() tar.close() data_folders = [ os.path.join(root, d) for d in sorted(os.listdir(root)) if os.path.isdir(os.path.join(root, d))] if len(data_folders) != num_classes: raise Exception( 'Expected %d folders, one per class. Found %d instead.' % ( num_classes, len(data_folders))) print(data_folders) return data_folders train_folders = maybe_extract(train_filename) test_folders = maybe_extract(test_filename) ###Output Extracting data for notMNIST_large. This may take a while. Please wait. ['notMNIST_large/A', 'notMNIST_large/B', 'notMNIST_large/C', 'notMNIST_large/D', 'notMNIST_large/E', 'notMNIST_large/F', 'notMNIST_large/G', 'notMNIST_large/H', 'notMNIST_large/I', 'notMNIST_large/J'] Extracting data for notMNIST_small. This may take a while. Please wait. ['notMNIST_small/A', 'notMNIST_small/B', 'notMNIST_small/C', 'notMNIST_small/D', 'notMNIST_small/E', 'notMNIST_small/F', 'notMNIST_small/G', 'notMNIST_small/H', 'notMNIST_small/I', 'notMNIST_small/J'] ###Markdown ---Problem 1---------Let's take a peek at some of the data to make sure it looks sensible. Each exemplar should be an image of a character A through J rendered in a different font. Display a sample of the images that we just downloaded. Hint: you can use the package IPython.display.--- ###Code from IPython.display import Image DIR = 'notMNIST_large/A/' files = os.listdir(DIR) ct = 10 for fil in files: filname = DIR + fil display(Image(filename=filname)) ct -= 1 if(ct == 0): break ###Output _____no_output_____ ###Markdown Now let's load the data in a more manageable format. Since, depending on your computer setup you might not be able to fit it all in memory, we'll load each class into a separate dataset, store them on disk and curate them independently. Later we'll merge them into a single dataset of manageable size.We'll convert the entire dataset into a 3D array (image index, x, y) of floating point values, normalized to have approximately zero mean and standard deviation ~0.5 to make training easier down the road. A few images might not be readable, we'll just skip them. ###Code image_size = 28 # Pixel width and height. pixel_depth = 255.0 # Number of levels per pixel. def load_letter(folder, min_num_images): """Load the data for a single letter label.""" image_files = os.listdir(folder) dataset = np.ndarray(shape=(len(image_files), image_size, image_size), dtype=np.float32) print(folder) num_images = 0 for image in image_files: image_file = os.path.join(folder, image) try: image_data = (ndimage.imread(image_file).astype(float) - pixel_depth / 2) / pixel_depth if image_data.shape != (image_size, image_size): raise Exception('Unexpected image shape: %s' % str(image_data.shape)) dataset[num_images, :, :] = image_data num_images = num_images + 1 except IOError as e: print('Could not read:', image_file, ':', e, '- it\'s ok, skipping.') dataset = dataset[0:num_images, :, :] if num_images < min_num_images: raise Exception('Many fewer images than expected: %d < %d' % (num_images, min_num_images)) print('Full dataset tensor:', dataset.shape) print('Mean:', np.mean(dataset)) print('Standard deviation:', np.std(dataset)) return dataset def maybe_pickle(data_folders, min_num_images_per_class, force=False): dataset_names = [] for folder in data_folders: set_filename = folder + '.pickle' dataset_names.append(set_filename) if os.path.exists(set_filename) and not force: # You may override by setting force=True. print('%s already present - Skipping pickling.' % set_filename) else: print('Pickling %s.' % set_filename) dataset = load_letter(folder, min_num_images_per_class) try: with open(set_filename, 'wb') as f: pickle.dump(dataset, f, pickle.HIGHEST_PROTOCOL) except Exception as e: print('Unable to save data to', set_filename, ':', e) return dataset_names train_datasets = maybe_pickle(train_folders, 45000) test_datasets = maybe_pickle(test_folders, 1800) ###Output Pickling notMNIST_large/A.pickle. notMNIST_large/A Could not read: notMNIST_large/A/Um9tYW5hIEJvbGQucGZi.png : cannot identify image file 'notMNIST_large/A/Um9tYW5hIEJvbGQucGZi.png' - it's ok, skipping. Could not read: notMNIST_large/A/RnJlaWdodERpc3BCb29rSXRhbGljLnR0Zg==.png : cannot identify image file 'notMNIST_large/A/RnJlaWdodERpc3BCb29rSXRhbGljLnR0Zg==.png' - it's ok, skipping. Could not read: notMNIST_large/A/SG90IE11c3RhcmQgQlROIFBvc3Rlci50dGY=.png : cannot identify image file 'notMNIST_large/A/SG90IE11c3RhcmQgQlROIFBvc3Rlci50dGY=.png' - it's ok, skipping. Full dataset tensor: (52909, 28, 28) Mean: -0.12825 Standard deviation: 0.443121 Pickling notMNIST_large/B.pickle. notMNIST_large/B Could not read: notMNIST_large/B/TmlraXNFRi1TZW1pQm9sZEl0YWxpYy5vdGY=.png : cannot identify image file 'notMNIST_large/B/TmlraXNFRi1TZW1pQm9sZEl0YWxpYy5vdGY=.png' - it's ok, skipping. Full dataset tensor: (52911, 28, 28) Mean: -0.00756303 Standard deviation: 0.454491 Pickling notMNIST_large/C.pickle. notMNIST_large/C Full dataset tensor: (52912, 28, 28) Mean: -0.142258 Standard deviation: 0.439807 Pickling notMNIST_large/D.pickle. notMNIST_large/D Could not read: notMNIST_large/D/VHJhbnNpdCBCb2xkLnR0Zg==.png : cannot identify image file 'notMNIST_large/D/VHJhbnNpdCBCb2xkLnR0Zg==.png' - it's ok, skipping. Full dataset tensor: (52911, 28, 28) Mean: -0.0573677 Standard deviation: 0.455647 Pickling notMNIST_large/E.pickle. notMNIST_large/E Full dataset tensor: (52912, 28, 28) Mean: -0.069899 Standard deviation: 0.452941 Pickling notMNIST_large/F.pickle. notMNIST_large/F Full dataset tensor: (52912, 28, 28) Mean: -0.125583 Standard deviation: 0.447089 Pickling notMNIST_large/G.pickle. notMNIST_large/G Full dataset tensor: (52912, 28, 28) Mean: -0.0945813 Standard deviation: 0.44624 Pickling notMNIST_large/H.pickle. notMNIST_large/H Full dataset tensor: (52912, 28, 28) Mean: -0.0685222 Standard deviation: 0.454232 Pickling notMNIST_large/I.pickle. notMNIST_large/I Full dataset tensor: (52912, 28, 28) Mean: 0.0307862 Standard deviation: 0.468899 Pickling notMNIST_large/J.pickle. notMNIST_large/J Full dataset tensor: (52911, 28, 28) Mean: -0.153359 Standard deviation: 0.443656 Pickling notMNIST_small/A.pickle. notMNIST_small/A Could not read: notMNIST_small/A/RGVtb2NyYXRpY2FCb2xkT2xkc3R5bGUgQm9sZC50dGY=.png : cannot identify image file 'notMNIST_small/A/RGVtb2NyYXRpY2FCb2xkT2xkc3R5bGUgQm9sZC50dGY=.png' - it's ok, skipping. Full dataset tensor: (1872, 28, 28) Mean: -0.132626 Standard deviation: 0.445128 Pickling notMNIST_small/B.pickle. notMNIST_small/B Full dataset tensor: (1873, 28, 28) Mean: 0.00535608 Standard deviation: 0.457115 Pickling notMNIST_small/C.pickle. notMNIST_small/C Full dataset tensor: (1873, 28, 28) Mean: -0.141521 Standard deviation: 0.44269 Pickling notMNIST_small/D.pickle. notMNIST_small/D Full dataset tensor: (1873, 28, 28) Mean: -0.0492167 Standard deviation: 0.459759 Pickling notMNIST_small/E.pickle. notMNIST_small/E Full dataset tensor: (1873, 28, 28) Mean: -0.0599148 Standard deviation: 0.45735 Pickling notMNIST_small/F.pickle. notMNIST_small/F Could not read: notMNIST_small/F/Q3Jvc3NvdmVyIEJvbGRPYmxpcXVlLnR0Zg==.png : cannot identify image file 'notMNIST_small/F/Q3Jvc3NvdmVyIEJvbGRPYmxpcXVlLnR0Zg==.png' - it's ok, skipping. Full dataset tensor: (1872, 28, 28) Mean: -0.118185 Standard deviation: 0.452279 Pickling notMNIST_small/G.pickle. notMNIST_small/G Full dataset tensor: (1872, 28, 28) Mean: -0.0925503 Standard deviation: 0.449006 Pickling notMNIST_small/H.pickle. notMNIST_small/H Full dataset tensor: (1872, 28, 28) Mean: -0.0586892 Standard deviation: 0.458759 Pickling notMNIST_small/I.pickle. notMNIST_small/I Full dataset tensor: (1872, 28, 28) Mean: 0.0526451 Standard deviation: 0.471894 Pickling notMNIST_small/J.pickle. notMNIST_small/J Full dataset tensor: (1872, 28, 28) Mean: -0.151689 Standard deviation: 0.448014 ###Markdown ---Problem 2---------Let's verify that the data still looks good. Displaying a sample of the labels and images from the ndarray. Hint: you can use matplotlib.pyplot.--- ###Code train_dataset = pickle.load(open(train_datasets[0], "rb")) idx=np.random.randint(0, len(train_dataset)) %matplotlib inline plt.imshow(train_dataset[idx]) plt.title('A') ###Output _____no_output_____ ###Markdown ---Problem 3---------Another check: we expect the data to be balanced across classes. Verify that.--- ###Code for ch in range(ord('a'), ord('j') + 1): with open(train_datasets[ch - ord('a')], "rb") as fil: data = pickle.load(fil) print("Size for class " + chr(ch) + " is " + str(len(data))) ###Output Size for class a is 52909 Size for class b is 52911 Size for class c is 52912 Size for class d is 52911 Size for class e is 52912 Size for class f is 52912 Size for class g is 52912 Size for class h is 52912 Size for class i is 52912 Size for class j is 52911 ###Markdown Merge and prune the training data as needed. Depending on your computer setup, you might not be able to fit it all in memory, and you can tune `train_size` as needed. The labels will be stored into a separate array of integers 0 through 9.Also create a validation dataset for hyperparameter tuning. ###Code def make_arrays(nb_rows, img_size): if nb_rows: dataset = np.ndarray((nb_rows, img_size, img_size), dtype=np.float32) labels = np.ndarray(nb_rows, dtype=np.int32) else: dataset, labels = None, None return dataset, labels def merge_datasets(pickle_files, train_size, valid_size=0): num_classes = len(pickle_files) valid_dataset, valid_labels = make_arrays(valid_size, image_size) train_dataset, train_labels = make_arrays(train_size, image_size) vsize_per_class = valid_size // num_classes tsize_per_class = train_size // num_classes start_v, start_t = 0, 0 end_v, end_t = vsize_per_class, tsize_per_class end_l = vsize_per_class+tsize_per_class for label, pickle_file in enumerate(pickle_files): try: with open(pickle_file, 'rb') as f: letter_set = pickle.load(f) # let's shuffle the letters to have random validation and training set np.random.shuffle(letter_set) if valid_dataset is not None: valid_letter = letter_set[:vsize_per_class, :, :] valid_dataset[start_v:end_v, :, :] = valid_letter valid_labels[start_v:end_v] = label start_v += vsize_per_class end_v += vsize_per_class train_letter = letter_set[vsize_per_class:end_l, :, :] train_dataset[start_t:end_t, :, :] = train_letter train_labels[start_t:end_t] = label start_t += tsize_per_class end_t += tsize_per_class except Exception as e: print('Unable to process data from', pickle_file, ':', e) raise return valid_dataset, valid_labels, train_dataset, train_labels train_size = 200000 valid_size = 10000 test_size = 10000 valid_dataset, valid_labels, train_dataset, train_labels = merge_datasets( train_datasets, train_size, valid_size) _, _, test_dataset, test_labels = merge_datasets(test_datasets, test_size) print('Training:', train_dataset.shape, train_labels.shape) print('Validation:', valid_dataset.shape, valid_labels.shape) print('Testing:', test_dataset.shape, test_labels.shape) ###Output Training: (200000, 28, 28) (200000,) Validation: (10000, 28, 28) (10000,) Testing: (10000, 28, 28) (10000,) ###Markdown Next, we'll randomize the data. It's important to have the labels well shuffled for the training and test distributions to match. ###Code def randomize(dataset, labels): permutation = np.random.permutation(labels.shape[0]) shuffled_dataset = dataset[permutation,:,:] shuffled_labels = labels[permutation] return shuffled_dataset, shuffled_labels train_dataset, train_labels = randomize(train_dataset, train_labels) test_dataset, test_labels = randomize(test_dataset, test_labels) valid_dataset, valid_labels = randomize(valid_dataset, valid_labels) ###Output _____no_output_____ ###Markdown ---Problem 4---------Convince yourself that the data is still good after shuffling!--- ###Code %matplotlib inline idx=np.random.randint(0, len(train_dataset)) plt.imshow(train_dataset[idx]) plt.title(chr(train_labels[idx]+ord('A'))) ###Output _____no_output_____ ###Markdown Finally, let's save the data for later reuse: ###Code pickle_file = 'notMNIST.pickle' try: f = open(pickle_file, 'wb') save = { 'train_dataset': train_dataset, 'train_labels': train_labels, 'valid_dataset': valid_dataset, 'valid_labels': valid_labels, 'test_dataset': test_dataset, 'test_labels': test_labels, } pickle.dump(save, f, pickle.HIGHEST_PROTOCOL) f.close() except Exception as e: print('Unable to save data to', pickle_file, ':', e) raise statinfo = os.stat(pickle_file) print('Compressed pickle size:', statinfo.st_size) ###Output Compressed pickle size: 690800441 ###Markdown ---Problem 5---------By construction, this dataset might contain a lot of overlapping samples, including training data that's also contained in the validation and test set! Overlap between training and test can skew the results if you expect to use your model in an environment where there is never an overlap, but are actually ok if you expect to see training samples recur when you use it.Measure how much overlap there is between training, validation and test samples.Optional questions:- What about near duplicates between datasets? (images that are almost identical)- Create a sanitized validation and test set, and compare your accuracy on those in subsequent assignments.--- ###Code from hashlib import md5 %time train = set([md5(x).hexdigest() for x in train_dataset]) %time test = set([md5(x).hexdigest() for x in test_dataset]) %time valid = set([md5(x).hexdigest() for x in valid_dataset]) print("Overlap TRAIN TEST = ", len(train.intersection(test))) print("Overlap TRAIN VALID = ", len(train.intersection(valid))) print("Overlap VALID TEST = ", len(valid.intersection(test))) total_dataset = np.concatenate((train_dataset, test_dataset, valid_dataset)) total_labels = np.concatenate((train_labels, test_labels, valid_labels)) dataset = [] labels = [] hashes=set() for i in xrange(len(total_dataset)): cur = md5(total_dataset[i]).hexdigest() if not cur in hashes: hashes.add(cur) dataset.append(total_dataset[i]) labels.append(total_labels[i]) def randomize(dataset, labels): permutation = np.random.permutation(labels.shape[0]) shuffled_dataset = dataset[permutation,:,:] shuffled_labels = labels[permutation] return shuffled_dataset, shuffled_labels dataset, labels = randomize(np.array(dataset), np.array(labels)) valid_dataset = dataset[:10000] valid_labels = labels[:10000] test_dataset = dataset[10000:20000] test_labels = labels[10000:20000] train_dataset = dataset[20000:] train_labels = labels[20000:] sanitized_save = { 'train_dataset': train_dataset, 'train_labels': train_labels, 'valid_dataset': valid_dataset, 'valid_labels': valid_labels, 'test_dataset': test_dataset, 'test_labels': test_labels, } pickle_file = 'sanitized_notMNIST.pickle' try: f = open(pickle_file, 'wb') pickle.dump(sanitized_save, f, pickle.HIGHEST_PROTOCOL) f.close() except Exception as e: print('Unable to save data to', pickle_file, ':', e) raise ###Output _____no_output_____ ###Markdown ---Problem 6---------Let's get an idea of what an off-the-shelf classifier can give you on this data. It's always good to check that there is something to learn, and that it's a problem that is not so trivial that a canned solution solves it.Train a simple model on this data using 50, 100, 1000 and 5000 training samples. Hint: you can use the LogisticRegression model from sklearn.linear_model.Optional question: train an off-the-shelf model on all the data!--- ###Code from sklearn import linear_model from six.moves import cPickle as pickle def randomize(dataset, labels): permutation = np.random.permutation(labels.shape[0]) shuffled_dataset = dataset[permutation,:] shuffled_labels = labels[permutation] return shuffled_dataset, shuffled_labels model = linear_model.LogisticRegression() with open("notMNIST.pickle", "rb") as f: overlapped_dataset = pickle.load(f) train_dataset = [x.flatten() for x in overlapped_dataset['train_dataset']] train_labels = overlapped_dataset['train_labels'] test_dataset = [x.flatten() for x in overlapped_dataset['test_dataset']] test_labels = overlapped_dataset['test_labels'] train_dataset, train_labels = randomize(np.array(train_dataset), np.array(train_labels)) test_dataset, test_labels = randomize(np.array(test_dataset), np.array(test_labels)) model_50 = model.fit(train_dataset[:50], train_labels[:50]) model_100 = model.fit(train_dataset[:100], train_labels[:100]) model_1000 = model.fit(train_dataset[:1000], train_labels[:1000]) model_5000 = model.fit(train_dataset[:5000], train_labels[:5000]) print("score 50 data samples " + str(model_50.score(test_dataset, test_labels))) print("score 100 data samples " + str(model_100.score(test_dataset, test_labels))) print("score 1000 data samples " + str(model_1000.score(test_dataset, test_labels))) print("score 5000 data samples " + str(model_5000.score(test_dataset, test_labels))) print("Done.") with open("sanitized_notMNIST.pickle", "rb") as f: sanitized_dataset = pickle.load(f) train_dataset = [x.flatten() for x in sanitized_dataset['train_dataset']] train_labels = sanitized_dataset['train_labels'] test_dataset = [x.flatten() for x in sanitized_dataset['test_dataset']] test_labels = sanitized_dataset['test_labels'] train_dataset, train_labels = randomize(np.array(train_dataset), np.array(train_labels)) test_dataset, test_labels = randomize(np.array(test_dataset), np.array(test_labels)) model_50 = model.fit(train_dataset[:50], train_labels[:50]) model_100 = model.fit(train_dataset[:100], train_labels[:100]) model_1000 = model.fit(train_dataset[:1000], train_labels[:1000]) model_5000 = model.fit(train_dataset[:5000], train_labels[:5000]) print("sanitized score 50 data samples " + str(model_50.score(test_dataset, test_labels))) print("sanitized score 100 data samples " + str(model_100.score(test_dataset, test_labels))) print("sanitized score 1000 data samples " + str(model_1000.score(test_dataset, test_labels))) print("sanitized score 5000 data samples " + str(model_5000.score(test_dataset, test_labels))) print("Done.") ###Output _____no_output_____

08_Average Brightness Feature Extraction/Average Brightness.ipynb

###Markdown Day and Night Image Classifier---The day/night image dataset consists of 200 RGB color images in two categories: day and night. There are equal numbers of each example: 100 day images and 100 night images.We'd like to build a classifier that can accurately label these images as day or night, and that relies on finding distinguishing features between the two types of images!*Note: All images come from the [AMOS dataset](http://cs.uky.edu/~jacobs/datasets/amos/) (Archive of Many Outdoor Scenes).* Import resourcesBefore you get started on the project code, import the libraries and resources that you'll need. ###Code import cv2 # computer vision library import helpers import numpy as np import matplotlib.pyplot as plt import matplotlib.image as mpimg %matplotlib inline ###Output _____no_output_____ ###Markdown Training and Testing DataThe 200 day/night images are separated into training and testing datasets. * 60% of these images are training images, for you to use as you create a classifier.* 40% are test images, which will be used to test the accuracy of your classifier.First, we set some variables to keep track of some where our images are stored: image_dir_training: the directory where our training image data is stored image_dir_test: the directory where our test image data is stored ###Code # Image data directories image_dir_training = "../00_Data/day_night_images/training/" image_dir_test = "../00_Data/day_night_images/test/" ###Output _____no_output_____ ###Markdown Load the datasetsThese first few lines of code will load the training day/night images and store all of them in a variable, `IMAGE_LIST`. This list contains the images and their associated label ("day" or "night"). For example, the first image-label pair in `IMAGE_LIST` can be accessed by index: ``` IMAGE_LIST[0][:]```. ###Code # Using the load_dataset function in helpers.py # Load training data IMAGE_LIST = helpers.load_dataset(image_dir_training) ###Output _____no_output_____ ###Markdown Construct a `STANDARDIZED_LIST` of input images and output labels.This function takes in a list of image-label pairs and outputs a **standardized** list of resized images and numerical labels. ###Code # Standardize all training images STANDARDIZED_LIST = helpers.standardize(IMAGE_LIST) ###Output _____no_output_____ ###Markdown Visualize the standardized dataDisplay a standardized image from STANDARDIZED_LIST. ###Code # Display a standardized image and its label # Select an image by index image_num = 0 selected_image = STANDARDIZED_LIST[image_num][0] selected_label = STANDARDIZED_LIST[image_num][1] # Display image and data about it plt.imshow(selected_image) print("Shape: "+str(selected_image.shape)) print("Label [1 = day, 0 = night]: " + str(selected_label)) ###Output Shape: (600, 1100, 3) Label [1 = day, 0 = night]: 1 ###Markdown Feature ExtractionCreate a feature that represents the brightness in an image. We'll be extracting the **average brightness** using HSV colorspace. Specifically, we'll use the V channel (a measure of brightness), add up the pixel values in the V channel, then divide that sum by the area of the image to get the average Value of the image. RGB to HSV conversionBelow, a test image is converted from RGB to HSV colorspace and each component is displayed in an image. ###Code # Convert and image to HSV colorspace # Visualize the individual color channels image_num = 0 test_im = STANDARDIZED_LIST[image_num][0] test_label = STANDARDIZED_LIST[image_num][1] # Convert to HSV hsv = cv2.cvtColor(test_im, cv2.COLOR_RGB2HSV) # Print image label print('Label: ' + str(test_label)) # HSV channels h = hsv[:,:,0] s = hsv[:,:,1] v = hsv[:,:,2] # Plot the original image and the three channels f, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, figsize=(20,10)) ax1.set_title('Standardized image') ax1.imshow(test_im) ax2.set_title('H channel') ax2.imshow(h, cmap='gray') ax3.set_title('S channel') ax3.imshow(s, cmap='gray') ax4.set_title('V channel') ax4.imshow(v, cmap='gray') ###Output Label: 1 ###Markdown --- Find the average brightness using the V channelThis function takes in a **standardized** RGB image and returns a feature (a single value) that represent the average level of brightness in the image. We'll use this value to classify the image as day or night. ###Code # Find the average Value or brightness of an image def avg_brightness(rgb_image): # Convert image to HSV hsv = cv2.cvtColor(rgb_image, cv2.COLOR_RGB2HSV) # Add up all the pixel values in the V channel sum_brightness = np.sum(hsv[:,:,2]) ## TODO: Calculate the average brightness using the area of the image # and the sum calculated above avg = sum_brightness / return avg # Testing average brightness levels # Look at a number of different day and night images and think about # what average brightness value separates the two types of images # As an example, a "night" image is loaded in and its avg brightness is displayed image_num = 190 test_im = STANDARDIZED_LIST[image_num][0] avg = avg_brightness(test_im) print('Avg brightness: ' + str(avg)) plt.imshow(test_im) ###Output _____no_output_____

RECOMMENDATION SYSTEMS LOKESH DUVVURU PROJECT (1).ipynb

###Markdown RECOMMENDATION SYSTEMS PROJECT BY DUVVURU LOKESH DATASET : ELECTRONICS DATASET FROM Amazon reviews data ###Code # importing necessary libraries import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns from surprise import KNNWithMeans from surprise.model_selection import train_test_split from surprise import Reader from surprise import Dataset from surprise import accuracy import os from collections import defaultdict from surprise import SVD from sklearn.decomposition import TruncatedSVD ###Output _____no_output_____ ###Markdown 1-- READ AND EXPLORE THE DATASET ###Code #reading the data and re-naming the columns data = pd.read_csv("ratings_Electronics.csv" ,names=['userId', 'productId','Rating','timestamp']) #head of the data data.head() # shape of the data data.shape ###Output _____no_output_____ ###Markdown There are 7824482 rows and 4 columns ###Code # 5 point summary data.describe() # No of unique users len(np.unique(data.userId)) ###Output _____no_output_____ ###Markdown There are 4201696 users who rated ###Code # No of unique products len(np.unique(data.productId)) ###Output _____no_output_____ ###Markdown There are 476002 products ###Code # dropping the time stamp column df=data.drop(['timestamp'], axis = 1) ###Output _____no_output_____ ###Markdown timestamp column dropped as it is not useful in this case ###Code # head of the new dataset df.head() #Info of new dataset df.info() df.isna().apply(pd.value_counts) #checking the presence of missing values ###Output _____no_output_____ ###Markdown No missing values ###Code # countplot sns.countplot(data=df , x='Rating') plt.show() ###Output _____no_output_____ ###Markdown Here maximum number products gave rating of 5 2-- TAKE SUBSET OF DATA ###Code # NO of ratings given by each user no_of_rated_products_per_user = df.groupby(by='userId')['Rating'].count().sort_values(ascending=False) no_of_rated_products_per_user.head() # NO of users who rated 75 or more products sum(no_of_rated_products_per_user >= 75) ###Output _____no_output_____ ###Markdown 582 users rated atleast 75 products ###Code # creating subset of of original data e_df=df.groupby("productId").filter(lambda x:x['Rating'].count() >=75) ###Output _____no_output_____ ###Markdown Here i am creating subset with users who atleast rated 75 products ###Code #Head of subset data e_df.head() e_df.shape ###Output _____no_output_____ ###Markdown 4-- POPULARITY RECOMMENDER MODEL ###Code e_df.groupby('productId')['Rating'].mean().head() ###Output _____no_output_____ ###Markdown Mean rating for each product is determined by grouping productID and rating ###Code e_df.groupby('productId')['Rating'].mean().sort_values(ascending=False).head() ###Output _____no_output_____ ###Markdown Mean rating of products in descending order. This gives the most highly rated product at top ###Code e_df.groupby('productId')['Rating'].count().sort_values(ascending=False).head() ###Output _____no_output_____ ###Markdown Most ratings for a single product is at the top of this count values ###Code ratings_mean_count = pd.DataFrame(e_df.groupby('productId')['Rating'].mean()) ###Output _____no_output_____ ###Markdown New dataframe ratings_mean_count is created and mean values are included ###Code ratings_mean_count['Rating_counts'] = pd.DataFrame(e_df.groupby('productId')['Rating'].count()) ###Output _____no_output_____ ###Markdown Rating_counts values are included to the ratings_mean_count dataframe ###Code ratings_mean_count.head() ###Output _____no_output_____ ###Markdown Head of the ratings_mean_count dataframe is shown above ###Code ratings_mean_count.sort_values(by='Rating_counts', ascending=False).head(10) ###Output _____no_output_____ ###Markdown The most popular products are given by assembling ratings_mean_count dataframe in descending order ###Code popular_products = pd.DataFrame(e_df.groupby('productId')['Rating'].count()) most_popular = popular_products.sort_values('Rating', ascending=False) most_popular.head(15).plot(kind = "bar") ###Output _____no_output_____ ###Markdown By the above graph we can see the top 15 products recommended 3-- SPLITTING THE DATA 70/30 RATIO ###Code #Reading the dataset reader = Reader(rating_scale=(1, 5)) ee_df = Dataset.load_from_df(e_df,reader) trainset, testset = train_test_split(ee_df, test_size=0.3,random_state=10) ###Output _____no_output_____ ###Markdown 5 & 7-- COLABARATIVE FILTERING MODEL BY USING K=5 ###Code # Fitting the data with k = 5 e_algo = KNNWithMeans(k=5, sim_options={'name': 'pearson_baseline', 'user_based': False}) #Training the dataset e_algo.fit(trainset) #Test set test_pred = e_algo.test(testset) #Test predictions test_pred ###Output _____no_output_____ ###Markdown Top five recommendations for each user is given above 6-- RMSE VALUE ###Code print("Item-Item collobarative model : Test Set") accuracy.rmse(test_pred, verbose=True) ###Output Item-Item collobarative model : Test Set RMSE: 1.3313 ###Markdown Here RMSE value is close to one which not bad MODEL BASED COLLABARATIVE FILTERING TO GIVE TOP 5 PRODUCT RECOMMENDATIONS ###Code # pivot table for first 50000 users et_df=e_df.head(50000) ratings_matrix = et_df.pivot_table(values='Rating', index='userId', columns='productId', fill_value=0) ratings_matrix.head() #Shape of ratings_matrix ratings_matrix.shape # Transpose of ratings_matrix X = ratings_matrix.T X.head() #shape of X matrix X.shape #Using truncated SVD to find decomposed matrix SVD = TruncatedSVD(n_components=10) decomposed_matrix = SVD.fit_transform(X) decomposed_matrix.shape decomposed_matrix correlation_matrix = np.corrcoef(decomposed_matrix) correlation_matrix.shape correlation_matrix X.index[119] # index of the product purchased by customer i = "B00004UE2R" product_names = list(X.index) product_ID = product_names.index(i) product_ID # Correlation matrix correlation_product_ID = correlation_matrix[product_ID] correlation_product_ID.shape Recommend = list(X.index[correlation_product_ID > 0.45]) # Removes the item already bought by the customer Recommend.remove(i) Recommend[0:5] ###Output _____no_output_____

9-Coordinates-Projections-and-Grids.ipynb

###Markdown Coordinates, Projections, and Grids Synopisis- Review of coordinate systems and projections of the sphere onto the 2d placne- Discussion about lengths and areas in finite volume grids used by ESMs ###Code %run -i figure-scripts/init.py ###Output _____no_output_____ ###Markdown Coordinate systemsA coordinate system allows us to (uniquely) specify points in space. You should be familiar with the Cartesian 2d coordinate system where, by convention, (x,y) are the normal distances, measured in the same units, from two perpendicular lines through the origin.We live in a 3d world (referring to spatial dimensions) and so require 3 numerical values to label a point in space. In Cartesian coordinates they might be (x,y,z) referenced to the center of the Earth, with z being height above the equatorial plane (positive in the direction of the North pole), y being the distance from a plane through the poles and a reference meridian, and x the distance from the plane perpendicular to both other planes. The equations of motion used by many models are often derived starting in this Cartesian coordinate system. However, these Cartesian coordinates are inconvenient to use in practice because we live on the surface of a sphere and "up", as defined by gravity, is sometimes increasing z (at the North Pole), and sometimes changing x or y (at the Equator). Spherical coordinatesIn ESMs we typically use spherical coordinates, $\lambda$, $\phi$ and $r$, where $\lambda$ is "longitude", a rotation angle eastward around the poles starting at a reference meridian; $\phi$ is "latitude", an elevation angle from the Equatorial plane (positive in Northern hemisphere), and $r$ is the radial distance from the center of the Earth. $\lambda,\phi,r$ are related to Cartesian $x,y,z$ by some simple relations:$$\begin{pmatrix}x \\ y \\ z\end{pmatrix} =\begin{pmatrix}r \cos \phi \cos \lambda \\ r \cos \phi \sin \lambda \\ r \sin \phi\end{pmatrix}$$Note that $r, x, y, z$ are all in the same units (eg. kilometets or meters) and $\lambda,\phi$ are angles usually given in degrees or radians.__Coordinate singularities:__ At the North and South poles of the coordinate system, $\phi = \pm \pi/2 = \pm 90^\circ$, all values of longitude refer to the same point. There is no "east" when you are positioned at the pole. This has many consequences, but one of the more fundamental is that spherical coordinates are not a good coordinate to use to design a discretization of the spherical domain.__Periodic coordinates:__ While a tuple of longitude, latitude and radius unambiguously define a point in space, given a point in space you there are multiple valid longitudes that refer to the same point. Longitude is cyclic ($\pm360^\circ$ is equivalent to $0^\circ$). This can cause problems in practice, particularly for plotting spherical data for which effort is sometimes needed to handle the periodicity. Geographic coordinatesWe live on the surface of the Earth and to precisely refer to points near the Earth's surface requires a properly defined geographic coordinate system. A common choice of coordinates is latitude, longitude and altitude, where altitude is height above a particular surface. Unfortunately the Earth is not spherical and that reference surface is better approximated as an ellipsoidal.In order to be unambiguous about the definition of coordinates, map-makers choose a reference ellipse with a agreed upon scale and orientation. They then choose the most appropriate mapping of the spherical coordinate system onto that ellipsoid, called a _geodetic datum_. A widely used global datum includes the [World Geodetic System](https://en.wikipedia.org/wiki/World_Geodetic_System) (WGS 84), the default datum used for the Global Positioning System. When you are given a latitude-longitude pair of values, strictly speaking without the geodetic datum, the is some ambiguity about the actual physical point being referred to. For ESMs, the datum is rarely provided and this is because ESMs almost universally approximate the Earth as a sphere and use spherical coordinates for referencing locations. This means some approximation is required when comparing real-world positions and model positions.The latitude and longitude using these horizontal datums are the spherical coordinates of the point on an ellipse. It you draw a straight line from the point on the ellipsoidal to the center, if passes through all spheres co-centered with the same latitude and longitude.Different datum have different reference points and scales, and so longitude and latitude can differ between geodetic datum. ProjectionsTo view data covering the surface of a sphere, or the Earth, we have to project that 3d surface into 2d. Imagine peeling the rind off an orange in one piece and then trying to flatten it onto a table top; the curvature in the peel requires you to distort the rind or make cuts, in order to flatten it fully. This is the function of the map projections and distortion is inevitable. Some projection preserve properties such as relative angles between lines, or relative area, but there is no projection of the surface of the sphere that can avoid distortion of some form.A projection maps the longitude and latitude of spherical coordinates into a new coordinate system. Very confusingly, sometimes the projection coordinates will be called longitude and latitude too! The projection coordinates are meaningless unless you know what the projection is so you often find a reference to the projection in the meta-data of coordinates; it means the longitude and latitude are not spherical coordinate but projection coordinates. ###Code %run -i figure-scripts/some-projections.py ###Output _____no_output_____ ###Markdown Figure 1: The colored circles in these plots are circles in the tangent plane to the sphere and projected onto the surface. The various projections can distort the circles. The circles are separated zonally or meridionally by 60$^\circ$. In 1a, a perspective image of the sphere, the circles appear non-circular because of the viewing angle. The blue circle appears circular because we are viewing it from directly overhead. The projection in 1b is the easy to use Plate-Carrée projection, a "lat-lon" plot, in which circles are stretched zonally with distance from the equator. 1d shows the Mercator projection in which circles remain circles but are expanded in size away from th equator. 1c shows the Robinson projection which compromises between the two. The purple dashed lines is a straight line in latitude-longitude coordinates, and the yellow dashed line is a straight line in the Mercator coordinates. The cyan dashed line is a great arc, and is straight in the perspective view because we are viewing it from directly overhead.The two most useful projections are the equirectangular and Mercator projections. Equirectangular projectionThis is the simplest projection, sometimes thought of a non-projection which is incorrect. In general it takes the form$$\begin{align}x & = R \left( \lambda - \lambda_0 \right) \cos \phi_0 \\y & = R \left( \phi - \phi_0 \right)\end{align}$$The origin of the plot, $(x,y)=(0,0)$ corresponds to $(\lambda,\phi)=(\lambda_0,\phi_0)$. The $\cos \phi_0$ term is a constant and the most common choice of $\phi_0=0$ gives the plate carrée projection, which means "flat square" in French. In this case, the projection is simply$$\begin{align}x & = R \left( \lambda - \lambda_0 \right) \\y & = R \phi\end{align}$$Distances in the y-direction are proportional to the meridional direction on the sphere, but the x-direction are stretched zonally, more so further from the equator. This is apparent in the orange and green circles in figure 1b, where the heights or the loops are the same as circles on the equator but the width is markedly increased.In the cartopy package, this projection is called "Plate-Carrée" which is French for flat square. Other names for this projection are equidistant cylindrical projection and geographic projection. See https://en.wikipedia.org/wiki/Equirectangular_projection. Mercator projectionThe Mercator projection has the same stretching in the x-direction as the equirectangular projection but, in order to preserve shape, it also stretches the y direction so that infinitesimal elements are stretched isotropically (the y-stretching is equal to the x-stretching).$$\begin{align}x & = R \left( \lambda - \lambda_0 \right) \\y & = R \tanh^{-1} \left( \sin \phi \right)\end{align}$$At the polar singularities, the x-stretching is infinite so y becomes infinite and the Mercator projection can never show the poles. See https://en.wikipedia.org/wiki/Mercator_projection. LinesA length of a line between two points is a function of the path taken. On the surface of sphere, the shortest path between two given points is a great arc. A great arc does not appear straight in many projections. Unfortunately, many grid calculations use a great arc for the length of a line between nodes on a model grid, which can be inconsistent with the constraints or assumptions about the grid.The dashed curves in figure 1 are "straight" lines between two points in various projections. The cyan dashed curve is a great arc. The purple dashed curve is a straight line in the Plate-Carree projection (latitude-longitude space) and the yellow dashed curve is a straight line in the Mercator projection. All are curved in most other projections. To describe a straight line in some projection then _the projection must be known_, irrespective of the coordinate system defining the end points. That is, we can define the end points of the line in latitude-longitude coordinates but say a line is straight in the Mercator projection, and by so doing unambiguously define that line.In the Mercator projection, the length of a line is $\frac{R}{\cos \alpha} \Delta \phi$ where $\tan \alpha = \frac{\Delta y}{\Delta x}$ ESM gridsMany ESMs use quadrilateral grids to discretize the surface of the sphere. The following discussion also applies to fully unstructured grids built from polygons but here we use quadrilateral grids for simplicity. There are also grids that have cuts and joins but here we'll stick to space-filling grids that are logically rectangular, meaning they can be stored in rectangular arrays in computer memory and referenced with a pair of indices ($i,j$ by convention).A quadrilateral grid is a rectangular mesh of adjacent quadrilateral cells that share edges and vertexes. Although the mesh and the cell are logically rectangular they might be physically curvilinear. From the grid we require positions of nodes, distances along edges, and areas of cells.If we choose a coordinate system with which to record the locations of mesh nodes, say spherical latitude-longitude with appropriate definitions, then we can unambiguously define those node locations. We could describe the exact same grid using a different coordinate system, say 3D Cartesian coordinates. The physical positions of the nodes of the grids are part of what define the grid, but the choice of coordinates with which we describe those positions does not change the grid.The edges of each cell are a curve between two adjacent nodes but the particular path of the curve has to be defined. Different paths will have different lengths. Similarly, the particular paths of the cell edges will determine the cell area. Thus the path of the cell edges is a fundamental component of a model grid needed for calculating the lengths and areas on a grid. Simple spherical coordinate gridBefore we discuss the best choice for defining a curve between points, let's briefly define a simple spherical-coordinate grid.The mesh is formed of lines of constant longitude and lines of constant latitude.Let $i \in 0,1,\ldots, n_i$ and $j \in 0,1,\ldots, n_j$, then node $i,j$ is at longitude $\lambda_i$ and latitude $\phi_j$ where $\lambda_i=\lambda_0 + i \Delta \lambda$, $\phi_j=\phi_0 + j \Delta \phi$.Here, $\Delta \lambda$ and $\Delta \phi$ are grid spacings. In practice, these can be smooth functions of $i$ and $j$ respectively but here we treat them as constant.An example simple spherical grid is shown below. The red dots are the nodes of the mesh with positions $\lambda_i,\phi_j$. The dashed lines are the cell edges that for a regular net. Notice that in the Plate-Carrée projection the grid is regular because the grid-spacing in constant in longitude-latitude coordinates.The lengths and areas of the grid are measured on the surface of sphere. We defined the edges to be either lines of constant longitude or latitude. Using spherical geometry, the length of a meridionally-oriented (constant longitude) cell edge is $R \Delta \phi$. For a zonally-oriented edge at constant latitude $\phi_j$, the length is $R \Delta \lambda \cos \phi_j$. The area of a cell labelled $i+\frac{1}{2},j+\frac{1}{2}$ bounded by four edges is $R^2 \Delta \lambda \left( \sin \phi_{j+1} - \sin \phi_j \right)$.The metric factors for this grid are the same as for a Plate-Carrée projection because we are defining the paths of the cell edges to be straight in the Plate-Carrée projection. The use of the Plate-Carrée coordinates for position, namely longitude and latitude, is a happy coincidence which means everything, positions and metrics, are defined by one projection. ###Code %run -i figure-scripts/simple-spherical-grid.py ###Output _____no_output_____

doc/source/quickstart/6)_Volume_Rendering.ipynb

###Markdown If we want to apply a clipping, we can specify the `sigma_clip`. This will clip the upper bounds to this value times the standard deviation of the values in the image array. ###Code sc.show(sigma_clip=4) ###Output _____no_output_____ ###Markdown There are several other options we can specify. Note that here we have turned on the use of ghost zones, shortened the data interval for the transfer function, and widened our gaussian layers. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, 'kpc')) source = sc.sources['source_00'] source.set_fields('density', no_ghost=False) tf = yt.ColorTransferFunction((-28, -25)) tf.add_layers(4, w=0.03) source.set_transfer_function(tf) sc.show(sigma_clip=4.0) ###Output _____no_output_____ ###Markdown A Brief Demo of Volume RenderingThis shows a small amount of volume rendering. Really, just enough to get your feet wet! ###Code import yt ds = yt.load("IsolatedGalaxy/galaxy0030/galaxy0030") ###Output _____no_output_____ ###Markdown To create a volume rendering, we need a camera and a transfer function. We'll use the `ColorTransferFunction`, which accepts (in log space) the minimum and maximum bounds of our transfer function. This means behavior for data outside these values is undefined.We then add on "layers" like an onion. This function can accept a width (here specified) in data units, and also a color map. Here we add on four layers.Finally, we create a camera. The focal point is `[0.5, 0.5, 0.5]`, the width is 20 kpc (including front-to-back integration) and we specify a transfer function. Once we've done that, we call `show` to actually cast our rays and display them inline. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, 'kpc')) source = sc.sources['source_00'] tf = yt.ColorTransferFunction((-28, -24)) tf.add_layers(4, w=0.01) source.set_transfer_function(tf) sc.show() ###Output _____no_output_____ ###Markdown A Brief Demo of Volume RenderingThis shows a small amount of volume rendering. Really, just enough to get your feet wet! ###Code import yt ds = yt.load_sample("IsolatedGalaxy") ###Output _____no_output_____ ###Markdown To create a volume rendering, we need a camera and a transfer function. We'll use the `ColorTransferFunction`, which accepts (in log space) the minimum and maximum bounds of our transfer function. This means behavior for data outside these values is undefined.We then add on "layers" like an onion. This function can accept a width (here specified) in data units, and also a color map. Here we add on four layers.Finally, we create a camera. The focal point is `[0.5, 0.5, 0.5]`, the width is 20 kpc (including front-to-back integration) and we specify a transfer function. Once we've done that, we call `show` to actually cast our rays and display them inline. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, "kpc")) source = sc.sources["source_00"] tf = yt.ColorTransferFunction((-28, -24)) tf.add_layers(4, w=0.01) source.set_transfer_function(tf) sc.show() ###Output _____no_output_____ ###Markdown If we want to apply a clipping, we can specify the `sigma_clip`. This will clip the upper bounds to this value times the standard deviation of the values in the image array. ###Code sc.show(sigma_clip=4) ###Output _____no_output_____ ###Markdown There are several other options we can specify. Note that here we have turned on the use of ghost zones, shortened the data interval for the transfer function, and widened our gaussian layers. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, "kpc")) source = sc.sources["source_00"] source.field = "density" tf = yt.ColorTransferFunction((-28, -25)) tf.add_layers(4, w=0.03) source.transfer_function = tf sc.show(sigma_clip=4.0) ###Output _____no_output_____ ###Markdown A Brief Demo of Volume RenderingThis shows a small amount of volume rendering. Really, just enough to get your feet wet! ###Code import yt ds = yt.load_sample("IsolatedGalaxy") ###Output _____no_output_____ ###Markdown To create a volume rendering, we need a camera and a transfer function. We'll use the `ColorTransferFunction`, which accepts (in log space) the minimum and maximum bounds of our transfer function. This means behavior for data outside these values is undefined.We then add on "layers" like an onion. This function can accept a width (here specified) in data units, and also a color map. Here we add on four layers.Finally, we create a camera. The focal point is `[0.5, 0.5, 0.5]`, the width is 20 kpc (including front-to-back integration) and we specify a transfer function. Once we've done that, we call `show` to actually cast our rays and display them inline. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, 'kpc')) source = sc.sources['source_00'] tf = yt.ColorTransferFunction((-28, -24)) tf.add_layers(4, w=0.01) source.set_transfer_function(tf) sc.show() ###Output _____no_output_____ ###Markdown If we want to apply a clipping, we can specify the `sigma_clip`. This will clip the upper bounds to this value times the standard deviation of the values in the image array. ###Code sc.show(sigma_clip=4) ###Output _____no_output_____ ###Markdown There are several other options we can specify. Note that here we have turned on the use of ghost zones, shortened the data interval for the transfer function, and widened our gaussian layers. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, 'kpc')) source = sc.sources['source_00'] source.field = 'density' tf = yt.ColorTransferFunction((-28, -25)) tf.add_layers(4, w=0.03) source.transfer_function = tf sc.show(sigma_clip=4.0) ###Output _____no_output_____ ###Markdown A Brief Demo of Volume RenderingThis shows a small amount of volume rendering. Really, just enough to get your feet wet! ###Code import yt ds = yt.load("IsolatedGalaxy/galaxy0030/galaxy0030") ###Output _____no_output_____ ###Markdown To create a volume rendering, we need a camera and a transfer function. We'll use the `ColorTransferFunction`, which accepts (in log space) the minimum and maximum bounds of our transfer function. This means behavior for data outside these values is undefined.We then add on "layers" like an onion. This function can accept a width (here specified) in data units, and also a color map. Here we add on four layers.Finally, we create a camera. The focal point is `[0.5, 0.5, 0.5]`, the width is 20 kpc (including front-to-back integration) and we specify a transfer function. Once we've done that, we call `show` to actually cast our rays and display them inline. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, 'kpc')) source = sc.sources['source_00'] tf = yt.ColorTransferFunction((-28, -24)) tf.add_layers(4, w=0.01) source.set_transfer_function(tf) sc.show() ###Output _____no_output_____ ###Markdown If we want to apply a clipping, we can specify the `sigma_clip`. This will clip the upper bounds to this value times the standard deviation of the values in the image array. ###Code sc.show(sigma_clip=4) ###Output _____no_output_____ ###Markdown There are several other options we can specify. Note that here we have turned on the use of ghost zones, shortened the data interval for the transfer function, and widened our gaussian layers. ###Code sc = yt.create_scene(ds) sc.camera.set_width(ds.quan(20, 'kpc')) source = sc.sources['source_00'] source.field = 'density' tf = yt.ColorTransferFunction((-28, -25)) tf.add_layers(4, w=0.03) source.transfer_function = tf sc.show(sigma_clip=4.0) ###Output _____no_output_____

notebooks/single_window/.ipynb_checkpoints/1_make_noh_avg_fit_dcd-checkpoint.ipynb

###Markdown Step 1: Initialize ###Code host = 'a_tract_21mer' type_na = 'bdna+bdna' n_bp = 21 begin_frame = 1 frame_num = 50000 agent = avg_dcd_noh.AvgcrddcdAgent(host, type_na, rootfolder) ###Output /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer exists /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer/bdna+bdna exists /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer/bdna+bdna/input exists /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer/bdna+bdna/input/allatoms exists /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer/bdna+bdna/input/heavyatoms exists /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer/bdna+bdna/charmm_inp exists /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer/bdna+bdna/charmm_dat exists /home/yizaochen/codes/dna_rna/all_systems/a_tract_21mer/bdna+bdna/make_crd exists ###Markdown Copy central.xtc from simulation folder ###Code xtc_0us_5us = path.join(simu_folder, host, type_na, 'data', 'roughtrj', '1000', f'{type_na}.nopbc.fit.1to50.1000.xtc') central_xtc = path.join(agent.aa_folder, f'{type_na}.central.xtc') copyfile(xtc_0us_5us, central_xtc) print(f'cp {xtc_0us_5us} {central_xtc}') ###Output cp /home/ytcdata/simulation/tat_21mer/bdna+bdna/data/roughtrj/1000/bdna+bdna.nopbc.fit.1to50.1000.xtc /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/allatoms/bdna+bdna.central.xtc ###Markdown Step 2: Prepare dcd and pdb ###Code inish = path.join(na_mechfolder, 'shell_scripts', 'initialize_input.sh') cmd = f'bash {inish} {rootfolder} {host} {type_na}' print(cmd) cmd = f'r 1-{n_bp}' print(cmd) # Manual Delete aafolder = agent.aa_folder single_na = d_single_na[type_na] temp_pdb = path.join(aafolder, f'{single_na}1.central.pdb') cmd = f'vim {temp_pdb}' print(cmd) temp_pdb = path.join(aafolder, f'{single_na}2.central.pdb') cmd = f'vim {temp_pdb}' print(cmd) pdbcharmmsh = path.join(na_mechfolder, 'shell_scripts', 'pdb_gro2charmm.sh') cmd = f'bash {pdbcharmmsh} {rootfolder} {host} {type_na} 1' print(cmd) cmd = f'bash {pdbcharmmsh} {rootfolder} {host} {type_na} 2' print(cmd) temp_pdb = path.join(agent.aa_folder, f'{type_na}.central.pdb') temp_xtc = path.join(agent.aa_folder, f'{type_na}.central.xtc') temp_dcd = path.join(agent.aa_folder, f'{type_na}.central.dcd') cmd = f'{vmd} {temp_pdb} {temp_xtc}' print(cmd) cmd = f'animate write dcd {temp_dcd} beg 1 end 50001 waitfor all' print(cmd) cmd = f'{vmd} {temp_pdb} {temp_dcd}' print(cmd) ###Output /usr/local/bin/vmd /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/allatoms/bdna+bdna.central.pdb /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/allatoms/bdna+bdna.central.xtc animate write dcd /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/allatoms/bdna+bdna.central.dcd beg 1 end 50001 waitfor all /usr/local/bin/vmd /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/allatoms/bdna+bdna.central.pdb /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/allatoms/bdna+bdna.central.dcd ###Markdown Step 3: Make CRD (split two strands, then combine) ###Code agent.make_crd_input(amber=True, firstter='amber_5ter', lastter='amber_3ter') agent.make_crd() # Reset Resid for bdna2.1.pdb, if need execute = False if execute: offset = -21 agent.reset_na2_pdb_resid(offset) ###Output /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/make_crd/bdna2.1.pdb /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/make_crd/bdna2.1.backup.pdb Write PDB: /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/make_crd/bdna2.1.pdb Reset /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/make_crd/bdna2.1.pdb resid by offset -21! Check by... vim /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/make_crd/bdna2.1.pdb ###Markdown Step 4: Make CRD and DCD without hydrogen atoms ###Code agent.make_no_h_crd_input(amber=True, firstter='amber_5ter', lastter='amber_3ter') agent.make_no_h_crd() agent.make_no_h_dcd_input(amber=True, begin=begin_frame, frame_num=frame_num, firstter='amber_5ter', lastter='amber_3ter') agent.make_no_h_dcd() ###Output charmm< /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/charmm_inp/write_no_h_dcd.inp > /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/charmm_dat/write_no_h_dcd.dat ###Markdown Step 5: Make Average CRD and fitting no-H dcd to average crd ###Code agent.make_avg_crd_input(amber=True, firstter='amber_5ter', lastter='amber_3ter') agent.make_avg_crd() agent.fit_dcd_to_avg_input(amber=True, begin=begin_frame, frame_num=frame_num, firstter='amber_5ter', lastter='amber_3ter') agent.fit_dcd_to_avg() ###Output charmm< /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/charmm_inp/fit_dcd_to_avg.inp > /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/charmm_dat/fit_dcd_to_avg.dat ###Markdown Step 6: Check By VMD ###Code crd = path.join(agent.heavy_folder, f'{type_na}.nohydrogen.avg.crd') dcd = path.join(agent.heavy_folder, f'{type_na}.nohydrogen.fitavg.dcd') print(f'vmd -cor {crd} {dcd}') ###Output vmd -cor /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/heavyatoms/bdna+bdna.nohydrogen.avg.crd /home/yizaochen/codes/dna_rna/all_systems/tat_21mer/bdna+bdna/input/heavyatoms/bdna+bdna.nohydrogen.fitavg.dcd ###Markdown Additional Part: Copy requried files to allsystem folder ###Code # Copy From simulation folder simu_folder = '/home/yizaochen/simulation' simu_datafolder = path.join(simu_folder, host, type_na, 'data') inputfolder = path.join(rootfolder, host, type_na, 'input', 'allatoms') old_f = path.join(simu_datafolder, 'gro', f'{type_na}.npt4.fit.gro') new_f = path.join(inputfolder, f'{type_na}.npt4.all.gro') copyfile(old_f, new_f) print(f'cp {old_f} {new_f}') old_f = path.join(simu_datafolder, 'roughtrj', '1000', f'{type_na}.nopbc.fit.1to10.1000.xtc') new_f = path.join(inputfolder, f'{type_na}.all.xtc') copyfile(old_f, new_f) print(f'cp {old_f} {new_f}') old_f = path.join(simu_folder, host, type_na, f'{type_na}.gro') new_f = path.join(inputfolder, f'{type_na}.perfect.gro') copyfile(old_f, new_f) print(f'cp {old_f} {new_f}') ###Output cp /home/yizaochen/simulation/gcgc_21mer/bdna+bdna/data/gro/bdna+bdna.npt4.fit.gro /home/yizaochen/codes/dna_rna/all_systems/gcgc_21mer/bdna+bdna/input/allatoms/bdna+bdna.npt4.all.gro cp /home/yizaochen/simulation/gcgc_21mer/bdna+bdna/data/roughtrj/1000/bdna+bdna.nopbc.fit.1to10.1000.xtc /home/yizaochen/codes/dna_rna/all_systems/gcgc_21mer/bdna+bdna/input/allatoms/bdna+bdna.all.xtc cp /home/yizaochen/simulation/gcgc_21mer/bdna+bdna/bdna+bdna.gro /home/yizaochen/codes/dna_rna/all_systems/gcgc_21mer/bdna+bdna/input/allatoms/bdna+bdna.perfect.gro ###Markdown Reload Function ###Code from imp import reload reload(avg_dcd_noh) ###Output _____no_output_____

model_pipeline/07_process_model_software_engineer_over_time.ipynb

###Markdown Model Parameters ###Code parameters = { "min_salary_records":100, # Filter out all jobs with less than specified salary records "min_job_summaries":1000, # Filter out all jobs with less than specified job summaries "min_ngram":2, # For TD-IDF vectorizer "max_ngram":4, # For TD-IDF vectorizer "min_df":0, # For TD-IDF vectorizer, ignore features in less than this number of documents "train_test_split":0.05, # For train-test split "random_state":1, # For train-test split "alpha":0.1, # For Naive Bayes model "num_skills":50, # Number of skill to show per job } ###Output _____no_output_____ ###Markdown Load Job Summaries ###Code # Load resume data data = pd.read_csv(directory+'02_resumes_work.csv') data = data[data.cleaned_job_title == 'software engineer'] # Remove duplicate data data = data[['cleaned_job_title','descript','from_year']].drop_duplicates() data['range'] = 'none' data.loc[data.from_year >= 2013, 'range'] = '2013-2018' data.loc[(data.from_year >= 2008) & (data.from_year < 2013), 'range'] = '2008-2013' data.loc[(data.from_year >= 2003) & (data.from_year < 2008), 'range'] = '2003-2008' data.loc[(data.from_year >= 1998) & (data.from_year < 2003), 'range'] = '1998-2003' data.loc[data.from_year < 1998, 'range'] = '1900-1998' data.groupby('range').count() ###Output _____no_output_____ ###Markdown Data Preprocess Unbalanced Classes ###Code # Down sample the first model # SMOTE up sample the second model # Run the model on different periods of time (just for software engineers) x_data = preprocess_list(data.descript) y_labels = data.range # Split the data into test and train datasets X_train, X_test, y_train, y_test = train_test_split(x_data, y_labels, test_size=parameters['train_test_split'], random_state=parameters['random_state']) print("X_train: ",len(X_train)) print("X_test: ",len(X_test)) print("Start:", datetime.datetime.now()) # Train TF-IDF vectorizer model vect = TfidfVectorizer(min_df=parameters['min_df'], ngram_range=(parameters['min_ngram'], parameters['max_ngram']) ).fit(X_train) X_train_vectorized = vect.transform(X_train) print("End:", datetime.datetime.now()) print('Vocabulary len:', len(vect.get_feature_names())) sm = SMOTE(kind='regular') X_res, y_res = sm.fit_sample(X_train_vectorized, y_train) temp_display = pd.DataFrame(y_res) temp_display.columns = ['range'] temp_display['counter'] = 1 temp_display.groupby('range').count().reset_index() ###Output _____no_output_____ ###Markdown Train Model ###Code # Train Multinomial Naive Bayes model model = MultinomialNB(alpha=parameters['alpha']) model.fit(X_res, y_res) y_pred = model.predict(vect.transform(X_test)) print('Accuracy: %.2f%%' % (accuracy_score(y_test, y_pred) * 100)) # predictions = pd.DataFrame(list(zip(y_test, y_pred))) # predictions.columns=['actual','prediction'] # predictions['count']=1 # predictions.groupby(['actual','prediction']).count().reset_index().to_csv('most_confusion.csv') print('f1_score: ', f1_score(y_test, y_pred, average="macro")) print('precision_score: ', precision_score(y_test, y_pred, average="macro")) print('recall_score: ', recall_score(y_test, y_pred, average="macro")) precision, recall, fscore, support = score(y_test, y_pred) '{:.1%}'.format(1/3.0) metrics = pd.DataFrame(list(zip(model.classes_, precision, recall, fscore, support))) metrics.columns = ['class','precision', 'recall', 'fscore', 'support'] metrics_samples = metrics.sort_values(by='fscore',ascending=False).head(5) metrics_samples.precision = metrics_samples.precision.map(lambda x: '{:.2%}'.format(x)) metrics_samples.recall = metrics_samples.recall.map(lambda x: '{:.2%}'.format(x)) metrics_samples.fscore = metrics_samples.fscore.map(lambda x: '{:.2%}'.format(x)) metrics_samples.sort_values(by='fscore',ascending=True).to_csv('temp.csv') metrics_samples ###Output _____no_output_____ ###Markdown List Most Relevant Skills ###Code # This code finds the top parameters['num_skills'] of features to show the user. It filters out any # ngram where the same n-1 version of the ngram is shown. This cuts down on repetition. label_id = 4 print(model.classes_[label_id]) print('-------') features_list = [] topn_class1 = sorted(zip(model.coef_[label_id], vect.get_feature_names()))[-parameters['num_skills']:] for coef, feat in topn_class1: features_list.append(feat) accepted_skill_list = [model.classes_[label_id]] for potential_skill in sorted(features_list, key=lambda x: -len(x.split())): highest_match = len(potential_skill.split()) for accepted_skill in accepted_skill_list: leftovers = list(set(potential_skill.split()) - set(accepted_skill.split())) if len(leftovers) < highest_match: highest_match = len(leftovers) if highest_match > 1: accepted_skill_list.append(potential_skill) accepted_skill_list = accepted_skill_list[1:] shuffle(accepted_skill_list) for skill in accepted_skill_list: print(skill) ###Output 2013-2018 ------- version control unit testing web application using visual studio full stack develop maintain store procedure technology use new feature code review agile scrum rest api design implement using asp net entity framework management system development team software engineer sql server ruby rail front end test case continuous integration html5 css3 html cs javascript user interface ###Markdown Save New Model ###Code # This code saves the model to the models folder save_time = re.sub('[^A-Za-z0-9]+', '', str(datetime.datetime.now())) print(save_time) write_param = open(directory+"models/" + save_time + '_parameters.txt','w') for key in parameters: write_param.write(key + "=" + str(parameters[key]) + '\n') write_param.close() # Save preprocessed x data pickling_on = open(directory+"models/"+save_time+"_x_data.pkl","wb") pickle.dump(x_data, pickling_on) pickling_on.close() # Save preprocessed y labels pickling_on = open(directory+"models/"+save_time+"_y_labels.pkl","wb") pickle.dump(y_labels, pickling_on) pickling_on.close() # Save preprocessed x SMOTE data pickling_on = open(directory+"models/"+save_time+"_x_SMOTE_data.pkl","wb") pickle.dump(X_res, pickling_on) pickling_on.close() # Save preprocessed y SMOTE labels pickling_on = open(directory+"models/"+save_time+"_y_SMOTE_labels.pkl","wb") pickle.dump(y_res, pickling_on) pickling_on.close() # Save TD-IDF vectorizer pickling_on = open(directory+"models/"+save_time+"_tdidf_vect.pkl","wb") pickle.dump(vect, pickling_on) pickling_on.close() # Save vectorized x_train pickling_on = open(directory+"models/"+save_time+"_x_trained_tdidf_vect.pkl","wb") pickle.dump(X_train_vectorized, pickling_on) pickling_on.close() # Save NB model pickling_on = open(directory+"models/"+save_time+"_nb_model.pkl","wb") pickle.dump(model, pickling_on) pickling_on.close() ###Output 20180718171406220007 ###Markdown Load Model ###Code # This code loads an old model save_time = '20180718171406220007' # for software_engineer pickling_on = open(directory+"models/"+save_time+"_x_data.pkl","rb") x_data = pickle.load(pickling_on) pickling_on.close() # Save preprocessed y labels pickling_on = open(directory+"models/"+save_time+"_y_labels.pkl","rb") y_labels = pickle.load(pickling_on) pickling_on.close() # Save TD-IDF vectorizer pickling_on = open(directory+"models/"+save_time+"_tdidf_vect.pkl","rb") vect = pickle.load(pickling_on) pickling_on.close() # Save vectorized x_train pickling_on = open(directory+"models/"+save_time+"_x_trained_tdidf_vect.pkl","rb") X_train_vectorized = pickle.load(pickling_on) pickling_on.close() # Save NB model pickling_on = open(directory+"models/"+save_time+"_nb_model.pkl","rb") model = pickle.load(pickling_on) pickling_on.close() ###Output /Users/kwheatley/anaconda/envs/python36/lib/python3.6/site-packages/sklearn/base.py:312: UserWarning: Trying to unpickle estimator TfidfTransformer from version 0.18.1 when using version 0.19.0. This might lead to breaking code or invalid results. Use at your own risk. UserWarning)

notebooks-spanish/04-entrenando_y_generalizando.ipynb

###Markdown Entrenamiento y test===========Para evaluar que tal generalizan nuestros modelos supervisados, podemos dividir los datos en un conjunto de entrenamiento y otro de test: ###Code from sklearn.datasets import load_iris from sklearn.neighbors import KNeighborsClassifier iris = load_iris() X, y = iris.data, iris.target classifier = KNeighborsClassifier() ###Output _____no_output_____ ###Markdown Si pensamos la forma en que normalmente se aplica el aprendizaje automático, la idea de una partición de entrenamiento y test tiene sentido. Los sistemas del mundo real se entrenan utilizando los datos de los que se dispone y, conforme otros datos llegan (de nuevos clientes, de otros sensores o de otras fuentes), el modelo que fue previamente entrenado debe predecir *nuevos* datos. Podemos simular esto durante el aprendizaje mediante una partición train/test -- los datos de test serán una simulación de "datos futuros" que vendrán al sistema en la etapa de producción.Específicamente para iris, las 150 etiquetas están ordenadas, lo que significa que si dividimos los datos de forma directa y proporcional, alteraremos la distribución de las clases. Por ejemplo, si realizaremos una partición bastante común consistente en 2/3 para entrenamiento y 1/3 para test, nuestros datos de entrenamiento solo tendrían flores de las clases 0 y 1 (Setosa and Versicolor), y nuestros datos de test solo tendrían flores de la clase 2 (Virginica).Bajo la suposición de que todos los ejemplos son independientes entre si (que no puede hacerse con datos de series temporales), sería necesario **barajar aleatoriamente** el dataset antes de dividirlo. Ahora tenemos que hacer la partición. Afortunadamente, esto es bastante común en aprendizaje automático y scikit-learn tiene una función ya implementada para dividir en entrenamiento y test. Vamos a utilizar el 50% de los datos para entrenamiento y el 50% restante para test. Un 80% y un 20% es otra opción bastante común, aunque realmente depende mucho de los problemas tratados. Lo más importante para realizar una evaluación justa es que **la evaluación se haga utilizando datos que no han sido utilizados para el entrenamiento**. ###Code y from sklearn.model_selection import train_test_split train_X, test_X, train_y, test_y = train_test_split(X, y, train_size=0.5, test_size=0.5, random_state=123) print("Etiquetas para los datos de entrenamiento y test") print(train_y) print(test_y) ###Output _____no_output_____ ###Markdown **Consejo: partición estratificada**Especialmente cuando tratamos conjuntos de datos relativamente pequeños, es mejor estratificar la partición. La estratificación significa que mantenemos la proporción de datos por clase que había originalmente en los subconjuntos generados. Por ejemplo, después de dividir aleatoriamente el dataset como hicimos en el ejemplo anterior, podemos comprobar que tenemos las siguientes proporciones por clase: ###Code print('Todos:', np.bincount(y) / float(len(y)) * 100.0) print('Entrenamiento:', np.bincount(train_y) / float(len(train_y)) * 100.0) print('Test:', np.bincount(test_y) / float(len(test_y)) * 100.0) ###Output _____no_output_____ ###Markdown Para conseguir realizar una partición estratificada, tenemos que incluir el array de etiquetas cuando invocamos a la función `train_test_split`: ###Code train_X, test_X, train_y, test_y = train_test_split(X, y, train_size=0.5, test_size=0.5, random_state=123, stratify=y) print('Todos:', np.bincount(y) / float(len(y)) * 100.0) print('Entrenamiento:', np.bincount(train_y) / float(len(train_y)) * 100.0) print('Test:', np.bincount(test_y) / float(len(test_y)) * 100.0) ###Output _____no_output_____ ###Markdown --- Si evaluamos el rendimiento de nuestro clasificador con datos que se han empleado para el entrenamiento, podríamos llegar a unos resultados demasiado optimistas. En el peor caso, el modelo puede simplemente memorizar los datos de entrenamiento, pero fallar estrepitosamente cuando tenga que clasificar nuevos datos similares - nunca querríamos tener un sistema así en producción.En lugar de usar el mismo dataset para entrenamiento y test (lo que se conoce como "evaluación por resubstitución"), es mucho mejor usar una partición de entrenamiento y test para así estimar como de bien se comporta el modelo entrenado con datos nuevos. ###Code classifier.fit(train_X, train_y) pred_y = classifier.predict(test_X) print("CCR [Accuracy]:") print(np.mean(pred_y == test_y)) ###Output _____no_output_____ ###Markdown Podemos visualizar los aciertos y los fallos: ###Code print('Ejemplos correctamente clasificados:') correct_idx = np.where(pred_y == test_y)[0] print(correct_idx) print('\nEjemplos incorrectamente clasificados:') incorrect_idx = np.where(pred_y != test_y)[0] print(incorrect_idx) # Representar en 2D colors = ["darkblue", "darkgreen", "gray"] for n, color in enumerate(colors): idx = np.where(test_y == n)[0] plt.scatter(test_X[idx, 1], test_X[idx, 2], color=color, label="Clase %s" % str(n)) plt.scatter(test_X[incorrect_idx, 1], test_X[incorrect_idx, 2], color="darkred") plt.xlabel('sepal width [cm]') plt.ylabel('petal length [cm]') plt.legend(loc=3) plt.title("Resultados de clasificación en iris con KNN") plt.show() ###Output _____no_output_____ ###Markdown Entrenamiento y test===========Para evaluar que tal generalizan nuestros modelos supervisados, podemos dividir los datos en un conjunto de entrenamiento y otro de test: ###Code from sklearn.datasets import load_iris from sklearn.neighbors import KNeighborsClassifier iris = load_iris() X, y = iris.data, iris.target classifier = KNeighborsClassifier() ###Output _____no_output_____ ###Markdown Si pensamos la forma en que normalmente se aplica el aprendizaje automático, la idea de una partición de entrenamiento y test tiene sentido. Los sistemas del mundo real se entrenan utilizando los datos de los que se dispone y, conforme otros datos llegan (de nuevos clientes, de otros sensores o de otras fuentes), el modelo que fue previamente entrenado debe predecir *nuevos* datos. Podemos simular esto durante el aprendizaje mediante una partición train/test -- los datos de test serán una simulación de "datos futuros" que vendrán al sistema en la etapa de producción.Específicamente para iris, las 150 etiquetas están ordenadas, lo que significa que si dividimos los datos de forma directa y proporcional, alteraremos la distribución de las clases. Por ejemplo, si realizaremos una partición bastante común consistente en 2/3 para entrenamiento y 1/3 para test, nuestros datos de entrenamiento solo tendrían flores de las clases 0 y 1 (Setosa and Versicolor), y nuestros datos de test solo tendrían flores de la clase 2 (Virginica).Bajo la suposición de que todos los ejemplos son independientes entre si (que no puede hacerse con datos de series temporales), sería necesario **barajar aleatoriamente** el dataset antes de dividirlo. Ahora tenemos que hacer la partición. Afortunadamente, esto es bastante común en aprendizaje automático y scikit-learn tiene una función ya implementada para dividir en entrenamiento y test. Vamos a utilizar el 50% de los datos para entrenamiento y el 50% restante para test. Un 80% y un 20% es otra opción bastante común, aunque realmente depende mucho de los problemas tratados. Lo más importante para realizar una evaluación justa es que **la evaluación se haga utilizando datos que no han sido utilizados para el entrenamiento**. ###Code y from sklearn.model_selection import train_test_split train_X, test_X, train_y, test_y = train_test_split(X, y, train_size=0.5, test_size=0.5, random_state=123) print("Etiquetas para los datos de entrenamiento y test") print(train_y) print(test_y) ###Output _____no_output_____ ###Markdown **Consejo: partición estratificada**Especialmente cuando tratamos conjuntos de datos relativamente pequeños, es mejor estratificar la partición. La estratificación significa que mantenemos la proporción de datos por clase que había originalmente en los subconjuntos generados. Por ejemplo, después de dividir aleatoriamente el dataset como hicimos en el ejemplo anterior, podemos comprobar que tenemos las siguientes proporciones por clase: ###Code print('Todos:', np.bincount(y) / float(len(y)) * 100.0) print('Entrenamiento:', np.bincount(train_y) / float(len(train_y)) * 100.0) print('Test:', np.bincount(test_y) / float(len(test_y)) * 100.0) ###Output _____no_output_____ ###Markdown Para conseguir realizar una partición estratificada, tenemos que incluir el array de etiquetas cuando invocamos a la función `train_test_split`: ###Code train_X, test_X, train_y, test_y = train_test_split(X, y, train_size=0.5, test_size=0.5, random_state=123, stratify=y) print('Todos:', np.bincount(y) / float(len(y)) * 100.0) print('Entrenamiento:', np.bincount(train_y) / float(len(train_y)) * 100.0) print('Test:', np.bincount(test_y) / float(len(test_y)) * 100.0) ###Output _____no_output_____ ###Markdown --- Si evaluamos el rendimiento de nuestro clasificador con datos que se han empleado para el entrenamiento, podríamos llegar a unos resultados demasiado optimistas. En el peor caso, el modelo puede simplemente memorizar los datos de entrenamiento, pero fallar estrepitosamente cuando tenga que clasificar nuevos datos similares - nunca querríamos tener un sistema así en producción.En lugar de usar el mismo dataset para entrenamiento y test (lo que se conoce como "evaluación por resubstitución"), es mucho mejor usar una partición de entrenamiento y test para así estimar como de bien se comporta el modelo entrenado con datos nuevos. ###Code classifier.fit(train_X, train_y) pred_y = classifier.predict(test_X) print("CCR [Accuracy]:") print(np.mean(pred_y == test_y)) ###Output _____no_output_____ ###Markdown Podemos visualizar los aciertos y los fallos: ###Code print('Ejemplos correctamente clasificados:') correct_idx = np.where(pred_y == test_y)[0] print(correct_idx) print('\nEjemplos incorrectamente clasificados:') incorrect_idx = np.where(pred_y != test_y)[0] print(incorrect_idx) # Representar en 2D colors = ["darkblue", "darkgreen", "gray"] for n, color in enumerate(colors): idx = np.where(test_y == n)[0] plt.scatter(test_X[idx, 1], test_X[idx, 2], color=color, label="Clase %s" % str(n)) plt.scatter(test_X[incorrect_idx, 1], test_X[incorrect_idx, 2], color="darkred") plt.xlabel('sepal width [cm]') plt.ylabel('petal length [cm]') plt.legend(loc=3) plt.title("Resultados de clasificación en iris con KNN") plt.show() ###Output _____no_output_____

Python/Exercise_3_DrugInteractions.ipynb

###Markdown FHIR for Research Workshop - Exercise 3 Learning Objectives and Key ConceptsIn this exercise, you will: - Apply Knowledge from Exercises 0, 1, and 2- Attempt to complete each activity on your own individually- Query active Prescriptions in our Patient cohort- Understand the (non-FHIR) Drug-on-Drug Interaction API and learn how to query it- Combine the FHIR data with the non-FHIR API to determine Drug-on-Drug Interactions. Drug on Drug InteractionsFor this exercise we will explore potential drug on drug interactions in a sizable patient cohort stored in FHIR combined with drug interaction data from the NIH's Drug RxNAV database. Motivation/PurposeFrom a research persective we can envision leveraging these sorts of analyses to do post-market surveillance of drugs to determine both the rate of known adverse events among patients, as well as to potentially flag additional risks not yet identified. From a clinical perspective, this exercise demonstrates the ability for third-party data (in this case Drug on Drug interaction data), can be pulled in, paired with FHIR formatted clinical data, and then leveraged to better inform patient care in the form of Clinical Decision Support tools. Icons in this Guide 📘 A link to a useful external reference related to the section the icon appears in 🖐 A hands-on section where you will code something or interact with the server Step 1: Query all active prescriptions in our patient cohortFor this exercise we will call on the `MedicationRequest` which represents a medication prescription in FHIR.📘[Read more about the MedicationRequest Resource](https://www.hl7.org/fhir/medicationrequest.html) Each `MedicationRequest` represents a single prescription, such that you may have a many-to-one relationship between MedicationRequests and patients, as it is often the case that patients will have multiple prescriptions.(This fact will be critical for our exercise, as determining a potential drug on drug interaction will require effectively grouping `MedicationRequest` resources by patient, to determine if the patient is on multiple concurrent prescriptions. We will therefore want to make sure we can include the relevant patient information to ensure we can map multiple prescriptions to individual patients.) ###Code # Python standard library API for dealing with json import json # For making HTTP requests to the FHIR server import requests # Python data analysis library import pandas as pd FHIR_SERVER = 'https://api.logicahealth.org/researchonfhir/open' # Configure requests session with standard headers s = requests.Session() s.headers.update({'Accept':'application/fhir+json', 'Content-Type': 'application/fhir+json'}) # Optional: Turn off SSL verification. Useful when dealing with a corporate proxy with self-signed certificates. s.verify = False requests.packages.urllib3.disable_warnings() ###Output _____no_output_____ ###Markdown Compose the FHIR queryFirst compose a query to pull the `MedicationRequest` resource from the FHIR server. Then convert it to JSON format. Optionally, you could output the resulting JSON file to confirm that you've successfully queried the database.🖐 Fill in the URL to for retrieving `MedicationRequest` Resources ###Code r = s.get(f"{FHIR_SERVER}/FILLMEIN") bundle = r.json() ###Output _____no_output_____ ###Markdown We can now leverage the methods we deployed previously in Exercises 1 and 2 to create a python list which contains only the Bundle.entry.resource elements from the bundle returned in the previous step. As a first step let's leverage the list mapping lambda function we deployed in Exercise 2 Section 1.1 ([Link to Exercise 2 solution here](https://github.com/mitre/fhir-exercises/blob/main/Solutions/Exercise_2_KidsFirst-SOLUTION.ipynb) for reference) to map out our JSON file (entering the entire bundle, and mapping by resource) As a sanity test let's return the first resource item (index 0 or [0]) so we can get a better look at what information we have to work with.🖐 Create a list of just the patient resources from the entries in the bundle ###Code prescriptions = # To be completed... prescriptions[0] ###Output _____no_output_____ ###Markdown Convert Data onto a Pandas Dataframe Now that we've confirmed that we've extracted information we need from our FHIR server, we will then take the FHIR formatted data and convert it into a pandas dataframe for subsequent analysis.Based on our previous exercises we know we can use the `json_normalize` function parse the JSON into a pandas dataframe. 📘[Read more about `pandas.json_normalize`](https://pandas.pydata.org/docs/reference/api/pandas.json_normalize.html)You may want to use the `max_level` argument with `json_normalize` to cap the number of levels for the function to parse (in previous exercises we set the number = 10)Let's do that now and then output the resulting dataframe to confirm we've successfully converted it.🖐 Convert your json file into a pandas dataframe ###Code pd.set_option('display.max_columns', None) df_prescriptions = # 🖐 Fill in this code... df_prescriptions.head() ###Output _____no_output_____ ###Markdown Depending on how you've parsed it, certain fields are immediately usable in their current form. For others, we're going to need to do further work to parse out the precise information we want to work with. For now though, we'll pause any additional feature engineering until we have a better sense of precisely what we'll want to use. So we now have a basic datafame with drug and patient information. Let's examine the drug interaction api to see what data we'll need to extract from our dataframe Step 2: Understanding the Drug API and using that API with FHIR data📘[Review the NIH's RXNav API documentation](https://lhncbc.nlm.nih.gov/RxNav/APIs/index.html)We see one clear option we have to use the six-digit RxNorm identifier code to query for drug interactions📘[Review RXNav API findInteractionsFromList API documentation](https://lhncbc.nlm.nih.gov/RxNav/APIs/api-Interaction.findInteractionsFromList.html)This correlates with our Patient data column: `resource.medicationCodeableConcept.coding.codes` (quite a mouthful! But we'll deal with that shortly).Let's pull two sample interactions using the following general notation:`https://rxnav.nlm.nih.gov/REST/interaction/list.json?rxcuis=[code 1]+[code 2]`Two combinations we can try are: - 207106 and 656659 - 762675 and 859258 🖐 For each drug combination call the API and display the JSON response ###Code url = '' # Solve for for 207106 and 656659 response = s.get(url, headers={'accept': 'application/json'}) response.json() url = '' # Solve for for 762675 and 859258 response = s.get(url, headers={'accept': 'application/json'}) response.json() ###Output _____no_output_____ ###Markdown Feel free to experiment with additional drug combinations, including 3 or more drugs to see how the information varies.Reviewing the returned output we can begin to analyze the information provided, and assess our approach. Why are the RxNorm codes in the interactionPair different than what we sent? Do we need to care about severity? What other elements could be present and where are the descriptions indicating what each element represents (hint should we be looking back at the API docs to interpret?)Taking stock, we have successfully accessed the Drug API, and hopefully now have an understanding of what the API returns when there is a drug interaction versus when there isn't.We now have important information informing our next steps. First, we have a structured target to work toward for submitting our patient data to the Drug API. For each patient, we will need to compile a list of RxNorm codes of the prescriptions they are on, and then append them to our API query with a `+` or `%20` between each code. For our next step we'll go about constructing that!Second, we have an understanding of how the Drug API returns a known interaction, versus how it returns when there isn't one. We can begin to consider how the format of this data can be used to indicate - in bulk - the presence or absence of a reaction. Step 3: Construct a composite list of all drugs per-patient (so we can determine a potential Drug on Drug interactionSo now we know that in order to engage our RxNorm server we need to extract and submit our patient's six digit RxNorm code, let's go back to our original mapped JSON data and try to do a list comprehension to extract just the RxNorm specific codes first. ###Code pd.DataFrame([codings['code'] for MedicationRequest in prescriptions for codings in MedicationRequest['medicationCodeableConcept']['coding'] if codings['system'] == 'http://www.nlm.nih.gov/research/umls/rxnorm']).head() ###Output _____no_output_____ ###Markdown If we look back at our `df_prescriptions` DataFrame we can see that we already have a column for `medicationCodeableConcept.coding`. Let's take a similar approach to what we did in exercise 2 to extend what we just did and write a function to extract rxnorm codes based on just the coding. From there we can apply it to the DataFrame to generate a new column with just the rxnorm code. ###Code def get_rx_norm_code(medication_codeable_concept_coding): # Bonus points for error checking for medicationReference! return next(coding['code'] for coding in medication_codeable_concept_coding if coding['system'] == 'http://www.nlm.nih.gov/research/umls/rxnorm') get_rx_norm_code(prescriptions[0]['medicationCodeableConcept']['coding']) rxcodes = pd.Series([codings['code'] for MedicationRequest in prescriptions for codings in MedicationRequest['medicationCodeableConcept']['coding']], name='rxcode') dfcode = rxcodes.to_frame() dfcode.head() ###Output _____no_output_____ ###Markdown Let's now consolidate our dataframe to retain the information we need. Specifically we'll need information identifying the patient, an indication on whether or not the prescription is active or not (as only active prescriptions could cause a drug interaction, and finally the RXCUI code we previously extracted. Construct your final dataframe and then output the result to confirm you've retained the desired information. ###Code # `.apply` Approach df_prescriptions['rxcode'] = df_prescriptions['medicationCodeableConcept.coding'].apply(get_rx_norm_code) # `.map` Approach #df_prescriptions['rxcode'] = df_prescriptions['medicationCodeableConcept.coding'].map(lambda c: get_rx_norm_code(c)) rx_df = df_prescriptions[['subject.reference', 'status', 'rxcode']] rx_df.head() ###Output _____no_output_____ ###Markdown Filter data to only include active prescriptionsWe want to ensure that we're only querying active prescriptions. If a patient is no longer taking a drug, the risk of a Drug-on-Drug interaction is no longer applicable. If any inactive prescriptions are present, then filter your dataframe to ensure that only active prescrptions are included. We can do this by calling the Pandas `value_counts()` method on the column to determine what statuses are present and in what numbers, or even simply calling the pandas `unique()` method to determine the presence of any inactive prescriptions in our dataframe. 📘[Review the Pandas value_counts() documentation](https://pandas.pydata.org/docs/reference/api/pandas.Series.value_counts.html)📘[Review Pandas unique() documentation](https://pandas.pydata.org/docs/reference/api/pandas.Series.unique.html) 🖐 Using either of these methods, confirm that there are only active prescriptions in your data frame. It is worth noting that a more complex analysis might also take `MedicationRequest.dispenseRequest.initialFill`, `MedicationRequest.dispenseRequest.dispenseInterval`, and `MedicationRequest.dispenseRequest.validityPeriod` into account since an active medication may also define a `MedicationRequest` for the future which has yet to be prescribed and some medications may not be taken concurrently. Merge our prescriptions into a list by patientWe now need to create a list of drug codes for each patient, in order to feed that list into the RXNav API. Our desired output will look something like this where we have a tuple-like structure of patient ID, and a list of codes:Hint: to accomplish this try modifying the groupby function to merge our drugs by patient, and then apply a lambda function, to append the code values to a list.📘[Review Pandas groupby() documentation](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.groupby.html) 🖐 Fill in the appropriate columns to create a list of RxNorm Codes for each patient. ###Code # HINT: What column do we want to group by? and which column values do we want as a list? groups_by_patient = rx_df.groupby('FILLMEIN', sort=False)['FILLMEIN'].apply(list) groups_by_patient = pd.DataFrame({'patient':groups_by_patient.index, 'rxcode_list':groups_by_patient.values}) groups_by_patient.head() ###Output _____no_output_____ ###Markdown So now we've generated a list of active prescriptions for each patient, we can append this list to the RXNav query and determine whether each of these patients are at risk for a drug interaction. Step 4: Loop through our entire cohort and determine each patient's drug interactionsTo recap: we now have a list of patients with associated drug codes in list form, and we know how to query the RXNav API to determine if a drug interaction exists. As a last step, create a series of functions to iterate through our patient list and for each patient return whether or not a Drug on Drug interaction could occur.It might help to compose a helper function for taking a string of RXCodes (e.g., `123456+654321`) and submit it to the API, and returns the result as a formatted JSON. ###Code # Function for calling NIH API def has_drug_interaction(drug_list): drugs = "+".join(drug_list) try: url = 'https://rxnav.nlm.nih.gov/REST/interaction/list.json?rxcuis=' + drugs response = s.get(url, headers={'accept': 'application/json'}) response_json = response.json() return 'fullInteractionTypeGroup' in response_json except Exception as e: raise e ###Output _____no_output_____ ###Markdown 🖐 Test our original two drug combinations to ensure that it is outputting the expected responses. ###Code # HINT: Note that this function takes as its input a list of strings # so it will have to be formatted that way ###Output _____no_output_____

notebooks/lesson_1_predict_boston_housing_prices.ipynb

###Markdown Boston House Prices dataset=========================== Data Set Characteristics: Number of Instances: 506 :Number of Attributes: 13 numeric/categorical predictive :Median Value (attribute 14) is usually the target :Attribute Information (in order): - CRIM per capita crime rate by town - ZN proportion of residential land zoned for lots over 25,000 sq.ft. - INDUS proportion of non-retail business acres per town - CHAS Charles River dummy variable (= 1 if tract bounds river; 0 otherwise) - NOX nitric oxides concentration (parts per 10 million) - RM average number of rooms per dwelling - AGE proportion of owner-occupied units built prior to 1940 - DIS weighted distances to five Boston employment centres - RAD index of accessibility to radial highways - TAX full-value property-tax rate per 10,000 dollars - PTRATIO pupil-teacher ratio by town - B 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town - LSTAT % lower status of the population - MEDV Median value of owner-occupied homes in 1000's :Missing Attribute Values: None :Creator: Harrison, D. and Rubinfeld, D.L.This is a copy of UCI ML housing dataset.http://archive.ics.uci.edu/ml/datasets/Housing ###Code # compute pairwise pearson correlation of each feature and prices for column_name in column_names[:-1]: correlation = boston_df[column_name].corr(boston_df['target']) if abs(correlation) >= 0.5: print(f'Correlation between {column_name} and Target') print(correlation) trace = go.Scatter( x = boston_df['LSTAT'], y = boston_df['target'], mode = 'markers' ) data = [trace] layout = go.Layout( title='Low income family rate vs House Prices', xaxis=dict( title='Low income family rate', titlefont=dict( family='Courier New, monospace', size=18, color='#7f7f7f' ) ), yaxis=dict( title='House Prices', titlefont=dict( family='Courier New, monospace', size=18, color='#7f7f7f' ) ) ) config={'showLink': False} fig = go.Figure(data=data, layout=layout) iplot(fig, filename='basic-scatter', config=config) ###Output _____no_output_____ ###Markdown Linear Regression with One Variable Pseudocode from Andrew Ng's Machine Learning Course ###Code Image(filename="../imgs/lesson_1_linear_regression.png", width=700, height=400) X = np.array(boston_df['LSTAT']).reshape(-1, 1) ones = np.ones((len(X),1)) X = np.hstack((ones, X)) y = np.array(boston_df['target']) X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state=42) m = X_train.shape[0] def cost_function(X, y, theta, deriv=False): hypothesis = X.dot(theta) error = hypothesis - y if deriv: gradient = (1/m) * X.T.dot(error) return gradient, error else: J = 1/(2*m) * error.dot(error) return J def gradient_descent(X, y, alpha, epochs, batch_size, theta): theta_list = [] cost_list = [] for epoch_num in range(epochs): cost = cost_function(X, y, theta) cost_list.append(cost) theta_list.append(theta) gradient, error = cost_function(X, y, theta, deriv=True) theta = theta - alpha * gradient if epoch_num % 1000 == 0: print(f"cost: {cost}") return cost_list, theta_list # randomly initialize theta theta = np.array([1, -0.5]) alpha = 0.001 epochs = 10000 batch_size = X_train.shape[0] # batch gradient descent cost_list, theta_list = gradient_descent(X_train, y_train, alpha, epochs, batch_size, theta) final_theta = theta_list[-1] print(final_theta) ## TODO Create animation for updated line and contour plots ###Output _____no_output_____ ###Markdown Linear Regression with Multiple Variables ###Code # combine top three correlated features # complete algorithm lstat = np.array(boston_df['LSTAT']).reshape(-1, 1) full_set_size = lstat.shape[0] ones = np.ones((full_set_size,1)) pupil_teacher_ratio = np.array(boston_df['PTRATIO']).reshape(-1, 1) rooms = np.array(boston_df['RM']).reshape(-1, 1) X_multi = np.hstack((ones, lstat, pupil_teacher_ratio, rooms)) y_multi = np.array(boston_df['target']) X_train_multi, X_test_multi, y_train_multi, y_test_multi = train_test_split(X_multi, y_multi, test_size=0.20, random_state=42) m = X_train_multi.shape[0] ###Output _____no_output_____ ###Markdown Gradient Descent Approach ###Code Image(filename="../imgs/lesson_1_multi_variable_linear_regression.png", width=700, height=400) # randomly initialize theta theta_multi = np.array([1, -0.7, -0.5, 0.7]) alpha_multi = 0.001 epochs_multi = 10000 batch_size_multi = m # batch gradient descent cost_multi_list, theta_multi_list = gradient_descent(X_train_multi, y_train_multi, alpha_multi, epochs_multi, batch_size_multi, theta_multi) final_theta_multi = theta_multi_list[-1] print(final_theta_multi) ###Output [ 2.04801055 -0.50381761 -0.65300886 6.17587267] ###Markdown Feature Scaling ###Code from sklearn.preprocessing import StandardScaler lstat_scaler = StandardScaler() ptratio_scaler = StandardScaler() rm_scaler = StandardScaler() print(lstat_scaler) lstat_scaled = lstat_scaler.fit_transform(lstat) full_set_size = lstat.shape[0] ones = np.ones((full_set_size,1)) pupil_teacher_ratio_scaled = ptratio_scaler.fit_transform(pupil_teacher_ratio) rooms_scaled = rm_scaler.fit_transform(rooms) X_multi_normalized = np.hstack((ones, lstat_scaled, pupil_teacher_ratio_scaled, rooms_scaled)) X_train_multi, X_test_multi, y_train_multi, y_test_multi = train_test_split(X_multi_normalized, y_multi, test_size=0.20, random_state=42) m = X_train_multi.shape[0] y_train_multi.shape # randomly initialize theta theta_multi = np.array([1, -0.7, -0.5, 0.7]) alpha_multi = 0.001 epochs_multi = 10000 batch_size_multi = m # batch gradient descent cost_multi_list, theta_multi_list = gradient_descent(X_train_multi, y_train_multi, alpha_multi, epochs_multi, batch_size_multi, theta_multi) final_theta_multi = theta_multi_list[-1] print(final_theta_multi) ###Output [22.48285741 -4.02720936 -2.07026507 3.34308824] ###Markdown Normal EquationYou can also use the normal equation instead of gradient descent to avoid the iterations and get the final theta list in one go.This works best when there are fewer n features than m training examples because the computation cost can get expensive as n increases. O(n^3) ###Code Image(filename="../imgs/lesson_1_gd_vs_ne.png", width=1000, height=700) final_theta_list = np.linalg.inv(X_train_multi.T.dot(X_train_multi)).dot(X_train_multi.T).dot(y_train_multi) final_theta_list ###Output _____no_output_____

docs/gallery/plot_skewsurge.ipynb

###Markdown Skew surge examples ###Code import pandas as pd import toto import matplotlib.pyplot as plt from toto.inputs.nc import NCfile import os # read the file filename='https://raw.githubusercontent.com/calypso-science/Toto/master/_tests/nc_file/elevation.nc' os.system('wget %s '% filename) df=NCfile('elevation.nc')._toDataFrame() # Processing df_new=df[0].TideAnalysis.skew_surge(mag='elev40',args={'latitude':-36}) # Plot the results fig, ax = plt.subplots(1) ax.plot(df[0].index,df[0]['elev40'],label='Elevation') ax.plot(df_new.index,df_new['skew_surge'],label='Skew surge') ax.legend() fig.autofmt_xdate() plt.show() ###Output _____no_output_____

docs/content/04_auto_naive.ipynb

###Markdown Automatically selecting a naive model to use as a benchmarkforecast-tools provides a `auto_naive` function that uses point-forecast cross validation to select the 'best' naive model to use as a benchmark. The function tests all of the naive `Forecast` methods.This notebook covers how to use `auto_naive` and also how to trouble shoot it use if there are conflicts between parameters. Imports ###Code import sys # if running in Google Colab install forecast-tools if 'google.colab' in sys.modules: !pip install forecast-tools import numpy as np from forecast_tools.datasets import load_emergency_dept from forecast_tools.model_selection import auto_naive help(auto_naive) ###Output Help on function auto_naive in module forecast_tools.model_selection: auto_naive(y_train, horizon=1, seasonal_period=1, min_train_size='auto', method='cv', step=1, window_size='auto', metric='mae') Automatic selection of the 'best' naive benchmark on a 'single' series The selection process uses out-of-sample cv performance. By default auto_naive uses cross validation to estimate the mean point forecast peformance of all naive methods. It selects the method with the lowest point forecast metric on average. If there is limited data for training a basic holdout sample could be used. Dev note: the plan is to update this to work with multiple series. It would be best to use MASE for multiple series comparison. Parameters: ---------- y_train: array-like training data. typically in a pandas.Series, pandas.DataFrame or numpy.ndarray format. horizon: int, optional (default=1) Forecast horizon. seasonal_period: int, optional (default=1) Frequency of the data. E.g. 7 for weekly pattern, 12 for monthly 365 for daily. min_train_size: int or str, optional (default='auto') The size of the initial training set (if method=='ro' or 'sw'). If 'auto' then then min_train_size is set to len(y_train) // 3 If main_train_size='auto' and method='holdout' then min_train_size = len(y_train) - horizon. method: str, optional (default='cv') out of sample selection method. 'ro' - rolling forecast origin 'sw' - sliding window 'cv' - scores from both ro and sw 'holdout' - single train/test split Methods'ro' and 'sw' are similar, however, sw has a fixed window_size and drops older data from training. step: int, optional (default=1) The stride/step of the cross-validation. I.e. the number of observations to move forward between folds. window_size: str or int, optional (default='auto') The window_size if using sliding window cross validation When 'auto' and method='sw' then window_size=len(y_train) // 3 metric: str, optional (default='mae') The metric to measure out of sample accuracy. Options: mase, mae, mape, smape, mse, rmse, me. Returns: -------- dict 'model': baseline.Forecast f'{metric}': float Contains the model and its CV performance. Raises: ------- ValueError For invalid method, metric, window_size parameters See Also: -------- forecast_tools.baseline.Naive1 forecast_tools.baseline.SNaive forecast_tools.baseline.Drift forecast_tools.baseline.Average forecast_tools.baseline.EnsembleNaive forecast_tools.baseline.baseline_estimators forecast_tools.model_selection.rolling_forecast_origin forecast_tools.model_selection.sliding_window forecast_tools.model_selection.mase_cross_validation_score forecast_tools.metrics.mean_absolute_scaled_error Examples: --------- Measuring MAE and taking the best method using both rolling origin and sliding window cross validation of a 56 day forecast. >>> from forecast_tools.datasets import load_emergency_dept >>> y_train = load_emergency_dept >>> best = auto_naive(y_train, seasonal_period=7, horizon=56) >>> best {'model': Average(), 'mae': 19.63791579700355} Take a step of 7 days between cv folds. >>> from forecast_tools.datasets import load_emergency_dept >>> y_train = load_emergency_dept >>> best = auto_naive(y_train, seasonal_period=7, horizon=56, ... step=7) >>> best {'model': Average(), 'mae': 19.675635558539383} ###Markdown Load the training data ###Code y_train = load_emergency_dept() ###Output _____no_output_____ ###Markdown Select the best naive model for a h-step horizon of 7 days.Let's select a method for the emergency deparment daily level to predict 7 days ahead. By default the function using the **mean absolute error** to evaluate forecast accuracy. ###Code best = auto_naive(y_train, horizon=7, seasonal_period=7) best y_preds = best['model'].fit_predict(y_train, horizon=7) y_preds ###Output _____no_output_____ ###Markdown Using a different forecasting error metric ###Code best = auto_naive(y_train, horizon=7, seasonal_period=7, metric='mape') best ###Output _____no_output_____ ###Markdown Using a single train-test split when data are limited.If your forecast horizon means that h-step cross-validation is infeasible then you can automatically select using a single holdout sample. ###Code best = auto_naive(y_train, horizon=7, seasonal_period=7, method='holdout') best ###Output _____no_output_____ ###Markdown Trouble shooting use of `auto_naive`**Problem 1:** Training data is shorter than the `min_train_size` + `horizon`For any validation to take place, including a simple holdout - the time series used must allow at least one train test split to take place. This can be a problem when seasonal_period is set to a length similar to the length of the time series. ###Code # generate a synthetic daily time series of exactly one year in length. y_train = np.random.randint(100, 250, size=365) ###Output _____no_output_____ ###Markdown Let's set seasonal period to `seasonal_period=365` (the length of the time series) and `horizon=7`.We will also manually set `min_train_size=365`This will generate a `ValueError` reporting that the "The training data is shorter than min_train_size + horizon No validation can be performed." ###Code best = auto_naive(y_train, horizon=7, seasonal_period=365, method='ro', min_train_size=365, metric='mae') best ###Output _____no_output_____ ###Markdown A longer time series or a shorter seasonal period will fix this problem. ###Code # a longer synthetic time series. y_train = np.random.randint(100, 250, size=365+7) best = auto_naive(y_train, horizon=7, seasonal_period=365, method='ro', min_train_size=365, metric='mae') best # a shorter seasonal period and minimum training size y_train = np.random.randint(100, 250, size=365) best = auto_naive(y_train, horizon=7, seasonal_period=7, method='ro', min_train_size=7, metric='mae') best ###Output _____no_output_____

5. Computer Vision/.ipynb_checkpoints/Feature Detection-checkpoint.ipynb

###Markdown Author: Vo, Huynh Quang Nguyen ###Code import cv2 import numpy as np import random import matplotlib.pyplot as plt from ipywidgets import interact from sklearn.preprocessing import minmax_scale ###Output _____no_output_____

Pytorch/tensor/tensor.ipynb

###Markdown Tensor - 判断obj是否为一个pytorch对象，是则返回Truetorch.is_tensor(obj)- 判断obj是否为一个Pytorch storage对象，是则返回Truetorch.is_storage(obj)- 设置当前tensor的默认数据类型torch.set_default_tensor_type(t) ###Code torch.tensor([1.2, 3]).dtype torch.set_default_tensor_type(torch.DoubleTensor) torch.tensor([1.2, 3]).dtype ###Output _____no_output_____ ###Markdown - 返回input张量中的元素个数.input(Tensor)表示输入张量torch.numel(input)->int ###Code a = torch.randn(1, 2, 3, 4, 5) torch.numel(a) a = torch.zeros(4, 4) torch.numel(a) ###Output _____no_output_____

deeplearning1/nbs/fisheries_daniel.ipynb

###Markdown Major Key: SGD did way better than Adam on this ###Code myModel.optimizer.lr=1e-3 myModel.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=2, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/2 307/307 [==============================] - 11s - loss: 1.0734 - acc: 0.7199 - val_loss: 1.9440 - val_acc: 0.4883 Epoch 2/2 307/307 [==============================] - 11s - loss: 0.7735 - acc: 0.8274 - val_loss: 1.7796 - val_acc: 0.4883 ###Markdown Increased lr by a factor of 10--went even better! 60.56% on validation but 97% on training... underfitting??? ###Code from keras.optimizers import Nadam myModel.summary() myModel.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=2, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/2 307/307 [==============================] - 11s - loss: 0.6615 - acc: 0.8697 - val_loss: 1.8520 - val_acc: 0.5634 Epoch 2/2 307/307 [==============================] - 11s - loss: 0.5587 - acc: 0.9055 - val_loss: 1.7588 - val_acc: 0.5775 ###Markdown Let's try some data augmentation! I'll also now try 10 epochs and see if things improve. ###Code gen_t = image.ImageDataGenerator(width_shift_range=0.1) batches = get_batches(path+'train', gen_t, batch_size=batch_size) myModel = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Convolution2D(3,3,32,activation='relu'), BatchNormalization(axis=1), MaxPooling2D(pool_size=(2,2)), Flatten(), Dense(8,activation='softmax', W_regularizer=l2(0.01)) ]) newModel = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Convolution2D(3,3,32,activation='relu'), BatchNormalization(axis=1), MaxPooling2D(pool_size=(2,2)), Flatten(), Dense(8,activation='softmax', W_regularizer=l2(0.01)) ]) def nadam1(batches): model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Convolution2D(3,3,32,activation='relu'), BatchNormalization(axis=1), MaxPooling2D(pool_size=(2,2)), Flatten(), Dense(8,activation='softmax', W_regularizer=l2(0.01)) ]) model.compile(Nadam(lr=1e-4), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(batches, batches.nb_sample, nb_epoch=10, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr = 0.001 model.fit_generator(batches, batches.nb_sample, nb_epoch=10, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) return model # print("Nadam:") # myModel.compile(Nadam, loss='categorical_crossentropy',metrics=['accuracy']) # myModel.fit_generator(batches, batches.nb_sample, nb_epoch=10, # validation_data=val_batches, nb_val_samples=val_batches.nb_sample) print("Nadam w slower rate, 5 epochs") model = nadam1(batches) ###Output Nadam w slower rate, 5 epochs Epoch 1/10 307/307 [==============================] - 12s - loss: 2.5352 - acc: 0.3811 - val_loss: 2.7860 - val_acc: 0.4648 Epoch 2/10 307/307 [==============================] - 11s - loss: 1.9833 - acc: 0.4919 - val_loss: 2.4024 - val_acc: 0.4695 Epoch 3/10 307/307 [==============================] - 11s - loss: 1.6503 - acc: 0.5700 - val_loss: 2.1790 - val_acc: 0.4225 Epoch 4/10 307/307 [==============================] - 11s - loss: 1.4354 - acc: 0.6384 - val_loss: 2.1610 - val_acc: 0.4930 Epoch 5/10 307/307 [==============================] - 11s - loss: 1.3813 - acc: 0.6319 - val_loss: 2.0069 - val_acc: 0.5117 Epoch 6/10 307/307 [==============================] - 11s - loss: 1.3305 - acc: 0.6645 - val_loss: 2.3662 - val_acc: 0.4742 Epoch 7/10 307/307 [==============================] - 11s - loss: 1.1625 - acc: 0.7068 - val_loss: 1.8504 - val_acc: 0.5822 Epoch 8/10 307/307 [==============================] - 11s - loss: 0.9239 - acc: 0.7590 - val_loss: 1.9372 - val_acc: 0.5493 Epoch 9/10 307/307 [==============================] - 11s - loss: 1.0125 - acc: 0.7459 - val_loss: 1.8556 - val_acc: 0.6150 Epoch 10/10 307/307 [==============================] - 11s - loss: 0.8473 - acc: 0.7915 - val_loss: 1.9488 - val_acc: 0.5634 Epoch 1/10 307/307 [==============================] - 12s - loss: 0.9930 - acc: 0.7362 - val_loss: 1.9149 - val_acc: 0.5728 Epoch 2/10 307/307 [==============================] - 11s - loss: 0.8264 - acc: 0.7948 - val_loss: 1.8654 - val_acc: 0.5962 Epoch 3/10 307/307 [==============================] - 11s - loss: 0.8495 - acc: 0.8078 - val_loss: 1.9818 - val_acc: 0.5822 Epoch 4/10 307/307 [==============================] - 11s - loss: 0.7029 - acc: 0.8469 - val_loss: 1.7591 - val_acc: 0.6103 Epoch 5/10 307/307 [==============================] - 11s - loss: 0.8047 - acc: 0.7948 - val_loss: 1.8144 - val_acc: 0.5869 Epoch 6/10 307/307 [==============================] - 11s - loss: 0.8310 - acc: 0.7948 - val_loss: 2.2518 - val_acc: 0.5681 Epoch 7/10 307/307 [==============================] - 11s - loss: 0.6199 - acc: 0.8534 - val_loss: 1.9282 - val_acc: 0.6103 Epoch 8/10 307/307 [==============================] - 10s - loss: 0.5734 - acc: 0.8697 - val_loss: 2.2699 - val_acc: 0.6103 Epoch 9/10 307/307 [==============================] - 11s - loss: 0.6346 - acc: 0.8404 - val_loss: 2.0220 - val_acc: 0.6197 Epoch 10/10 307/307 [==============================] - 11s - loss: 0.5734 - acc: 0.8958 - val_loss: 2.0441 - val_acc: 0.6197 ###Markdown Data augmentation with everything! ###Code gen_t = image.ImageDataGenerator(width_shift_range=0.1, height_shift_range=0.05, shear_range=0.1, rotation_range=15, channel_shift_range=20) batches = get_batches(path+'train', gen_t, batch_size=batch_size) model = nadam1(batches) ###Output Epoch 1/10 307/307 [==============================] - 12s - loss: 2.4586 - acc: 0.3876 - val_loss: 3.0396 - val_acc: 0.3427 Epoch 2/10 307/307 [==============================] - 11s - loss: 2.1106 - acc: 0.4658 - val_loss: 2.1184 - val_acc: 0.4789 Epoch 3/10 307/307 [==============================] - 11s - loss: 1.9526 - acc: 0.5081 - val_loss: 2.2154 - val_acc: 0.4695 Epoch 4/10 307/307 [==============================] - 11s - loss: 1.9679 - acc: 0.5277 - val_loss: 2.2608 - val_acc: 0.4554 Epoch 5/10 307/307 [==============================] - 11s - loss: 1.9388 - acc: 0.4853 - val_loss: 2.0875 - val_acc: 0.5023 Epoch 6/10 307/307 [==============================] - 11s - loss: 1.9619 - acc: 0.5277 - val_loss: 2.2217 - val_acc: 0.5070 Epoch 7/10 307/307 [==============================] - 11s - loss: 1.8347 - acc: 0.5537 - val_loss: 2.3904 - val_acc: 0.4930 Epoch 8/10 307/307 [==============================] - 11s - loss: 1.8023 - acc: 0.5635 - val_loss: 2.2147 - val_acc: 0.5258 Epoch 9/10 307/307 [==============================] - 11s - loss: 1.8591 - acc: 0.5603 - val_loss: 2.2778 - val_acc: 0.5164 Epoch 10/10 307/307 [==============================] - 11s - loss: 1.5403 - acc: 0.6059 - val_loss: 2.3472 - val_acc: 0.5164 Epoch 1/10 307/307 [==============================] - 12s - loss: 1.6693 - acc: 0.5993 - val_loss: 2.5966 - val_acc: 0.5352 Epoch 2/10 307/307 [==============================] - 11s - loss: 1.8011 - acc: 0.5765 - val_loss: 2.5407 - val_acc: 0.5117 Epoch 3/10 307/307 [==============================] - 11s - loss: 1.5340 - acc: 0.5961 - val_loss: 2.6173 - val_acc: 0.5634 Epoch 4/10 307/307 [==============================] - 11s - loss: 1.6147 - acc: 0.6059 - val_loss: 2.4969 - val_acc: 0.5258 Epoch 5/10 307/307 [==============================] - 11s - loss: 1.5844 - acc: 0.5896 - val_loss: 2.5623 - val_acc: 0.4742 Epoch 6/10 307/307 [==============================] - 11s - loss: 1.5849 - acc: 0.5961 - val_loss: 2.6317 - val_acc: 0.5305 Epoch 7/10 307/307 [==============================] - 11s - loss: 1.5488 - acc: 0.5896 - val_loss: 2.6498 - val_acc: 0.5399 Epoch 8/10 307/307 [==============================] - 11s - loss: 1.5577 - acc: 0.5668 - val_loss: 2.4135 - val_acc: 0.5352 Epoch 9/10 307/307 [==============================] - 11s - loss: 1.6690 - acc: 0.5961 - val_loss: 2.5189 - val_acc: 0.5211 Epoch 10/10 307/307 [==============================] - 11s - loss: 1.4140 - acc: 0.6417 - val_loss: 2.7212 - val_acc: 0.5540 ###Markdown It's getting better--let's try turning down lr and running more epochs! Findings:We keep getting better! Epoch 5 of Nadam w a slower rate seems to be best, but it looks like we're overfitting on the training data a little bit... Let's come back and see what we can do to reduce this overfitting. Also, for some reason when I take things out of functions it starts giving me errors. I can't use model.optimizer.lr when I have model as a function but when I take it out I get a host of other errors.I'm also getting some cases where as the epoch continues the accuracy gets worse... Also in this specific case my val_loss was the highest on the final epoch. ###Code model.optimizer.lr = 0.0001 model.fit_generator(batches, batches.nb_sample, nb_epoch=10, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/10 307/307 [==============================] - 12s - loss: 1.4011 - acc: 0.6678 - val_loss: 2.4876 - val_acc: 0.5540 Epoch 2/10 307/307 [==============================] - 11s - loss: 1.4969 - acc: 0.6482 - val_loss: 2.3973 - val_acc: 0.5634 Epoch 3/10 307/307 [==============================] - 11s - loss: 1.5251 - acc: 0.6254 - val_loss: 2.6143 - val_acc: 0.4977 Epoch 4/10 307/307 [==============================] - 11s - loss: 1.4222 - acc: 0.6124 - val_loss: 2.5558 - val_acc: 0.5587 Epoch 5/10 307/307 [==============================] - 11s - loss: 1.6291 - acc: 0.6059 - val_loss: 2.6840 - val_acc: 0.5446 Epoch 6/10 307/307 [==============================] - 11s - loss: 1.5204 - acc: 0.6319 - val_loss: 2.4550 - val_acc: 0.5352 Epoch 7/10 307/307 [==============================] - 11s - loss: 1.3750 - acc: 0.6384 - val_loss: 2.2908 - val_acc: 0.5681 Epoch 8/10 307/307 [==============================] - 11s - loss: 1.3818 - acc: 0.6710 - val_loss: 2.6775 - val_acc: 0.5915 Epoch 9/10 307/307 [==============================] - 11s - loss: 1.5074 - acc: 0.6450 - val_loss: 2.6073 - val_acc: 0.5258 Epoch 10/10 307/307 [==============================] - 11s - loss: 1.7378 - acc: 0.5896 - val_loss: 2.2587 - val_acc: 0.6056 ###Markdown What I know:We're most likely underfitting--val accuracy/loss gets worse as time goes on sometimes, it doesn't seem like there's a consistent improvement or decline though. I've added both data aug and L2 regularization, so I'm not sure what other ways might help with what I'm trying to do. Maybe remove L2 since it technically prevents ~overfitting?Let's also try less data aug. ###Code gen_t = image.ImageDataGenerator(width_shift_range=0.1, height_shift_range=0.05, shear_range=0.1, channel_shift_range=20) batches = get_batches(path+'train', gen_t, batch_size=batch_size) model.fit_generator(batches, batches.nb_sample, nb_epoch=10, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) def nadam2(batches): #same as before, just without L2! model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Convolution2D(3,3,32,activation='relu'), BatchNormalization(axis=1), MaxPooling2D(pool_size=(2,2)), Flatten(), Dense(8,activation='softmax') ]) model.compile(Nadam(lr=1e-4), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(batches, batches.nb_sample, nb_epoch=10, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr = 0.001 model.fit_generator(batches, batches.nb_sample, nb_epoch=10, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) return model model2 = nadam2(batches) ###Output Epoch 1/10 307/307 [==============================] - 12s - loss: 2.2928 - acc: 0.3909 - val_loss: 2.5572 - val_acc: 0.4413 Epoch 2/10 307/307 [==============================] - 11s - loss: 1.9985 - acc: 0.4756 - val_loss: 2.1686 - val_acc: 0.3709 Epoch 3/10 307/307 [==============================] - 11s - loss: 1.5476 - acc: 0.5700 - val_loss: 2.1391 - val_acc: 0.4460 Epoch 4/10 307/307 [==============================] - 11s - loss: 1.8373 - acc: 0.4886 - val_loss: 2.7411 - val_acc: 0.3709 Epoch 5/10 307/307 [==============================] - 11s - loss: 1.6762 - acc: 0.5570 - val_loss: 2.3732 - val_acc: 0.4789 Epoch 6/10 307/307 [==============================] - 11s - loss: 1.5732 - acc: 0.6091 - val_loss: 2.1126 - val_acc: 0.5728 Epoch 7/10 307/307 [==============================] - 11s - loss: 1.2451 - acc: 0.6515 - val_loss: 2.2953 - val_acc: 0.5070 Epoch 8/10 307/307 [==============================] - 11s - loss: 1.6839 - acc: 0.5961 - val_loss: 2.3208 - val_acc: 0.4836 Epoch 9/10 307/307 [==============================] - 11s - loss: 1.4500 - acc: 0.6352 - val_loss: 2.2735 - val_acc: 0.4695 Epoch 10/10 307/307 [==============================] - 11s - loss: 1.3605 - acc: 0.6319 - val_loss: 2.1790 - val_acc: 0.4930 Epoch 1/10 307/307 [==============================] - 12s - loss: 1.3481 - acc: 0.6384 - val_loss: 2.0906 - val_acc: 0.5634 Epoch 2/10 307/307 [==============================] - 11s - loss: 1.2524 - acc: 0.6840 - val_loss: 2.2438 - val_acc: 0.5164 Epoch 3/10 307/307 [==============================] - 11s - loss: 1.2339 - acc: 0.6515 - val_loss: 2.3701 - val_acc: 0.5258 Epoch 4/10 307/307 [==============================] - 11s - loss: 1.2960 - acc: 0.6221 - val_loss: 2.1161 - val_acc: 0.5446 Epoch 5/10 307/307 [==============================] - 11s - loss: 1.3181 - acc: 0.6352 - val_loss: 2.1475 - val_acc: 0.5493 Epoch 6/10 307/307 [==============================] - 11s - loss: 1.3639 - acc: 0.6287 - val_loss: 2.3719 - val_acc: 0.4554 Epoch 7/10 307/307 [==============================] - 11s - loss: 1.1513 - acc: 0.6612 - val_loss: 2.3568 - val_acc: 0.5070 Epoch 8/10 307/307 [==============================] - 11s - loss: 1.1248 - acc: 0.6515 - val_loss: 2.3735 - val_acc: 0.4742 Epoch 9/10 307/307 [==============================] - 11s - loss: 0.9928 - acc: 0.7362 - val_loss: 2.3203 - val_acc: 0.5540 Epoch 10/10 307/307 [==============================] - 11s - loss: 1.1045 - acc: 0.6808 - val_loss: 2.2094 - val_acc: 0.5446 ###Markdown Baseline: Simple Linear Model ###Code model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Flatten(), Dense(8,activation='softmax') ]) model.compile('Adam', loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(train_batches, train_batches.nb_sample,nb_epoch=3, validation_data = val_batches, nb_val_samples=val_batches.nb_sample) model.summary() np.round(model.predict_generator(train_batches, train_batches.N)[:10],2) ###Output _____no_output_____ ###Markdown Let's try a lower learning rate! ###Code model.compile(Adam(lr=1e-5), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 307/307 [==============================] - 12s - loss: 8.0328 - acc: 0.5016 - val_loss: 9.5571 - val_acc: 0.4038 Epoch 2/3 307/307 [==============================] - 11s - loss: 8.0328 - acc: 0.5016 - val_loss: 9.5918 - val_acc: 0.4038 Epoch 3/3 307/307 [==============================] - 11s - loss: 8.0328 - acc: 0.5016 - val_loss: 9.5874 - val_acc: 0.4038 ###Markdown Huh, val_acc = 0.4038 for every one of the above--that's interesting consistency. ###Code model.optimizer.lr = 0.001 model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 307/307 [==============================] - 12s - loss: 8.0328 - acc: 0.5016 - val_loss: 9.5942 - val_acc: 0.3991 Epoch 2/3 307/307 [==============================] - 11s - loss: 8.0328 - acc: 0.5016 - val_loss: 9.6017 - val_acc: 0.3991 Epoch 3/3 307/307 [==============================] - 12s - loss: 8.0328 - acc: 0.5016 - val_loss: 9.6053 - val_acc: 0.3991 ###Markdown Again, acc=0.5016 the same as before, while val_acc is lower but only slightly so at 0.3991--but they're all the same again!! So we've hit some sort of consistency but we're still probably at either some local minimum or jumping too far to hit the global?S ###Code rnd_batches = get_batches(path+'valid', batch_size=batch_size*2, shuffle=True) val_res = [model.evaluate_generator(rnd_batches, rnd_batches.nb_sample) for i in range(10)] np.round(val_res,2) ###Output _____no_output_____ ###Markdown From StackOverflow: evaluate_generator uses both your test input and output. It first predicts output using training input and then evaluates performance by comparing it against your test output. So it gives out a measure of performance, i.e. accuracy in your case.So what we just did above was see what the performance of our model is on 10 things so we can see if there are statstically significant differences in performance. Turns out it's pretty consistent:min_acc = 0.38max_acc = 0.42 Linear w/ L2 Regularization ###Code model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Flatten(), Dense(8,activation='softmax', W_regularizer=l2(0.01)) ]) model.compile(Adam(lr=10e-5), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 307/307 [==============================] - 13s - loss: 11.0260 - acc: 0.1889 - val_loss: 12.8843 - val_acc: 0.1784 Epoch 2/3 307/307 [==============================] - 11s - loss: 9.8730 - acc: 0.3453 - val_loss: 12.3482 - val_acc: 0.1737 Epoch 3/3 307/307 [==============================] - 11s - loss: 7.8282 - acc: 0.4788 - val_loss: 9.7379 - val_acc: 0.3709 ###Markdown So that got... worse? Except for the last val_acc=.3709 which seems close to what we had before but now val_acc is around .17 ###Code model.optimizer.lr=0.001 model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 307/307 [==============================] - 12s - loss: 6.9488 - acc: 0.5537 - val_loss: 8.8606 - val_acc: 0.4085 Epoch 2/3 307/307 [==============================] - 11s - loss: 6.4381 - acc: 0.5798 - val_loss: 7.6627 - val_acc: 0.5023 Epoch 3/3 307/307 [==============================] - 13s - loss: 5.8013 - acc: 0.6287 - val_loss: 7.6443 - val_acc: 0.5258 ###Markdown woahhhh we jumped like 10 whole percents Single layer! ###Code model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Flatten(), Dense(100, activation='relu'), BatchNormalization(), Dense(8,activation='softmax') ]) model.compile(Adam(lr=1e-5), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 307/307 [==============================] - 12s - loss: 2.4102 - acc: 0.1107 - val_loss: 5.9550 - val_acc: 0.0516 Epoch 2/3 307/307 [==============================] - 11s - loss: 2.2192 - acc: 0.1433 - val_loss: 3.3458 - val_acc: 0.0704 Epoch 3/3 307/307 [==============================] - 11s - loss: 2.1259 - acc: 0.1759 - val_loss: 2.7295 - val_acc: 0.0939 ###Markdown Full Dataset? Let's try our models on the full dataset to see wtf happens ###Code #redefine location: path = "data/fisheries/" batch_size=64 val_batches = get_batches(path+'valid', shuffle = False, batch_size=batch_size) train_batches = get_batches(path+'train', shuffle = False, batch_size=batch_size) train_data = get_data(path+'train') val_data = get_data(path+'valid') model_path = path + 'models/' if not os.path.exists(model_path): os.mkdir(model_path) save_array(model_path+'train_data.bc',train_data) save_array(model_path+'val_data.bc',val_data) train_data = load_array(model_path+'train_data.bc') val_data = load_array(model_path+'val_data.bc') train_classes = train_batches.classes train_labels = onehot(train_classes) val_classes = val_batches.classes val_labels = onehot(val_classes) model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Flatten(), Dense(100, activation='relu'), BatchNormalization(), Dense(8,activation='softmax') ]) model.compile(Adam(lr=1e-5), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=5, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr=0.001 model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=5, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/5 3021/3021 [==============================] - 88s - loss: 2.0324 - acc: 0.2171 - val_loss: 1.9101 - val_acc: 0.2540 Epoch 2/5 3021/3021 [==============================] - 74s - loss: 2.0216 - acc: 0.2122 - val_loss: 1.8664 - val_acc: 0.2844 Epoch 3/5 3021/3021 [==============================] - 73s - loss: 2.0090 - acc: 0.2105 - val_loss: 1.8136 - val_acc: 0.3280 Epoch 4/5 3021/3021 [==============================] - 74s - loss: 1.9979 - acc: 0.2387 - val_loss: 1.7976 - val_acc: 0.3836 Epoch 5/5 3021/3021 [==============================] - 74s - loss: 1.9893 - acc: 0.2483 - val_loss: 1.7904 - val_acc: 0.3730 ###Markdown Let's try a different batch size. ###Code batch_size=32 val_batches = get_batches(path+'valid', shuffle = False, batch_size=batch_size) train_batches = get_batches(path+'train', shuffle = False, batch_size=batch_size) ###Output Found 756 images belonging to 8 classes. Found 3021 images belonging to 8 classes. ###Markdown ok we need to actually do smth w batch size ###Code val_batches = get_batches(path+'valid', shuffle = False, batch_size=batch_size) train_batches = get_batches(path+'train', shuffle = False, batch_size=batch_size) model.optimizer.lr=0.001 model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 3021/3021 [==============================] - 86s - loss: 2.0613 - acc: 0.1837 - val_loss: 1.7948 - val_acc: 0.3611 Epoch 2/3 3021/3021 [==============================] - 79s - loss: 2.0496 - acc: 0.1870 - val_loss: 1.7940 - val_acc: 0.3505 Epoch 3/3 3021/3021 [==============================] - 78s - loss: 2.0377 - acc: 0.1903 - val_loss: 1.8203 - val_acc: 0.3148 ###Markdown Data Augmentation ###Code gen_t = image.ImageDataGenerator(width_shift_range=0.1, height_shift_range=0.05, shear_range=0.1, rotation_range=15, channel_shift_range=20) batches = get_batches(path+'train', gen_t, batch_size=batch_size) model.compile(Adam(lr=1e-5), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(batches, batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr = 0.001 model.fit_generator(batches, batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 3021/3021 [==============================] - 86s - loss: 1.3066 - acc: 0.6001 - val_loss: 0.9981 - val_acc: 0.7050 Epoch 2/3 3021/3021 [==============================] - 79s - loss: 1.3039 - acc: 0.5995 - val_loss: 1.0082 - val_acc: 0.7183 Epoch 3/3 3021/3021 [==============================] - 78s - loss: 1.2326 - acc: 0.6379 - val_loss: 0.8996 - val_acc: 0.7474 ###Markdown Let's try yet another batch size! ###Code batch_size=4 val_batches = get_batches(path+'valid', shuffle = False, batch_size=batch_size) train_batches = get_batches(path+'train', shuffle = False, batch_size=batch_size) gen_t = image.ImageDataGenerator(width_shift_range=0.1, height_shift_range=0.05, shear_range=0.1, rotation_range=15, channel_shift_range=20) batches = get_batches(path+'train', gen_t, batch_size=batch_size) model.fit_generator(batches, batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr = 0.001 model.fit_generator(batches, batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 3021/3021 [==============================] - 87s - loss: 1.5894 - acc: 0.4869 - val_loss: 1.1775 - val_acc: 0.6429 Epoch 2/3 3021/3021 [==============================] - 91s - loss: 1.5771 - acc: 0.4796 - val_loss: 1.2394 - val_acc: 0.6336 Epoch 3/3 3021/3021 [==============================] - 85s - loss: 1.5593 - acc: 0.4856 - val_loss: 1.1184 - val_acc: 0.6521 ###Markdown Multiple Conv Layers, No Dropout ###Code model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Convolution2D(32,3,3,activation='relu'), BatchNormalization(axis=1), MaxPooling2D((3,3)), Convolution2D(64,3,3,activation='relu'), BatchNormalization(axis=1), MaxPooling2D((3,3)), Flatten(), Dense(8,activation='softmax') ]) model.compile(Adam(lr=1e-4), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr = 0.001 model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 3021/3021 [==============================] - 85s - loss: 5.7406 - acc: 0.6319 - val_loss: 11.6924 - val_acc: 0.2407 Epoch 2/3 3021/3021 [==============================] - 84s - loss: 9.2482 - acc: 0.4035 - val_loss: 12.6926 - val_acc: 0.2050 Epoch 3/3 3021/3021 [==============================] - 84s - loss: 7.7163 - acc: 0.4975 - val_loss: 8.3025 - val_acc: 0.4153 Epoch 1/3 3021/3021 [==============================] - 84s - loss: 6.3223 - acc: 0.5885 - val_loss: 10.1639 - val_acc: 0.3280 Epoch 2/3 3021/3021 [==============================] - 83s - loss: 5.3827 - acc: 0.6485 - val_loss: 9.4309 - val_acc: 0.3545 Epoch 3/3 3021/3021 [==============================] - 83s - loss: 5.6896 - acc: 0.6236 - val_loss: 11.1571 - val_acc: 0.2632 ###Markdown Now with augmented data! ###Code model.compile(Adam(lr=1e-4), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(batches, batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr = 0.001 model.fit_generator(batches, batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 3021/3021 [==============================] - 87s - loss: 6.5129 - acc: 0.5081 - val_loss: 4.5715 - val_acc: 0.6548 Epoch 2/3 3021/3021 [==============================] - 86s - loss: 4.8140 - acc: 0.5770 - val_loss: 4.6160 - val_acc: 0.5979 Epoch 3/3 3021/3021 [==============================] - 84s - loss: 4.3397 - acc: 0.6071 - val_loss: 3.0918 - val_acc: 0.7063 Epoch 1/3 3021/3021 [==============================] - 85s - loss: 3.8087 - acc: 0.6200 - val_loss: 3.2387 - val_acc: 0.7011 Epoch 2/3 3021/3021 [==============================] - 85s - loss: 3.3493 - acc: 0.6352 - val_loss: 2.8213 - val_acc: 0.7143 Epoch 3/3 3021/3021 [==============================] - 84s - loss: 2.9250 - acc: 0.6614 - val_loss: 2.1025 - val_acc: 0.7646 ###Markdown Stanford-Recommended Model ###Code model = Sequential([ BatchNormalization(axis=1,input_shape=(3,224,224)), Convolution2D(32,3,3,activation='relu'), BatchNormalization(axis=1), MaxPooling2D((3,3)), Convolution2D(64,3,3,activation='relu'), BatchNormalization(axis=1), MaxPooling2D((3,3)), Flatten(), Dense(100,activation='relu'), BatchNormalization(axis=1), Dense(8,activation='softmax') ]) model.compile(Adam(lr=1e-5), loss='categorical_crossentropy', metrics=['accuracy']) model.fit_generator(train_batches, train_batches.nb_sample, nb_epoch=5, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) model.optimizer.lr = 0.001 model.fit_generator(batches, batches.nb_sample, nb_epoch=3, validation_data=val_batches, nb_val_samples=val_batches.nb_sample) ###Output Epoch 1/3 3021/3021 [==============================] - 86s - loss: 1.7861 - acc: 0.3853 - val_loss: 1.7726 - val_acc: 0.4683 Epoch 2/3 3021/3021 [==============================] - 85s - loss: 1.6163 - acc: 0.4657 - val_loss: 1.4920 - val_acc: 0.5251 Epoch 3/3 3021/3021 [==============================] - 85s - loss: 1.5182 - acc: 0.5197 - val_loss: 1.7912 - val_acc: 0.5860 ###Markdown Pseudo Labels First... Let's grab ImageNet. ###Code vgg = Vgg16() model = vgg.model #gets last convolutional layer in the model so we can grab its output shape last_conv_idx = [i for i,l in enumerate(model.layers) if type(l) is Convolution2D][-1] conv_layers = model.layers[:last_conv_idx+1] conv_model = Sequential(conv_layers) ###Output _____no_output_____ ###Markdown Now we'll make a bn model with a simplified version of vgg dense layers ###Code def get_bn_layers(p): return [ MaxPooling2D(input_shape=conv_layers[-1].output_shape[1:]), Flatten(), Dropout(p/2), Dense(128,activation='relu'), BatchNormalization(), Dropout(p/2), Dense(128,activation='relu'), BatchNormalization(), Dropout(p), Dense(8,activation='softmax') ] ###Output _____no_output_____ ###Markdown Now we'll create features from vgg ###Code batches = get_batches(path+'train', batch_size=64, shuffle=False) #test_batches = get_batches(path+'test_stg1', shuffle=False, batch_size=1) (val_classes, trn_classes, val_labels, trn_labels, val_filenames, filenames, test_filenames) = get_classes(path) conv_feat = conv_model.predict_generator(batches,batches.nb_sample) conv_val_feat = conv_model.predict_generator(val_batches,val_batches.nb_sample) conv_test_feat = conv_model.predict_generator(test_batches,test_batches.nb_sample) save_array(path+'results/conv_val_feat.dat', conv_val_feat) save_array(path+'results/conv_test_feat.dat', conv_test_feat) save_array(path+'results/conv_feat.dat', conv_feat) conv_feat = load_array(path+'results/conv_feat.dat') conv_val_feat = load_array(path+'results/conv_val_feat.dat') conv_val_feat.shape def get_bn_da_layers(p): return [ MaxPooling2D(input_shape=conv_layers[-1].output_shape[1:]), Flatten(), Dropout(p), Dense(256, activation='relu'), BatchNormalization(), Dropout(p), Dense(256, activation='relu'), BatchNormalization(), Dropout(p), Dense(10, activation='softmax') ] p=0.8 bn_model=Sequential(get_bn_da_layers(p)) bn_model.compile(Adam(lr=1e-5), loss="categorical_crossentropy",metrics=["accuracy"]) #data aug gen_t = image.ImageDataGenerator(rotation_range=15, height_shift_range=0.05, shear_range=0.1, channel_shift_range=20, width_shift_range=0.1) da_batches = get_batches(path+'train', gen_t, batch_size=batch_size, shuffle=False) da_conv_feat = conv_model.predict_generator(da_batches,da_batches.nb_sample*5) save_array(path+'results/da_conv_feat2.dat', da_conv_feat) da_conv_feat = load_array(path+'results/da_conv_feat2.dat') da_conv_feat = np.concatenate([da_conv_feat, conv_feat]) da_trn_labels = np.concatenate([trn_labels]*6) ###Output _____no_output_____ ###Markdown Now for pseudo labeling! ###Code val_pseudo = bn_model.predict(conv_val_feat,batch_size=batch_size) comb_pseudo = np.concatenate([da_trn_labels,val_pseudo]) comb_feat = np.concatenate([da_conv_feat, conv_val_feat]) ###Output _____no_output_____ ###Markdown To tune the model up we'll need to train the conv thing ###Code bn_model.fit(da_conv_feat, da_trn_labels, batch_size=batch_size, nb_epoch=1, validation_data=(conv_val_feat, val_labels)) bn_model.optimizer.lr=0.01 bn_model.fit(da_conv_feat, da_trn_labels, batch_size=batch_size, nb_epoch=4, validation_data=(conv_val_feat, val_labels)) bn_model.optimizer.lr=0.0001 bn_model.fit(da_conv_feat, da_trn_labels, batch_size=batch_size, nb_epoch=4, validation_data=(conv_val_feat, val_labels)) bn_model.save_weights(path+'models/da_conv8_1.h5') ###Output _____no_output_____ ###Markdown Now to load the model! ###Code bn_model.load_weights(path+'models/da_conv8_1.h5') bn_model.fit(comb_feat, comb_pseudo, batch_size=batch_size,nb_epoch=1, validation_data=(conv_val_feat,val_labels)) bn_model.fit(comb_feat, comb_pseudo, batch_size=batch_size, nb_epoch=4, validation_data=(conv_val_feat, val_labels)) bn_model.optimizer.lr=0.00001 bn_model.fit(comb_feat, comb_pseudo, batch_size=batch_size, nb_epoch=4, validation_data=(conv_val_feat, val_labels)) bn_model.save_weights(path+'models/bn-ps8.h5') ###Output _____no_output_____ ###Markdown Submit ###Code def do_clip(arr, mx): return np.clip(arr, (1-mx)/9, mx) keras.metrics.categorical_crossentropy(val_labels, do_clip(val_preds, 0.93)).eval() conv_test_feat = load_array(path+'results/conv_test_feat.dat') preds = bn_model.predict(conv_test_feat, batch_size=batch_size*2) subm = do_clip(preds,0.93) subm_name = path+'results/subm.gz' classes = sorted(batches.class_indices, key=batches.class_indices.get) submission = pd.DataFrame(subm, columns=classes) submission.insert(0, 'img', [a[4:] for a in test_filenames]) submission.head() submission.to_csv(subm_name, index=False, compression='gzip') FileLink(subm_name) ###Output _____no_output_____

HW1/0816183_1.ipynb

###Markdown Artificial Intelligence - Assignment 1 1. DescriptionIn this assignment, you are going to solve the 8-puzzle using any algorithm. The `EightPuzzle` class is written and provided by TAs, you don't need to implement the puzzle yourself, just import and use. 2. How to use `EightPuzzle````pythonfrom eight_puzzle import EightPuzzle importpuzzle = EightPuzzle()puzzle.init() initialize a solvable puzzle statepuzzle.init(seed) initialize a solvable puzzle state using a seedprint(puzzle) show current puzzle state movepuzzle.move('up')puzzle.move('down')puzzle.move('left')puzzle.move('right')if puzzle.state == puzzle.FINAL_STATE: print('You have solved the puzzle') Useful: get the next state after you move in a direction, this won't change the internal state of EightPuzzle.state_after_move_up = puzzle.get_state_after_move(current_state, 'up')``` ###Code # NOTE: PLEASE KEEP THIS CELL NOT MODIFIED! # download eight_puzzle.py (YOU SHOULD NOT MODIFY eight_puzzle.py) !wget https://lab.djosix.com/eight_puzzle.py -qO eight_puzzle.py !sha1sum eight_puzzle.py from eight_puzzle import EightPuzzle, test ###Output 1b9a6e8af95aed1010690788274f6c453ae88ed6 eight_puzzle.py ###Markdown 3. Implement a search algorithm to solve 8-puzzle ###Code def myfunc(e): return e[1] def solve(p): h=0 count=0 s=list (p.state) fs=list (p.FINAL_STATE) for i in range(0,9): if s[i]!=fs[i]: h+=1 #heruristic the numberof misplaced tile q = [(p.state,count+h)] # A* queue v = {p.state: []} # map: state -> path to that state while q: #count+=1 q.sort(key=myfunc) #print(q[0]) state = list(q.pop(0)) #print(state[1]) if state[0] == p.FINAL_STATE: return v[state[0]] for d in p.DIRECTIONS: next_state = p.get_state_after_move(state[0], d) if next_state is not None and next_state not in v: ns=list(next_state) v[next_state] = v[state[0]] + [d] tmp=0 for i in range(0,9): if ns[i]!=fs[i]: tmp+=1 q.append((next_state,tmp+count)) return [] ###Output _____no_output_____ ###Markdown 4. Test your algorithm ###Code # NOTE: PLEASE KEEP THIS CELL NOT MODIFIED! results = test(solve, seed=1, n=100) ###Output Running tests with seed: 1 Test | seed: 17532741 | puzzle: (8, 5, 6, 0, 4, 7, 2, 1, 3) | elapsed: 0.0339s | solved Test | seed: 74572392 | puzzle: (1, 7, 2, 0, 6, 4, 3, 8, 5) | elapsed: 0.0094s | solved Test | seed: 58954043 | puzzle: (1, 6, 0, 3, 2, 5, 4, 7, 8) | elapsed: 0.0261s | solved Test | seed: 86504015 | puzzle: (8, 1, 3, 4, 0, 5, 6, 7, 2) | elapsed: 0.0085s | solved Test | seed: 84410468 | puzzle: (4, 5, 8, 2, 7, 0, 1, 6, 3) | elapsed: 0.0288s | solved Test | seed: 36821992 | puzzle: (1, 3, 8, 0, 6, 7, 2, 4, 5) | elapsed: 0.0081s | solved Test | seed: 77742434 | puzzle: (5, 1, 0, 8, 2, 7, 4, 6, 3) | elapsed: 0.0337s | solved Test | seed: 65485614 | puzzle: (1, 0, 3, 8, 2, 5, 6, 4, 7) | elapsed: 0.0058s | solved Test | seed: 75085546 | puzzle: (2, 3, 5, 4, 0, 8, 7, 1, 6) | elapsed: 0.0260s | solved Test | seed: 57887538 | puzzle: (6, 7, 8, 0, 5, 4, 3, 1, 2) | elapsed: 0.0195s | solved Test | seed: 65623117 | puzzle: (6, 4, 7, 5, 0, 3, 2, 1, 8) | elapsed: 0.0376s | solved Test | seed: 56449792 | puzzle: (5, 2, 1, 8, 3, 4, 7, 6, 0) | elapsed: 0.0187s | solved Test | seed: 10212701 | puzzle: (2, 7, 3, 4, 5, 0, 1, 8, 6) | elapsed: 0.0190s | solved Test | seed: 82273400 | puzzle: (2, 7, 6, 4, 1, 0, 8, 3, 5) | elapsed: 0.0113s | solved Test | seed: 82492277 | puzzle: (1, 7, 4, 5, 0, 2, 8, 6, 3) | elapsed: 0.0326s | solved Test | seed: 93683337 | puzzle: (4, 7, 0, 1, 2, 5, 8, 6, 3) | elapsed: 0.0190s | solved Test | seed: 92201978 | puzzle: (4, 3, 0, 5, 2, 1, 7, 8, 6) | elapsed: 0.0198s | solved Test | seed: 54444516 | puzzle: (5, 8, 4, 0, 6, 1, 2, 3, 7) | elapsed: 0.0775s | solved Test | seed: 71491422 | puzzle: (6, 1, 4, 2, 5, 0, 3, 7, 8) | elapsed: 0.0256s | solved Test | seed: 90511200 | puzzle: (8, 3, 0, 2, 5, 7, 6, 4, 1) | elapsed: 0.0178s | solved Test | seed: 13754738 | puzzle: (0, 2, 4, 5, 1, 8, 3, 6, 7) | elapsed: 0.0090s | solved Test | seed: 40817065 | puzzle: (5, 8, 0, 3, 7, 2, 4, 1, 6) | elapsed: 0.0155s | solved Test | seed: 95278064 | puzzle: (8, 0, 1, 5, 6, 7, 3, 4, 2) | elapsed: 0.0594s | solved Test | seed: 33784892 | puzzle: (6, 5, 4, 3, 8, 2, 1, 7, 0) | elapsed: 0.0206s | solved Test | seed: 83921254 | puzzle: (4, 0, 8, 6, 5, 3, 1, 2, 7) | elapsed: 0.0302s | solved Test | seed: 88445010 | puzzle: (7, 3, 5, 1, 2, 6, 4, 8, 0) | elapsed: 0.0407s | solved Test | seed: 34264416 | puzzle: (2, 5, 4, 7, 0, 3, 1, 6, 8) | elapsed: 0.0151s | solved Test | seed: 22294532 | puzzle: (7, 0, 2, 5, 4, 6, 1, 3, 8) | elapsed: 0.0761s | solved Test | seed: 83957878 | puzzle: (5, 7, 2, 8, 0, 1, 6, 3, 4) | elapsed: 0.0232s | solved Test | seed: 44264986 | puzzle: (5, 8, 0, 2, 1, 4, 6, 7, 3) | elapsed: 0.0304s | solved Test | seed: 14356590 | puzzle: (4, 1, 3, 8, 6, 2, 5, 0, 7) | elapsed: 0.0089s | solved Test | seed: 19456105 | puzzle: (3, 0, 4, 1, 2, 7, 5, 6, 8) | elapsed: 0.0261s | solved Test | seed: 21171496 | puzzle: (6, 1, 4, 0, 7, 5, 3, 8, 2) | elapsed: 0.1140s | solved Test | seed: 12240178 | puzzle: (6, 2, 3, 5, 7, 0, 4, 1, 8) | elapsed: 0.0162s | solved Test | seed: 70800468 | puzzle: (1, 0, 5, 6, 2, 3, 4, 7, 8) | elapsed: 0.0167s | solved Test | seed: 11954206 | puzzle: (1, 3, 2, 7, 8, 5, 4, 0, 6) | elapsed: 0.0162s | solved Test | seed: 47741579 | puzzle: (5, 1, 0, 7, 4, 3, 6, 2, 8) | elapsed: 0.0673s | solved Test | seed: 43495272 | puzzle: (7, 6, 8, 5, 2, 0, 1, 4, 3) | elapsed: 0.0730s | solved Test | seed: 46056483 | puzzle: (3, 0, 2, 5, 7, 4, 6, 1, 8) | elapsed: 0.0103s | solved Test | seed: 24695314 | puzzle: (8, 1, 5, 4, 0, 3, 7, 6, 2) | elapsed: 0.0224s | solved Test | seed: 93859516 | puzzle: (4, 1, 6, 8, 5, 0, 2, 3, 7) | elapsed: 0.0926s | solved Test | seed: 34777959 | puzzle: (0, 4, 3, 7, 1, 6, 5, 2, 8) | elapsed: 0.0091s | solved Test | seed: 56227654 | puzzle: (3, 6, 5, 1, 7, 0, 4, 2, 8) | elapsed: 0.0170s | solved Test | seed: 48961302 | puzzle: (1, 7, 8, 3, 4, 0, 6, 2, 5) | elapsed: 0.0933s | solved Test | seed: 19330196 | puzzle: (5, 0, 3, 6, 8, 1, 4, 2, 7) | elapsed: 0.0837s | solved Test | seed: 32477484 | puzzle: (8, 3, 4, 1, 5, 0, 7, 2, 6) | elapsed: 0.0084s | solved Test | seed: 31424575 | puzzle: (3, 5, 8, 1, 4, 2, 7, 0, 6) | elapsed: 0.0069s | solved Test | seed: 44254527 | puzzle: (7, 2, 5, 8, 0, 1, 4, 6, 3) | elapsed: 0.0483s | solved Test | seed: 80783798 | puzzle: (1, 4, 5, 0, 6, 3, 2, 8, 7) | elapsed: 0.0234s | solved Test | seed: 32568032 | puzzle: (0, 2, 8, 7, 1, 5, 3, 4, 6) | elapsed: 0.0294s | solved Test | seed: 98134944 | puzzle: (6, 0, 4, 5, 3, 7, 2, 1, 8) | elapsed: 0.0133s | solved Test | seed: 46629955 | puzzle: (1, 0, 2, 7, 4, 5, 8, 3, 6) | elapsed: 0.0067s | solved Test | seed: 97000307 | puzzle: (6, 7, 3, 4, 1, 8, 2, 0, 5) | elapsed: 0.0688s | solved Test | seed: 49526151 | puzzle: (7, 6, 8, 3, 1, 0, 2, 4, 5) | elapsed: 0.0047s | solved Test | seed: 71029019 | puzzle: (2, 0, 6, 1, 5, 7, 4, 3, 8) | elapsed: 0.0505s | solved Test | seed: 53218345 | puzzle: (0, 5, 2, 3, 6, 7, 8, 1, 4) | elapsed: 0.1189s | solved Test | seed: 76638250 | puzzle: (8, 7, 6, 4, 0, 2, 1, 3, 5) | elapsed: 0.0090s | solved Test | seed: 73588469 | puzzle: (7, 4, 1, 6, 2, 0, 5, 8, 3) | elapsed: 0.0259s | solved Test | seed: 25326409 | puzzle: (8, 6, 1, 0, 3, 2, 7, 5, 4) | elapsed: 0.0123s | solved Test | seed: 13172179 | puzzle: (5, 1, 3, 6, 8, 7, 2, 0, 4) | elapsed: 0.0102s | solved Test | seed: 51876592 | puzzle: (2, 6, 5, 4, 1, 0, 3, 7, 8) | elapsed: 0.0234s | solved Test | seed: 61882816 | puzzle: (8, 1, 6, 4, 2, 0, 3, 7, 5) | elapsed: 0.0268s | solved Test | seed: 56082646 | puzzle: (5, 3, 0, 8, 1, 7, 4, 6, 2) | elapsed: 0.0233s | solved Test | seed: 66494748 | puzzle: (7, 6, 4, 5, 1, 3, 2, 0, 8) | elapsed: 0.0228s | solved Test | seed: 35238208 | puzzle: (7, 3, 6, 4, 2, 5, 1, 0, 8) | elapsed: 0.0256s | solved Test | seed: 44684657 | puzzle: (6, 8, 7, 3, 0, 1, 4, 5, 2) | elapsed: 0.0106s | solved Test | seed: 24597747 | puzzle: (1, 8, 5, 4, 2, 0, 6, 3, 7) | elapsed: 0.0139s | solved Test | seed: 44018576 | puzzle: (7, 8, 4, 1, 0, 6, 5, 2, 3) | elapsed: 0.0241s | solved Test | seed: 78466607 | puzzle: (3, 6, 5, 0, 7, 2, 8, 4, 1) | elapsed: 0.0519s | solved Test | seed: 38063717 | puzzle: (0, 1, 7, 6, 4, 8, 5, 2, 3) | elapsed: 0.0367s | solved Test | seed: 91288784 | puzzle: (8, 0, 5, 1, 6, 2, 4, 7, 3) | elapsed: 0.0055s | solved Test | seed: 67935826 | puzzle: (2, 7, 8, 3, 5, 6, 1, 4, 0) | elapsed: 0.0409s | solved Test | seed: 12794159 | puzzle: (8, 7, 4, 0, 3, 2, 6, 5, 1) | elapsed: 0.0208s | solved Test | seed: 40249188 | puzzle: (1, 2, 5, 6, 0, 8, 4, 3, 7) | elapsed: 0.0689s | solved Test | seed: 12397735 | puzzle: (7, 8, 4, 6, 5, 2, 3, 1, 0) | elapsed: 0.0186s | solved Test | seed: 63326766 | puzzle: (1, 2, 3, 6, 4, 8, 5, 7, 0) | elapsed: 0.0087s | solved Test | seed: 29657762 | puzzle: (6, 0, 3, 4, 5, 2, 1, 7, 8) | elapsed: 0.0256s | solved Test | seed: 14741381 | puzzle: (1, 6, 8, 0, 3, 5, 4, 7, 2) | elapsed: 0.0040s | solved Test | seed: 31505383 | puzzle: (7, 5, 4, 2, 0, 8, 3, 1, 6) | elapsed: 0.0274s | solved Test | seed: 69816615 | puzzle: (1, 0, 4, 3, 6, 2, 7, 5, 8) | elapsed: 0.0274s | solved Test | seed: 77955685 | puzzle: (6, 0, 1, 3, 5, 7, 8, 2, 4) | elapsed: 0.1145s | solved Test | seed: 67266010 | puzzle: (0, 4, 1, 8, 6, 7, 3, 5, 2) | elapsed: 0.0106s | solved Test | seed: 83108686 | puzzle: (7, 1, 0, 8, 3, 6, 5, 4, 2) | elapsed: 0.0294s | solved Test | seed: 39608396 | puzzle: (3, 7, 6, 2, 4, 0, 1, 8, 5) | elapsed: 0.0183s | solved Test | seed: 94660762 | puzzle: (8, 2, 1, 4, 6, 5, 0, 3, 7) | elapsed: 0.0173s | solved Test | seed: 79336813 | puzzle: (2, 0, 3, 6, 1, 8, 7, 4, 5) | elapsed: 0.0064s | solved Test | seed: 70511395 | puzzle: (7, 4, 1, 0, 6, 8, 5, 3, 2) | elapsed: 0.0046s | solved Test | seed: 39956830 | puzzle: (0, 6, 8, 1, 5, 7, 4, 3, 2) | elapsed: 0.0724s | solved Test | seed: 80316055 | puzzle: (4, 2, 8, 5, 0, 1, 3, 7, 6) | elapsed: 0.0144s | solved Test | seed: 97041058 | puzzle: (0, 2, 7, 4, 3, 5, 8, 1, 6) | elapsed: 0.0248s | solved Test | seed: 14120521 | puzzle: (5, 0, 6, 2, 3, 8, 1, 7, 4) | elapsed: 0.0119s | solved Test | seed: 63002313 | puzzle: (5, 3, 1, 2, 6, 8, 0, 7, 4) | elapsed: 0.0166s | solved Test | seed: 87288736 | puzzle: (0, 1, 2, 8, 3, 5, 7, 4, 6) | elapsed: 0.0638s | solved Test | seed: 53116882 | puzzle: (4, 8, 1, 7, 5, 2, 6, 0, 3) | elapsed: 0.0330s | solved Test | seed: 98560063 | puzzle: (2, 6, 7, 5, 1, 4, 8, 3, 0) | elapsed: 0.0367s | solved Test | seed: 94684388 | puzzle: (2, 5, 4, 7, 0, 6, 8, 3, 1) | elapsed: 0.0639s | solved Test | seed: 67216934 | puzzle: (1, 8, 7, 5, 3, 0, 4, 2, 6) | elapsed: 0.0842s | solved Test | seed: 17890004 | puzzle: (2, 4, 8, 1, 0, 5, 6, 3, 7) | elapsed: 0.0134s | solved Test | seed: 50078212 | puzzle: (0, 2, 6, 8, 4, 5, 1, 3, 7) | elapsed: 0.0119s | solved Test | seed: 26868929 | puzzle: (4, 2, 1, 6, 7, 0, 5, 8, 3) | elapsed: 0.0676s | solved ===> Solved: 100/100 ===> Average elapsed time: 0.0312s

convolutional-neural-networks/conv-visualization/maxpooling_visualization.ipynb

###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the size of the patch by a factor of 4. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # defines the convolutional layer, assumes there are 4 grayscale filters # torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True) self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLU activationA ReLU function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Copy files and install pytorch ###Code import sys try: import torch except: import os os.environ['TCMALLOC_LARGE_ALLOC_REPORT_THRESHOLD']='2000000000' # http://pytorch.org/ from os.path import exists from wheel.pep425tags import get_abbr_impl, get_impl_ver, get_abi_tag platform = '{}{}-{}'.format(get_abbr_impl(), get_impl_ver(), get_abi_tag()) cuda_output = !ldconfig -p|grep cudart.so|sed -e 's/.*\.\([0-9]*\)\.\([0-9]*\)$/cu\1\2/' accelerator = cuda_output[0] if exists('/dev/nvidia0') else 'cpu' !{sys.executable} -m pip install -q http://download.pytorch.org/whl/{accelerator}/torch-0.4.1-{platform}-linux_x86_64.whl torchvision >/dev/null ! curl -s https://codeload.github.com/udacity/deep-learning-v2-pytorch/tar.gz/master | tar -xz --strip=3 deep-learning-v2-pytorch-master/convolutional-neural-networks/conv-visualization/data/ >/dev/null 2>&1 ###Output _____no_output_____ ###Markdown Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.axis('off') plt.show(); ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. <img src='https://raw.githubusercontent.com/udacity/deep-learning-v2-pytorch/master/convolutional-neural-networks/conv-visualization/notebook_ims/relu_ex.png' height=50% width=50% /> ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer); ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import sys ros_path = '/opt/ros/kinetic/lib/python2.7/dist-packages' if ros_path in sys.path: sys.path.remove(ros_path) import cv2 sys.path.append('/opt/ros/kinetic/lib/python2.7/dist-packages') import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] (4, 4, 4) ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the size of the patch by a factor of 4. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # defines the convolutional layer, assumes there are 4 grayscale filters # torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True) self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLU activationA ReLU function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code !mkdir data !wget -c https://github.com/agungsantoso/deep-learning-v2-pytorch/raw/master/convolutional-neural-networks/conv-visualization/data/curved_lane.jpg !wget -c https://github.com/agungsantoso/deep-learning-v2-pytorch/raw/master/convolutional-neural-networks/conv-visualization/data/bridge_trees_example.jpg !wget -c https://github.com/agungsantoso/deep-learning-v2-pytorch/raw/master/convolutional-neural-networks/conv-visualization/data/sobel_ops.png !wget -c https://github.com/agungsantoso/deep-learning-v2-pytorch/raw/master/convolutional-neural-networks/conv-visualization/data/udacity_sdc.png !wget -c https://github.com/agungsantoso/deep-learning-v2-pytorch/raw/master/convolutional-neural-networks/conv-visualization/data/white_lines.jpg !mv bridge_trees_example.jpg data/bridge_trees_example.jpg !mv curved_lane.jpg data/curved_lane.jpg !mv sobel_ops.png data/sobel_ops.png !mv udacity_sdc.png data/udacity_sdc.png !mv white_lines.jpg data/white_lines.jpg import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code # http://pytorch.org/ from os.path import exists from wheel.pep425tags import get_abbr_impl, get_impl_ver, get_abi_tag platform = '{}{}-{}'.format(get_abbr_impl(), get_impl_ver(), get_abi_tag()) cuda_output = !ldconfig -p|grep cudart.so|sed -e 's/.*\.\([0-9]*\)\.\([0-9]*\)$/cu\1\2/' accelerator = cuda_output[0] if exists('/dev/nvidia0') else 'cpu' !pip install -q http://download.pytorch.org/whl/{accelerator}/torch-0.4.1-{platform}-linux_x86_64.whl torchvision import torch import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import sys sys.path.remove('/opt/ros/kinetic/lib/python2.7/dist-packages') import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown The maxpool layer has (2, 2) sized filters. As I've shown in `conv_visualization.ipynb`, with an image of this size (~ 300x200 pixels), such a filter is small enough not to make the features to blurry. Out of interest, let's compare the pooled image with a non-pooled image: ###Code viz_layer(F.relu(conv_layer)) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_3) ###Output Filter 1: [[-1 -1 -1 -1] [-1 -1 -1 -1] [ 1 1 1 1] [ 1 1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output 3 ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the size of the patch by a factor of 4. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # defines the convolutional layer, assumes there are 4 grayscale filters # torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True) self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLU activationA ReLU function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 print(gray_img) # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output [[0.13333334 0.13333334 0.11764706 ... 0.24313726 0.24313726 0.28627452] [0.16078432 0.14117648 0.13725491 ... 0.23921569 0.24705882 0.28627452] [0.1882353 0.17254902 0.16862746 ... 0.23529412 0.24705882 0.27058825] ... [0.7176471 0.72156864 0.69411767 ... 0.7921569 0.77254903 0.7411765 ] [0.7372549 0.74509805 0.6784314 ... 0.77254903 0.76862746 0.7490196 ] [0.72156864 0.7411765 0.6745098 ... 0.7137255 0.7137255 0.6901961 ]] ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the size of the patch by a factor of 4. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # defines the convolutional layer, assumes there are 4 grayscale filters # torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True) self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLU activationA ReLU function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) activated_layer.shape pooled_layer.shape ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) print ( weight ) print (weight.shape[2:]) model = Net(weight) # print out the layer in the network print(model) ###Output tensor([[[[-1., -1., 1., 1.], [-1., -1., 1., 1.], [-1., -1., 1., 1.], [-1., -1., 1., 1.]]], [[[ 1., 1., -1., -1.], [ 1., 1., -1., -1.], [ 1., 1., -1., -1.], [ 1., 1., -1., -1.]]], [[[-1., -1., -1., -1.], [-1., -1., -1., -1.], [ 1., 1., 1., 1.], [ 1., 1., 1., 1.]]], [[[ 1., 1., 1., 1.], [ 1., 1., 1., 1.], [-1., -1., -1., -1.], [-1., -1., -1., -1.]]]]) torch.Size([4, 4]) Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) print(gray_img_tensor) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output tensor([[[[0.1333, 0.1333, 0.1176, ..., 0.2431, 0.2431, 0.2863], [0.1608, 0.1412, 0.1373, ..., 0.2392, 0.2471, 0.2863], [0.1882, 0.1725, 0.1686, ..., 0.2353, 0.2471, 0.2706], ..., [0.7176, 0.7216, 0.6941, ..., 0.7922, 0.7725, 0.7412], [0.7373, 0.7451, 0.6784, ..., 0.7725, 0.7686, 0.7490], [0.7216, 0.7412, 0.6745, ..., 0.7137, 0.7137, 0.6902]]]]) ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters = 4): fig = plt.figure(figsize = (20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output Bad key axes.color_cycle in file /Users/mohamedabdelbary/.matplotlib/matplotlibrc, line 240 ('axes.color_cycle : 348ABD, A60628, 7A68A6, 467821,D55E00, CC79A7, 56B4E9, 009E73, F0E442, 0072B2 # color cycle for plot lines') You probably need to get an updated matplotlibrc file from https://github.com/matplotlib/matplotlib/blob/v3.3.3/matplotlibrc.template or from the matplotlib source distribution ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape:', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_1.T filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1:\n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() k_height, k_width = weight.shape[2:] self.conv = nn.Conv2d(1, 4, kernel_size=(k_height,k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a 2*2 pooling layer self.pool = nn.MaxPool2d(2,2) def forward(self, x): conv_x = self.conv(x) activated_x = F.relu(conv_x) pooled_x = self.pool(activated_x) return conv_x, activated_x, pooled_x weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20,20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline from IPython.core.interactiveshell import InteractiveShell InteractiveShell.ast_node_interactivity = "all" # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) filter_vals # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) filters ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer #self.pool = nn.AvgPool2d(2,2) self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): AvgPool2d(kernel_size=2, stride=2, padding=0) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) weight weight.shape[2:] ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODONE: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODONE: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the size of the patch by a factor of 4. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # defines the convolutional layer, assumes there are 4 grayscale filters # torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True) self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLU activationA ReLU function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. ###Code from google.colab import drive ROOT = "/content/drive" drive.mount(ROOT) %cd "/content/drive/My Drive/Learning/deep-learning-v2-pytorch/convolutional-neural-networks/conv-visualization" ###Output /content/drive/My Drive/Learning/deep-learning-v2-pytorch/convolutional-neural-networks/conv-visualization ###Markdown Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_4) ###Output Filter 1: [[ 1 1 1 1] [ 1 1 1 1] [-1 -1 -1 -1] [-1 -1 -1 -1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the size of the patch by a factor of 4. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # defines the convolutional layer, assumes there are 4 grayscale filters # torch.nn.Conv2d(in_channels, out_channels, kernel_size, stride=1, padding=0, dilation=1, groups=1, bias=True) self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLU activationA ReLU function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = '../../../Gharib.jpeg' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1] [-1 -1 1 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=2, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) viz_layer(conv_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! filter_vals = np.array([[-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, -1, 1, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output _____no_output_____ ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, applied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output _____no_output_____ ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____ ###Markdown Maxpooling LayerIn this notebook, we add and visualize the output of a maxpooling layer in a CNN. A convolutional layer + activation function, followed by a pooling layer, and a linear layer (to create a desired output size) make up the basic layers of a CNN. Import the image ###Code import cv2 import matplotlib.pyplot as plt %matplotlib inline # TODO: Feel free to try out your own images here by changing img_path # to a file path to another image on your computer! img_path = 'data/udacity_sdc.png' # load color image bgr_img = cv2.imread(img_path) # convert to grayscale gray_img = cv2.cvtColor(bgr_img, cv2.COLOR_BGR2GRAY) # normalize, rescale entries to lie in [0,1] gray_img = gray_img.astype("float32")/255 # plot image plt.imshow(gray_img, cmap='gray') plt.show() ###Output _____no_output_____ ###Markdown Define and visualize the filters ###Code import numpy as np ## TODO: Feel free to modify the numbers here, to try out another filter! # filter_values contains the coefficients of a filter of size 4 x 4. filter_vals = np.array([[-1, 0, 0, 1], [-1, -1, 1, 1], [-1, -1, 1, 1], [-1, 0, 0, 1]]) print('Filter shape: ', filter_vals.shape) # Defining four different filters, # all of which are linear combinations of the `filter_vals` defined above # define four filters filter_1 = filter_vals filter_2 = -filter_1 filter_3 = filter_1.T filter_4 = -filter_3 # filters contains 4 configuretions, each representing the four filters that # we mentioned before--- left/right vertical filter, top/bottom horizontal filter... filters = np.array([filter_1, filter_2, filter_3, filter_4]) # For an example, print out the values of filter 1 print('Filter 1: \n', filter_1) ###Output Filter 1: [[-1 0 0 1] [-1 -1 1 1] [-1 -1 1 1] [-1 0 0 1]] ###Markdown Define convolutional and pooling layersYou've seen how to define a convolutional layer, next is a:* Pooling layerIn the next cell, we initialize a convolutional layer so that it contains all the created filters. Then add a maxpooling layer, [documented here](http://pytorch.org/docs/stable/_modules/torch/nn/modules/pooling.html), with a kernel size of (2x2) so you can see that the image resolution has been reduced after this step!A maxpooling layer reduces the x-y size of an input and only keeps the most *active* pixel values. Below is an example of a 2x2 pooling kernel, with a stride of 2, appied to a small patch of grayscale pixel values; reducing the x-y size of the patch by a factor of 2. Only the maximum pixel values in 2x2 remain in the new, pooled output. ###Code import torch import torch.nn as nn import torch.nn.functional as F # define a neural network with a convolutional layer with four filters # AND a pooling layer of size (2, 2) class Net(nn.Module): def __init__(self, weight): super(Net, self).__init__() # initializes the weights of the convolutional layer to be the weights of the 4 defined filters k_height, k_width = weight.shape[2:] # assumes there are 4 grayscale filters self.conv = nn.Conv2d(1, 4, kernel_size=(k_height, k_width), bias=False) self.conv.weight = torch.nn.Parameter(weight) # define a pooling layer # nn.MaxPool2d(kernel_size, stride=None, padding=0, dilation=1, return_indices=False, ceil_mode=False) self.pool = nn.MaxPool2d(2, 2) def forward(self, x): # calculates the output of a convolutional layer # pre- and post-activation conv_x = self.conv(x) activated_x = F.relu(conv_x) # applies pooling layer pooled_x = self.pool(activated_x) # returns all layers return conv_x, activated_x, pooled_x # instantiate the model and set the weights weight = torch.from_numpy(filters).unsqueeze(1).type(torch.FloatTensor) model = Net(weight) # print out the layer in the network print(model) ###Output Net( (conv): Conv2d(1, 4, kernel_size=(4, 4), stride=(1, 1), bias=False) (pool): MaxPool2d(kernel_size=2, stride=1, padding=0, dilation=1, ceil_mode=False) ) ###Markdown Visualize the output of each filterFirst, we'll define a helper function, `viz_layer` that takes in a specific layer and number of filters (optional argument), and displays the output of that layer once an image has been passed through. ###Code # helper function for visualizing the output of a given layer # default number of filters is 4 def viz_layer(layer, n_filters= 4): fig = plt.figure(figsize=(20, 20)) for i in range(n_filters): ax = fig.add_subplot(1, n_filters, i+1) # grab layer outputs ax.imshow(np.squeeze(layer[0,i].data.numpy()), cmap='gray') ax.set_title('Output %s' % str(i+1)) ###Output _____no_output_____ ###Markdown Let's look at the output of a convolutional layer after a ReLu activation function is applied. ReLu activationA ReLu function turns all negative pixel values in 0's (black). See the equation pictured below for input pixel values, `x`. ###Code # plot original image plt.imshow(gray_img, cmap='gray') # visualize all filters fig = plt.figure(figsize=(12, 6)) fig.subplots_adjust(left=0, right=1.5, bottom=0.8, top=1, hspace=0.05, wspace=0.05) for i in range(4): ax = fig.add_subplot(1, 4, i+1, xticks=[], yticks=[]) ax.imshow(filters[i], cmap='gray') ax.set_title('Filter %s' % str(i+1)) # convert the image into an input Tensor gray_img_tensor = torch.from_numpy(gray_img).unsqueeze(0).unsqueeze(1) # get all the layers conv_layer, activated_layer, pooled_layer = model(gray_img_tensor) # visualize the output of the activated conv layer viz_layer(activated_layer) ###Output _____no_output_____ ###Markdown Visualize the output of the pooling layerThen, take a look at the output of a pooling layer. The pooling layer takes as input the feature maps pictured above and reduces the dimensionality of those maps, by some pooling factor, by constructing a new, smaller image of only the maximum (brightest) values in a given kernel area.Take a look at the values on the x, y axes to see how the image has changed size. ###Code # visualize the output of the pooling layer viz_layer(pooled_layer) ###Output _____no_output_____

openmm_simulation/combine_systems.ipynb

###Markdown Load protein system: ###Code #Load up CHARMM-GUI pdb, and create a PARMED structure from it. prot_pdb = PDBFile('./1xep-processed.pdb') omm_forcefield = app.ForceField('amber14-all.xml', 'amber14/tip3p.xml') prot_system = omm_forcefield.createSystem(prot_pdb.topology, rigidWater=False) prot_structure = parmed.openmm.load_topology(prot_pdb.topology, prot_system, xyz=prot_pdb.positions) ###Output _____no_output_____ ###Markdown Load drug system: ###Code #Load up the parameterized drug system, and again make it into a parmed structure: drug_system = XmlSerializer.deserialize(open('./drug_system.xml').read()) drug_pdbfile = PDBFile('./catechol_aligned.pdb') drug_structure = parmed.openmm.load_topology(drug_pdbfile.topology, drug_system, xyz=drug_pdbfile.positions) ###Output _____no_output_____ ###Markdown Combine: ###Code #This is the biggest step but it takes 1 second: complex_structure = prot_structure + drug_structure ###Output _____no_output_____ ###Markdown Turn back into an openmm system ###Code #set periodic boundary conditons (you get these from the processed pdb file, 1xep-processed.pdb) #64.871 64.871 64.871 60.00 60.00 90.00 P 1 1 #note parmed (and PBD files) uses angstrom by default. complex_structure.box = (64.871, 64.871, 64.871, 60, 60, 90) #Turn into an OpenMM System object for simulations: #These settings will be stuck unless you re-run this script! Luckily they're pretty standard settings. complex_system = complex_structure.createSystem(nonbondedMethod=PME, nonbondedCutoff=0.9*nanometer, constraints=HBonds, rigidWater=True) complex_structure.save('complex_plus_water.parm7') ###Output _____no_output_____ ###Markdown Save output as PDB, PSF, and serialized openmm system ###Code #Save output: complex_structure.save('./complex_coords.pdb', overwrite=True) #PSF files don't like having numbered atom types, because at 10,000 VMD fails #So just set them all to zero. for a in complex_structure.atoms: a.type = '0' complex_structure.save('./complex_struct_.psf', overwrite=True) with open('./complex_system_.xml', 'w') as f: f.write( XmlSerializer.serialize( complex_system ) ) ###Output _____no_output_____

Notebooks/RadarCOVID-Report/Daily/RadarCOVID-Report-2021-07-09.ipynb

###Markdown RadarCOVID-Report Data Extraction ###Code import datetime import json import logging import os import shutil import tempfile import textwrap import uuid import matplotlib.pyplot as plt import matplotlib.ticker import numpy as np import pandas as pd import pycountry import retry import seaborn as sns %matplotlib inline current_working_directory = os.environ.get("PWD") if current_working_directory: os.chdir(current_working_directory) sns.set() matplotlib.rcParams["figure.figsize"] = (15, 6) extraction_datetime = datetime.datetime.utcnow() extraction_date = extraction_datetime.strftime("%Y-%m-%d") extraction_previous_datetime = extraction_datetime - datetime.timedelta(days=1) extraction_previous_date = extraction_previous_datetime.strftime("%Y-%m-%d") extraction_date_with_hour = datetime.datetime.utcnow().strftime("%Y-%m-%d@%H") current_hour = datetime.datetime.utcnow().hour are_today_results_partial = current_hour != 23 ###Output _____no_output_____ ###Markdown Constants ###Code from Modules.ExposureNotification import exposure_notification_io spain_region_country_code = "ES" germany_region_country_code = "DE" default_backend_identifier = spain_region_country_code backend_generation_days = 7 * 2 daily_summary_days = 7 * 4 * 3 daily_plot_days = 7 * 4 tek_dumps_load_limit = daily_summary_days + 1 ###Output _____no_output_____ ###Markdown Parameters ###Code environment_backend_identifier = os.environ.get("RADARCOVID_REPORT__BACKEND_IDENTIFIER") if environment_backend_identifier: report_backend_identifier = environment_backend_identifier else: report_backend_identifier = default_backend_identifier report_backend_identifier environment_enable_multi_backend_download = \ os.environ.get("RADARCOVID_REPORT__ENABLE_MULTI_BACKEND_DOWNLOAD") if environment_enable_multi_backend_download: report_backend_identifiers = None else: report_backend_identifiers = [report_backend_identifier] report_backend_identifiers environment_invalid_shared_diagnoses_dates = \ os.environ.get("RADARCOVID_REPORT__INVALID_SHARED_DIAGNOSES_DATES") if environment_invalid_shared_diagnoses_dates: invalid_shared_diagnoses_dates = environment_invalid_shared_diagnoses_dates.split(",") else: invalid_shared_diagnoses_dates = [] invalid_shared_diagnoses_dates ###Output _____no_output_____ ###Markdown COVID-19 Cases ###Code report_backend_client = \ exposure_notification_io.get_backend_client_with_identifier( backend_identifier=report_backend_identifier) @retry.retry(tries=10, delay=10, backoff=1.1, jitter=(0, 10)) def download_cases_dataframe(): return pd.read_csv("https://raw.githubusercontent.com/owid/covid-19-data/master/public/data/owid-covid-data.csv") confirmed_df_ = download_cases_dataframe() confirmed_df_.iloc[0] confirmed_df = confirmed_df_.copy() confirmed_df = confirmed_df[["date", "new_cases", "iso_code"]] confirmed_df.rename( columns={ "date": "sample_date", "iso_code": "country_code", }, inplace=True) def convert_iso_alpha_3_to_alpha_2(x): try: return pycountry.countries.get(alpha_3=x).alpha_2 except Exception as e: logging.info(f"Error converting country ISO Alpha 3 code '{x}': {repr(e)}") return None confirmed_df["country_code"] = confirmed_df.country_code.apply(convert_iso_alpha_3_to_alpha_2) confirmed_df.dropna(inplace=True) confirmed_df["sample_date"] = pd.to_datetime(confirmed_df.sample_date, dayfirst=True) confirmed_df["sample_date"] = confirmed_df.sample_date.dt.strftime("%Y-%m-%d") confirmed_df.sort_values("sample_date", inplace=True) confirmed_df.tail() confirmed_days = pd.date_range( start=confirmed_df.iloc[0].sample_date, end=extraction_datetime) confirmed_days_df = pd.DataFrame(data=confirmed_days, columns=["sample_date"]) confirmed_days_df["sample_date_string"] = \ confirmed_days_df.sample_date.dt.strftime("%Y-%m-%d") confirmed_days_df.tail() def sort_source_regions_for_display(source_regions: list) -> list: if report_backend_identifier in source_regions: source_regions = [report_backend_identifier] + \ list(sorted(set(source_regions).difference([report_backend_identifier]))) else: source_regions = list(sorted(source_regions)) return source_regions report_source_regions = report_backend_client.source_regions_for_date( date=extraction_datetime.date()) report_source_regions = sort_source_regions_for_display( source_regions=report_source_regions) report_source_regions def get_cases_dataframe(source_regions_for_date_function, columns_suffix=None): source_regions_at_date_df = confirmed_days_df.copy() source_regions_at_date_df["source_regions_at_date"] = \ source_regions_at_date_df.sample_date.apply( lambda x: source_regions_for_date_function(date=x)) source_regions_at_date_df.sort_values("sample_date", inplace=True) source_regions_at_date_df["_source_regions_group"] = source_regions_at_date_df. \ source_regions_at_date.apply(lambda x: ",".join(sort_source_regions_for_display(x))) source_regions_at_date_df.tail() #%% source_regions_for_summary_df_ = \ source_regions_at_date_df[["sample_date", "_source_regions_group"]].copy() source_regions_for_summary_df_.rename(columns={"_source_regions_group": "source_regions"}, inplace=True) source_regions_for_summary_df_.tail() #%% confirmed_output_columns = ["sample_date", "new_cases", "covid_cases"] confirmed_output_df = pd.DataFrame(columns=confirmed_output_columns) for source_regions_group, source_regions_group_series in \ source_regions_at_date_df.groupby("_source_regions_group"): source_regions_set = set(source_regions_group.split(",")) confirmed_source_regions_set_df = \ confirmed_df[confirmed_df.country_code.isin(source_regions_set)].copy() confirmed_source_regions_group_df = \ confirmed_source_regions_set_df.groupby("sample_date").new_cases.sum() \ .reset_index().sort_values("sample_date") confirmed_source_regions_group_df = \ confirmed_source_regions_group_df.merge( confirmed_days_df[["sample_date_string"]].rename( columns={"sample_date_string": "sample_date"}), how="right") confirmed_source_regions_group_df["new_cases"] = \ confirmed_source_regions_group_df["new_cases"].clip(lower=0) confirmed_source_regions_group_df["covid_cases"] = \ confirmed_source_regions_group_df.new_cases.rolling(7, min_periods=0).mean().round() confirmed_source_regions_group_df = \ confirmed_source_regions_group_df[confirmed_output_columns] confirmed_source_regions_group_df = confirmed_source_regions_group_df.replace(0, np.nan) confirmed_source_regions_group_df.fillna(method="ffill", inplace=True) confirmed_source_regions_group_df = \ confirmed_source_regions_group_df[ confirmed_source_regions_group_df.sample_date.isin( source_regions_group_series.sample_date_string)] confirmed_output_df = confirmed_output_df.append(confirmed_source_regions_group_df) result_df = confirmed_output_df.copy() result_df.tail() #%% result_df.rename(columns={"sample_date": "sample_date_string"}, inplace=True) result_df = confirmed_days_df[["sample_date_string"]].merge(result_df, how="left") result_df.sort_values("sample_date_string", inplace=True) result_df.fillna(method="ffill", inplace=True) result_df.tail() #%% result_df[["new_cases", "covid_cases"]].plot() if columns_suffix: result_df.rename( columns={ "new_cases": "new_cases_" + columns_suffix, "covid_cases": "covid_cases_" + columns_suffix}, inplace=True) return result_df, source_regions_for_summary_df_ confirmed_eu_df, source_regions_for_summary_df = get_cases_dataframe( report_backend_client.source_regions_for_date) confirmed_es_df, _ = get_cases_dataframe( lambda date: [spain_region_country_code], columns_suffix=spain_region_country_code.lower()) ###Output _____no_output_____ ###Markdown Extract API TEKs ###Code raw_zip_path_prefix = "Data/TEKs/Raw/" base_backend_identifiers = [report_backend_identifier] multi_backend_exposure_keys_df = \ exposure_notification_io.download_exposure_keys_from_backends( backend_identifiers=report_backend_identifiers, generation_days=backend_generation_days, fail_on_error_backend_identifiers=base_backend_identifiers, save_raw_zip_path_prefix=raw_zip_path_prefix) multi_backend_exposure_keys_df["region"] = multi_backend_exposure_keys_df["backend_identifier"] multi_backend_exposure_keys_df.rename( columns={ "generation_datetime": "sample_datetime", "generation_date_string": "sample_date_string", }, inplace=True) multi_backend_exposure_keys_df.head() early_teks_df = multi_backend_exposure_keys_df[ multi_backend_exposure_keys_df.rolling_period < 144].copy() early_teks_df["rolling_period_in_hours"] = early_teks_df.rolling_period / 6 early_teks_df[early_teks_df.sample_date_string != extraction_date] \ .rolling_period_in_hours.hist(bins=list(range(24))) early_teks_df[early_teks_df.sample_date_string == extraction_date] \ .rolling_period_in_hours.hist(bins=list(range(24))) multi_backend_exposure_keys_df = multi_backend_exposure_keys_df[[ "sample_date_string", "region", "key_data"]] multi_backend_exposure_keys_df.head() active_regions = \ multi_backend_exposure_keys_df.groupby("region").key_data.nunique().sort_values().index.unique().tolist() active_regions multi_backend_summary_df = multi_backend_exposure_keys_df.groupby( ["sample_date_string", "region"]).key_data.nunique().reset_index() \ .pivot(index="sample_date_string", columns="region") \ .sort_index(ascending=False) multi_backend_summary_df.rename( columns={"key_data": "shared_teks_by_generation_date"}, inplace=True) multi_backend_summary_df.rename_axis("sample_date", inplace=True) multi_backend_summary_df = multi_backend_summary_df.fillna(0).astype(int) multi_backend_summary_df = multi_backend_summary_df.head(backend_generation_days) multi_backend_summary_df.head() def compute_keys_cross_sharing(x): teks_x = x.key_data_x.item() common_teks = set(teks_x).intersection(x.key_data_y.item()) common_teks_fraction = len(common_teks) / len(teks_x) return pd.Series(dict( common_teks=common_teks, common_teks_fraction=common_teks_fraction, )) multi_backend_exposure_keys_by_region_df = \ multi_backend_exposure_keys_df.groupby("region").key_data.unique().reset_index() multi_backend_exposure_keys_by_region_df["_merge"] = True multi_backend_exposure_keys_by_region_combination_df = \ multi_backend_exposure_keys_by_region_df.merge( multi_backend_exposure_keys_by_region_df, on="_merge") multi_backend_exposure_keys_by_region_combination_df.drop( columns=["_merge"], inplace=True) if multi_backend_exposure_keys_by_region_combination_df.region_x.nunique() > 1: multi_backend_exposure_keys_by_region_combination_df = \ multi_backend_exposure_keys_by_region_combination_df[ multi_backend_exposure_keys_by_region_combination_df.region_x != multi_backend_exposure_keys_by_region_combination_df.region_y] multi_backend_exposure_keys_cross_sharing_df = \ multi_backend_exposure_keys_by_region_combination_df \ .groupby(["region_x", "region_y"]) \ .apply(compute_keys_cross_sharing) \ .reset_index() multi_backend_cross_sharing_summary_df = \ multi_backend_exposure_keys_cross_sharing_df.pivot_table( values=["common_teks_fraction"], columns="region_x", index="region_y", aggfunc=lambda x: x.item()) multi_backend_cross_sharing_summary_df multi_backend_without_active_region_exposure_keys_df = \ multi_backend_exposure_keys_df[multi_backend_exposure_keys_df.region != report_backend_identifier] multi_backend_without_active_region = \ multi_backend_without_active_region_exposure_keys_df.groupby("region").key_data.nunique().sort_values().index.unique().tolist() multi_backend_without_active_region exposure_keys_summary_df = multi_backend_exposure_keys_df[ multi_backend_exposure_keys_df.region == report_backend_identifier] exposure_keys_summary_df.drop(columns=["region"], inplace=True) exposure_keys_summary_df = \ exposure_keys_summary_df.groupby(["sample_date_string"]).key_data.nunique().to_frame() exposure_keys_summary_df = \ exposure_keys_summary_df.reset_index().set_index("sample_date_string") exposure_keys_summary_df.sort_index(ascending=False, inplace=True) exposure_keys_summary_df.rename(columns={"key_data": "shared_teks_by_generation_date"}, inplace=True) exposure_keys_summary_df.head() ###Output /opt/hostedtoolcache/Python/3.8.10/x64/lib/python3.8/site-packages/pandas/core/frame.py:4110: SettingWithCopyWarning: A value is trying to be set on a copy of a slice from a DataFrame See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy return super().drop( ###Markdown Dump API TEKs ###Code tek_list_df = multi_backend_exposure_keys_df[ ["sample_date_string", "region", "key_data"]].copy() tek_list_df["key_data"] = tek_list_df["key_data"].apply(str) tek_list_df.rename(columns={ "sample_date_string": "sample_date", "key_data": "tek_list"}, inplace=True) tek_list_df = tek_list_df.groupby( ["sample_date", "region"]).tek_list.unique().reset_index() tek_list_df["extraction_date"] = extraction_date tek_list_df["extraction_date_with_hour"] = extraction_date_with_hour tek_list_path_prefix = "Data/TEKs/" tek_list_current_path = tek_list_path_prefix + f"/Current/RadarCOVID-TEKs.json" tek_list_daily_path = tek_list_path_prefix + f"Daily/RadarCOVID-TEKs-{extraction_date}.json" tek_list_hourly_path = tek_list_path_prefix + f"Hourly/RadarCOVID-TEKs-{extraction_date_with_hour}.json" for path in [tek_list_current_path, tek_list_daily_path, tek_list_hourly_path]: os.makedirs(os.path.dirname(path), exist_ok=True) tek_list_base_df = tek_list_df[tek_list_df.region == report_backend_identifier] tek_list_base_df.drop(columns=["extraction_date", "extraction_date_with_hour"]).to_json( tek_list_current_path, lines=True, orient="records") tek_list_base_df.drop(columns=["extraction_date_with_hour"]).to_json( tek_list_daily_path, lines=True, orient="records") tek_list_base_df.to_json( tek_list_hourly_path, lines=True, orient="records") tek_list_base_df.head() ###Output _____no_output_____ ###Markdown Load TEK Dumps ###Code import glob def load_extracted_teks(mode, region=None, limit=None) -> pd.DataFrame: extracted_teks_df = pd.DataFrame(columns=["region"]) file_paths = list(reversed(sorted(glob.glob(tek_list_path_prefix + mode + "/RadarCOVID-TEKs-*.json")))) if limit: file_paths = file_paths[:limit] for file_path in file_paths: logging.info(f"Loading TEKs from '{file_path}'...") iteration_extracted_teks_df = pd.read_json(file_path, lines=True) extracted_teks_df = extracted_teks_df.append( iteration_extracted_teks_df, sort=False) extracted_teks_df["region"] = \ extracted_teks_df.region.fillna(spain_region_country_code).copy() if region: extracted_teks_df = \ extracted_teks_df[extracted_teks_df.region == region] return extracted_teks_df daily_extracted_teks_df = load_extracted_teks( mode="Daily", region=report_backend_identifier, limit=tek_dumps_load_limit) daily_extracted_teks_df.head() exposure_keys_summary_df_ = daily_extracted_teks_df \ .sort_values("extraction_date", ascending=False) \ .groupby("sample_date").tek_list.first() \ .to_frame() exposure_keys_summary_df_.index.name = "sample_date_string" exposure_keys_summary_df_["tek_list"] = \ exposure_keys_summary_df_.tek_list.apply(len) exposure_keys_summary_df_ = exposure_keys_summary_df_ \ .rename(columns={"tek_list": "shared_teks_by_generation_date"}) \ .sort_index(ascending=False) exposure_keys_summary_df = exposure_keys_summary_df_ exposure_keys_summary_df.head() ###Output _____no_output_____ ###Markdown Daily New TEKs ###Code tek_list_df = daily_extracted_teks_df.groupby("extraction_date").tek_list.apply( lambda x: set(sum(x, []))).reset_index() tek_list_df = tek_list_df.set_index("extraction_date").sort_index(ascending=True) tek_list_df.head() def compute_teks_by_generation_and_upload_date(date): day_new_teks_set_df = tek_list_df.copy().diff() try: day_new_teks_set = day_new_teks_set_df[ day_new_teks_set_df.index == date].tek_list.item() except ValueError: day_new_teks_set = None if pd.isna(day_new_teks_set): day_new_teks_set = set() day_new_teks_df = daily_extracted_teks_df[ daily_extracted_teks_df.extraction_date == date].copy() day_new_teks_df["shared_teks"] = \ day_new_teks_df.tek_list.apply(lambda x: set(x).intersection(day_new_teks_set)) day_new_teks_df["shared_teks"] = \ day_new_teks_df.shared_teks.apply(len) day_new_teks_df["upload_date"] = date day_new_teks_df.rename(columns={"sample_date": "generation_date"}, inplace=True) day_new_teks_df = day_new_teks_df[ ["upload_date", "generation_date", "shared_teks"]] day_new_teks_df["generation_to_upload_days"] = \ (pd.to_datetime(day_new_teks_df.upload_date) - pd.to_datetime(day_new_teks_df.generation_date)).dt.days day_new_teks_df = day_new_teks_df[day_new_teks_df.shared_teks > 0] return day_new_teks_df shared_teks_generation_to_upload_df = pd.DataFrame() for upload_date in daily_extracted_teks_df.extraction_date.unique(): shared_teks_generation_to_upload_df = \ shared_teks_generation_to_upload_df.append( compute_teks_by_generation_and_upload_date(date=upload_date)) shared_teks_generation_to_upload_df \ .sort_values(["upload_date", "generation_date"], ascending=False, inplace=True) shared_teks_generation_to_upload_df.tail() today_new_teks_df = \ shared_teks_generation_to_upload_df[ shared_teks_generation_to_upload_df.upload_date == extraction_date].copy() today_new_teks_df.tail() if not today_new_teks_df.empty: today_new_teks_df.set_index("generation_to_upload_days") \ .sort_index().shared_teks.plot.bar() generation_to_upload_period_pivot_df = \ shared_teks_generation_to_upload_df[ ["upload_date", "generation_to_upload_days", "shared_teks"]] \ .pivot(index="upload_date", columns="generation_to_upload_days") \ .sort_index(ascending=False).fillna(0).astype(int) \ .droplevel(level=0, axis=1) generation_to_upload_period_pivot_df.head() new_tek_df = tek_list_df.diff().tek_list.apply( lambda x: len(x) if not pd.isna(x) else None).to_frame().reset_index() new_tek_df.rename(columns={ "tek_list": "shared_teks_by_upload_date", "extraction_date": "sample_date_string",}, inplace=True) new_tek_df.tail() shared_teks_uploaded_on_generation_date_df = shared_teks_generation_to_upload_df[ shared_teks_generation_to_upload_df.generation_to_upload_days == 0] \ [["upload_date", "shared_teks"]].rename( columns={ "upload_date": "sample_date_string", "shared_teks": "shared_teks_uploaded_on_generation_date", }) shared_teks_uploaded_on_generation_date_df.head() estimated_shared_diagnoses_df = shared_teks_generation_to_upload_df \ .groupby(["upload_date"]).shared_teks.max().reset_index() \ .sort_values(["upload_date"], ascending=False) \ .rename(columns={ "upload_date": "sample_date_string", "shared_teks": "shared_diagnoses", }) invalid_shared_diagnoses_dates_mask = \ estimated_shared_diagnoses_df.sample_date_string.isin(invalid_shared_diagnoses_dates) estimated_shared_diagnoses_df[invalid_shared_diagnoses_dates_mask] = 0 estimated_shared_diagnoses_df.head() ###Output _____no_output_____ ###Markdown Hourly New TEKs ###Code hourly_extracted_teks_df = load_extracted_teks( mode="Hourly", region=report_backend_identifier, limit=25) hourly_extracted_teks_df.head() hourly_new_tek_count_df = hourly_extracted_teks_df \ .groupby("extraction_date_with_hour").tek_list. \ apply(lambda x: set(sum(x, []))).reset_index().copy() hourly_new_tek_count_df = hourly_new_tek_count_df.set_index("extraction_date_with_hour") \ .sort_index(ascending=True) hourly_new_tek_count_df["new_tek_list"] = hourly_new_tek_count_df.tek_list.diff() hourly_new_tek_count_df["new_tek_count"] = hourly_new_tek_count_df.new_tek_list.apply( lambda x: len(x) if not pd.isna(x) else 0) hourly_new_tek_count_df.rename(columns={ "new_tek_count": "shared_teks_by_upload_date"}, inplace=True) hourly_new_tek_count_df = hourly_new_tek_count_df.reset_index()[[ "extraction_date_with_hour", "shared_teks_by_upload_date"]] hourly_new_tek_count_df.head() hourly_summary_df = hourly_new_tek_count_df.copy() hourly_summary_df.set_index("extraction_date_with_hour", inplace=True) hourly_summary_df = hourly_summary_df.fillna(0).astype(int).reset_index() hourly_summary_df["datetime_utc"] = pd.to_datetime( hourly_summary_df.extraction_date_with_hour, format="%Y-%m-%d@%H") hourly_summary_df.set_index("datetime_utc", inplace=True) hourly_summary_df = hourly_summary_df.tail(-1) hourly_summary_df.head() ###Output _____no_output_____ ###Markdown Official Statistics ###Code import requests import pandas.io.json official_stats_response = requests.get("https://radarcovid.covid19.gob.es/kpi/statistics/basics") official_stats_response.raise_for_status() official_stats_df_ = pandas.io.json.json_normalize(official_stats_response.json()) official_stats_df = official_stats_df_.copy() official_stats_df["date"] = pd.to_datetime(official_stats_df["date"], dayfirst=True) official_stats_df.head() official_stats_column_map = { "date": "sample_date", "applicationsDownloads.totalAcummulated": "app_downloads_es_accumulated", "communicatedContagions.totalAcummulated": "shared_diagnoses_es_accumulated", } accumulated_suffix = "_accumulated" accumulated_values_columns = \ list(filter(lambda x: x.endswith(accumulated_suffix), official_stats_column_map.values())) interpolated_values_columns = \ list(map(lambda x: x[:-len(accumulated_suffix)], accumulated_values_columns)) official_stats_df = \ official_stats_df[official_stats_column_map.keys()] \ .rename(columns=official_stats_column_map) official_stats_df["extraction_date"] = extraction_date official_stats_df.head() official_stats_path = "Data/Statistics/Current/RadarCOVID-Statistics.json" previous_official_stats_df = pd.read_json(official_stats_path, orient="records", lines=True) previous_official_stats_df["sample_date"] = pd.to_datetime(previous_official_stats_df["sample_date"], dayfirst=True) official_stats_df = official_stats_df.append(previous_official_stats_df) official_stats_df.head() official_stats_df = official_stats_df[~(official_stats_df.shared_diagnoses_es_accumulated == 0)] official_stats_df.sort_values("extraction_date", ascending=False, inplace=True) official_stats_df.drop_duplicates(subset=["sample_date"], keep="first", inplace=True) official_stats_df.head() official_stats_stored_df = official_stats_df.copy() official_stats_stored_df["sample_date"] = official_stats_stored_df.sample_date.dt.strftime("%Y-%m-%d") official_stats_stored_df.to_json(official_stats_path, orient="records", lines=True) official_stats_df.drop(columns=["extraction_date"], inplace=True) official_stats_df = confirmed_days_df.merge(official_stats_df, how="left") official_stats_df.sort_values("sample_date", ascending=False, inplace=True) official_stats_df.head() official_stats_df[accumulated_values_columns] = \ official_stats_df[accumulated_values_columns] \ .astype(float).interpolate(limit_area="inside") official_stats_df[interpolated_values_columns] = \ official_stats_df[accumulated_values_columns].diff(periods=-1) official_stats_df.drop(columns="sample_date", inplace=True) official_stats_df.head() ###Output _____no_output_____ ###Markdown Data Merge ###Code result_summary_df = exposure_keys_summary_df.merge( new_tek_df, on=["sample_date_string"], how="outer") result_summary_df.head() result_summary_df = result_summary_df.merge( shared_teks_uploaded_on_generation_date_df, on=["sample_date_string"], how="outer") result_summary_df.head() result_summary_df = result_summary_df.merge( estimated_shared_diagnoses_df, on=["sample_date_string"], how="outer") result_summary_df.head() result_summary_df = result_summary_df.merge( official_stats_df, on=["sample_date_string"], how="outer") result_summary_df.head() result_summary_df = confirmed_eu_df.tail(daily_summary_days).merge( result_summary_df, on=["sample_date_string"], how="left") result_summary_df.head() result_summary_df = confirmed_es_df.tail(daily_summary_days).merge( result_summary_df, on=["sample_date_string"], how="left") result_summary_df.head() result_summary_df["sample_date"] = pd.to_datetime(result_summary_df.sample_date_string) result_summary_df = result_summary_df.merge(source_regions_for_summary_df, how="left") result_summary_df.set_index(["sample_date", "source_regions"], inplace=True) result_summary_df.drop(columns=["sample_date_string"], inplace=True) result_summary_df.sort_index(ascending=False, inplace=True) result_summary_df.head() with pd.option_context("mode.use_inf_as_na", True): result_summary_df = result_summary_df.fillna(0).astype(int) result_summary_df["teks_per_shared_diagnosis"] = \ (result_summary_df.shared_teks_by_upload_date / result_summary_df.shared_diagnoses).fillna(0) result_summary_df["shared_diagnoses_per_covid_case"] = \ (result_summary_df.shared_diagnoses / result_summary_df.covid_cases).fillna(0) result_summary_df["shared_diagnoses_per_covid_case_es"] = \ (result_summary_df.shared_diagnoses_es / result_summary_df.covid_cases_es).fillna(0) result_summary_df.head(daily_plot_days) def compute_aggregated_results_summary(days) -> pd.DataFrame: aggregated_result_summary_df = result_summary_df.copy() aggregated_result_summary_df["covid_cases_for_ratio"] = \ aggregated_result_summary_df.covid_cases.mask( aggregated_result_summary_df.shared_diagnoses == 0, 0) aggregated_result_summary_df["covid_cases_for_ratio_es"] = \ aggregated_result_summary_df.covid_cases_es.mask( aggregated_result_summary_df.shared_diagnoses_es == 0, 0) aggregated_result_summary_df = aggregated_result_summary_df \ .sort_index(ascending=True).fillna(0).rolling(days).agg({ "covid_cases": "sum", "covid_cases_es": "sum", "covid_cases_for_ratio": "sum", "covid_cases_for_ratio_es": "sum", "shared_teks_by_generation_date": "sum", "shared_teks_by_upload_date": "sum", "shared_diagnoses": "sum", "shared_diagnoses_es": "sum", }).sort_index(ascending=False) with pd.option_context("mode.use_inf_as_na", True): aggregated_result_summary_df = aggregated_result_summary_df.fillna(0).astype(int) aggregated_result_summary_df["teks_per_shared_diagnosis"] = \ (aggregated_result_summary_df.shared_teks_by_upload_date / aggregated_result_summary_df.covid_cases_for_ratio).fillna(0) aggregated_result_summary_df["shared_diagnoses_per_covid_case"] = \ (aggregated_result_summary_df.shared_diagnoses / aggregated_result_summary_df.covid_cases_for_ratio).fillna(0) aggregated_result_summary_df["shared_diagnoses_per_covid_case_es"] = \ (aggregated_result_summary_df.shared_diagnoses_es / aggregated_result_summary_df.covid_cases_for_ratio_es).fillna(0) return aggregated_result_summary_df aggregated_result_with_7_days_window_summary_df = compute_aggregated_results_summary(days=7) aggregated_result_with_7_days_window_summary_df.head() last_7_days_summary = aggregated_result_with_7_days_window_summary_df.to_dict(orient="records")[1] last_7_days_summary aggregated_result_with_14_days_window_summary_df = compute_aggregated_results_summary(days=13) last_14_days_summary = aggregated_result_with_14_days_window_summary_df.to_dict(orient="records")[1] last_14_days_summary ###Output _____no_output_____ ###Markdown Report Results ###Code display_column_name_mapping = { "sample_date": "Sample\u00A0Date\u00A0(UTC)", "source_regions": "Source Countries", "datetime_utc": "Timestamp (UTC)", "upload_date": "Upload Date (UTC)", "generation_to_upload_days": "Generation to Upload Period in Days", "region": "Backend", "region_x": "Backend\u00A0(A)", "region_y": "Backend\u00A0(B)", "common_teks": "Common TEKs Shared Between Backends", "common_teks_fraction": "Fraction of TEKs in Backend (A) Available in Backend (B)", "covid_cases": "COVID-19 Cases (Source Countries)", "shared_teks_by_generation_date": "Shared TEKs by Generation Date (Source Countries)", "shared_teks_by_upload_date": "Shared TEKs by Upload Date (Source Countries)", "shared_teks_uploaded_on_generation_date": "Shared TEKs Uploaded on Generation Date (Source Countries)", "shared_diagnoses": "Shared Diagnoses (Source Countries – Estimation)", "teks_per_shared_diagnosis": "TEKs Uploaded per Shared Diagnosis (Source Countries)", "shared_diagnoses_per_covid_case": "Usage Ratio (Source Countries)", "covid_cases_es": "COVID-19 Cases (Spain)", "app_downloads_es": "App Downloads (Spain – Official)", "shared_diagnoses_es": "Shared Diagnoses (Spain – Official)", "shared_diagnoses_per_covid_case_es": "Usage Ratio (Spain)", } summary_columns = [ "covid_cases", "shared_teks_by_generation_date", "shared_teks_by_upload_date", "shared_teks_uploaded_on_generation_date", "shared_diagnoses", "teks_per_shared_diagnosis", "shared_diagnoses_per_covid_case", "covid_cases_es", "app_downloads_es", "shared_diagnoses_es", "shared_diagnoses_per_covid_case_es", ] summary_percentage_columns= [ "shared_diagnoses_per_covid_case_es", "shared_diagnoses_per_covid_case", ] ###Output _____no_output_____ ###Markdown Daily Summary Table ###Code result_summary_df_ = result_summary_df.copy() result_summary_df = result_summary_df[summary_columns] result_summary_with_display_names_df = result_summary_df \ .rename_axis(index=display_column_name_mapping) \ .rename(columns=display_column_name_mapping) result_summary_with_display_names_df ###Output _____no_output_____ ###Markdown Daily Summary Plots ###Code result_plot_summary_df = result_summary_df.head(daily_plot_days)[summary_columns] \ .droplevel(level=["source_regions"]) \ .rename_axis(index=display_column_name_mapping) \ .rename(columns=display_column_name_mapping) summary_ax_list = result_plot_summary_df.sort_index(ascending=True).plot.bar( title=f"Daily Summary", rot=45, subplots=True, figsize=(15, 30), legend=False) ax_ = summary_ax_list[0] ax_.get_figure().tight_layout() ax_.get_figure().subplots_adjust(top=0.95) _ = ax_.set_xticklabels(sorted(result_plot_summary_df.index.strftime("%Y-%m-%d").tolist())) for percentage_column in summary_percentage_columns: percentage_column_index = summary_columns.index(percentage_column) summary_ax_list[percentage_column_index].yaxis \ .set_major_formatter(matplotlib.ticker.PercentFormatter(1.0)) ###Output /opt/hostedtoolcache/Python/3.8.10/x64/lib/python3.8/site-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead. layout[ax.rowNum, ax.colNum] = ax.get_visible() /opt/hostedtoolcache/Python/3.8.10/x64/lib/python3.8/site-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead. layout[ax.rowNum, ax.colNum] = ax.get_visible() /opt/hostedtoolcache/Python/3.8.10/x64/lib/python3.8/site-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead. if not layout[ax.rowNum + 1, ax.colNum]: /opt/hostedtoolcache/Python/3.8.10/x64/lib/python3.8/site-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead. if not layout[ax.rowNum + 1, ax.colNum]: ###Markdown Daily Generation to Upload Period Table ###Code display_generation_to_upload_period_pivot_df = \ generation_to_upload_period_pivot_df \ .head(backend_generation_days) display_generation_to_upload_period_pivot_df \ .head(backend_generation_days) \ .rename_axis(columns=display_column_name_mapping) \ .rename_axis(index=display_column_name_mapping) fig, generation_to_upload_period_pivot_table_ax = plt.subplots( figsize=(12, 1 + 0.6 * len(display_generation_to_upload_period_pivot_df))) generation_to_upload_period_pivot_table_ax.set_title( "Shared TEKs Generation to Upload Period Table") sns.heatmap( data=display_generation_to_upload_period_pivot_df .rename_axis(columns=display_column_name_mapping) .rename_axis(index=display_column_name_mapping), fmt=".0f", annot=True, ax=generation_to_upload_period_pivot_table_ax) generation_to_upload_period_pivot_table_ax.get_figure().tight_layout() ###Output _____no_output_____ ###Markdown Hourly Summary Plots ###Code hourly_summary_ax_list = hourly_summary_df \ .rename_axis(index=display_column_name_mapping) \ .rename(columns=display_column_name_mapping) \ .plot.bar( title=f"Last 24h Summary", rot=45, subplots=True, legend=False) ax_ = hourly_summary_ax_list[-1] ax_.get_figure().tight_layout() ax_.get_figure().subplots_adjust(top=0.9) _ = ax_.set_xticklabels(sorted(hourly_summary_df.index.strftime("%Y-%m-%d@%H").tolist())) ###Output _____no_output_____ ###Markdown Publish Results ###Code github_repository = os.environ.get("GITHUB_REPOSITORY") if github_repository is None: github_repository = "pvieito/Radar-STATS" github_project_base_url = "https://github.com/" + github_repository display_formatters = { display_column_name_mapping["teks_per_shared_diagnosis"]: lambda x: f"{x:.2f}" if x != 0 else "", display_column_name_mapping["shared_diagnoses_per_covid_case"]: lambda x: f"{x:.2%}" if x != 0 else "", display_column_name_mapping["shared_diagnoses_per_covid_case_es"]: lambda x: f"{x:.2%}" if x != 0 else "", } general_columns = \ list(filter(lambda x: x not in display_formatters, display_column_name_mapping.values())) general_formatter = lambda x: f"{x}" if x != 0 else "" display_formatters.update(dict(map(lambda x: (x, general_formatter), general_columns))) daily_summary_table_html = result_summary_with_display_names_df \ .head(daily_plot_days) \ .rename_axis(index=display_column_name_mapping) \ .rename(columns=display_column_name_mapping) \ .to_html(formatters=display_formatters) multi_backend_summary_table_html = multi_backend_summary_df \ .head(daily_plot_days) \ .rename_axis(columns=display_column_name_mapping) \ .rename(columns=display_column_name_mapping) \ .rename_axis(index=display_column_name_mapping) \ .to_html(formatters=display_formatters) def format_multi_backend_cross_sharing_fraction(x): if pd.isna(x): return "-" elif round(x * 100, 1) == 0: return "" else: return f"{x:.1%}" multi_backend_cross_sharing_summary_table_html = multi_backend_cross_sharing_summary_df \ .rename_axis(columns=display_column_name_mapping) \ .rename(columns=display_column_name_mapping) \ .rename_axis(index=display_column_name_mapping) \ .to_html( classes="table-center", formatters=display_formatters, float_format=format_multi_backend_cross_sharing_fraction) multi_backend_cross_sharing_summary_table_html = \ multi_backend_cross_sharing_summary_table_html \ .replace("<tr>","<tr style=\"text-align: center;\">") extraction_date_result_summary_df = \ result_summary_df[result_summary_df.index.get_level_values("sample_date") == extraction_date] extraction_date_result_hourly_summary_df = \ hourly_summary_df[hourly_summary_df.extraction_date_with_hour == extraction_date_with_hour] covid_cases = \ extraction_date_result_summary_df.covid_cases.item() shared_teks_by_generation_date = \ extraction_date_result_summary_df.shared_teks_by_generation_date.item() shared_teks_by_upload_date = \ extraction_date_result_summary_df.shared_teks_by_upload_date.item() shared_diagnoses = \ extraction_date_result_summary_df.shared_diagnoses.item() teks_per_shared_diagnosis = \ extraction_date_result_summary_df.teks_per_shared_diagnosis.item() shared_diagnoses_per_covid_case = \ extraction_date_result_summary_df.shared_diagnoses_per_covid_case.item() shared_teks_by_upload_date_last_hour = \ extraction_date_result_hourly_summary_df.shared_teks_by_upload_date.sum().astype(int) display_source_regions = ", ".join(report_source_regions) if len(report_source_regions) == 1: display_brief_source_regions = report_source_regions[0] else: display_brief_source_regions = f"{len(report_source_regions)} 🇪🇺" def get_temporary_image_path() -> str: return os.path.join(tempfile.gettempdir(), str(uuid.uuid4()) + ".png") def save_temporary_plot_image(ax): if isinstance(ax, np.ndarray): ax = ax[0] media_path = get_temporary_image_path() ax.get_figure().savefig(media_path) return media_path def save_temporary_dataframe_image(df): import dataframe_image as dfi df = df.copy() df_styler = df.style.format(display_formatters) media_path = get_temporary_image_path() dfi.export(df_styler, media_path) return media_path summary_plots_image_path = save_temporary_plot_image( ax=summary_ax_list) summary_table_image_path = save_temporary_dataframe_image( df=result_summary_with_display_names_df) hourly_summary_plots_image_path = save_temporary_plot_image( ax=hourly_summary_ax_list) multi_backend_summary_table_image_path = save_temporary_dataframe_image( df=multi_backend_summary_df) generation_to_upload_period_pivot_table_image_path = save_temporary_plot_image( ax=generation_to_upload_period_pivot_table_ax) ###Output [0709/230944.500629:WARNING:headless_browser_main_parts.cc(106)] Cannot create Pref Service with no user data dir. [0709/230944.552279:ERROR:gpu_init.cc(440)] Passthrough is not supported, GL is swiftshader ###Markdown Save Results ###Code report_resources_path_prefix = "Data/Resources/Current/RadarCOVID-Report-" result_summary_df.to_csv( report_resources_path_prefix + "Summary-Table.csv") result_summary_df.to_html( report_resources_path_prefix + "Summary-Table.html") hourly_summary_df.to_csv( report_resources_path_prefix + "Hourly-Summary-Table.csv") multi_backend_summary_df.to_csv( report_resources_path_prefix + "Multi-Backend-Summary-Table.csv") multi_backend_cross_sharing_summary_df.to_csv( report_resources_path_prefix + "Multi-Backend-Cross-Sharing-Summary-Table.csv") generation_to_upload_period_pivot_df.to_csv( report_resources_path_prefix + "Generation-Upload-Period-Table.csv") _ = shutil.copyfile( summary_plots_image_path, report_resources_path_prefix + "Summary-Plots.png") _ = shutil.copyfile( summary_table_image_path, report_resources_path_prefix + "Summary-Table.png") _ = shutil.copyfile( hourly_summary_plots_image_path, report_resources_path_prefix + "Hourly-Summary-Plots.png") _ = shutil.copyfile( multi_backend_summary_table_image_path, report_resources_path_prefix + "Multi-Backend-Summary-Table.png") _ = shutil.copyfile( generation_to_upload_period_pivot_table_image_path, report_resources_path_prefix + "Generation-Upload-Period-Table.png") ###Output _____no_output_____ ###Markdown Publish Results as JSON ###Code def generate_summary_api_results(df: pd.DataFrame) -> list: api_df = df.reset_index().copy() api_df["sample_date_string"] = \ api_df["sample_date"].dt.strftime("%Y-%m-%d") api_df["source_regions"] = \ api_df["source_regions"].apply(lambda x: x.split(",")) return api_df.to_dict(orient="records") summary_api_results = \ generate_summary_api_results(df=result_summary_df) today_summary_api_results = \ generate_summary_api_results(df=extraction_date_result_summary_df)[0] summary_results = dict( backend_identifier=report_backend_identifier, source_regions=report_source_regions, extraction_datetime=extraction_datetime, extraction_date=extraction_date, extraction_date_with_hour=extraction_date_with_hour, last_hour=dict( shared_teks_by_upload_date=shared_teks_by_upload_date_last_hour, shared_diagnoses=0, ), today=today_summary_api_results, last_7_days=last_7_days_summary, last_14_days=last_14_days_summary, daily_results=summary_api_results) summary_results = \ json.loads(pd.Series([summary_results]).to_json(orient="records"))[0] with open(report_resources_path_prefix + "Summary-Results.json", "w") as f: json.dump(summary_results, f, indent=4) ###Output _____no_output_____ ###Markdown Publish on README ###Code with open("Data/Templates/README.md", "r") as f: readme_contents = f.read() readme_contents = readme_contents.format( extraction_date_with_hour=extraction_date_with_hour, github_project_base_url=github_project_base_url, daily_summary_table_html=daily_summary_table_html, multi_backend_summary_table_html=multi_backend_summary_table_html, multi_backend_cross_sharing_summary_table_html=multi_backend_cross_sharing_summary_table_html, display_source_regions=display_source_regions) with open("README.md", "w") as f: f.write(readme_contents) ###Output _____no_output_____ ###Markdown Publish on Twitter ###Code enable_share_to_twitter = os.environ.get("RADARCOVID_REPORT__ENABLE_PUBLISH_ON_TWITTER") github_event_name = os.environ.get("GITHUB_EVENT_NAME") if enable_share_to_twitter and github_event_name == "schedule" and \ (shared_teks_by_upload_date_last_hour or not are_today_results_partial): import tweepy twitter_api_auth_keys = os.environ["RADARCOVID_REPORT__TWITTER_API_AUTH_KEYS"] twitter_api_auth_keys = twitter_api_auth_keys.split(":") auth = tweepy.OAuthHandler(twitter_api_auth_keys[0], twitter_api_auth_keys[1]) auth.set_access_token(twitter_api_auth_keys[2], twitter_api_auth_keys[3]) api = tweepy.API(auth) summary_plots_media = api.media_upload(summary_plots_image_path) summary_table_media = api.media_upload(summary_table_image_path) generation_to_upload_period_pivot_table_image_media = api.media_upload(generation_to_upload_period_pivot_table_image_path) media_ids = [ summary_plots_media.media_id, summary_table_media.media_id, generation_to_upload_period_pivot_table_image_media.media_id, ] if are_today_results_partial: today_addendum = " (Partial)" else: today_addendum = "" def format_shared_diagnoses_per_covid_case(value) -> str: if value == 0: return "–" return f"≤{value:.2%}" display_shared_diagnoses_per_covid_case = \ format_shared_diagnoses_per_covid_case(value=shared_diagnoses_per_covid_case) display_last_14_days_shared_diagnoses_per_covid_case = \ format_shared_diagnoses_per_covid_case(value=last_14_days_summary["shared_diagnoses_per_covid_case"]) display_last_14_days_shared_diagnoses_per_covid_case_es = \ format_shared_diagnoses_per_covid_case(value=last_14_days_summary["shared_diagnoses_per_covid_case_es"]) status = textwrap.dedent(f""" #RadarCOVID – {extraction_date_with_hour} Today{today_addendum}: - Uploaded TEKs: {shared_teks_by_upload_date:.0f} ({shared_teks_by_upload_date_last_hour:+d} last hour) - Shared Diagnoses: ≤{shared_diagnoses:.0f} - Usage Ratio: {display_shared_diagnoses_per_covid_case} Last 14 Days: - Usage Ratio (Estimation): {display_last_14_days_shared_diagnoses_per_covid_case} - Usage Ratio (Official): {display_last_14_days_shared_diagnoses_per_covid_case_es} Info: {github_project_base_url}#documentation """) status = status.encode(encoding="utf-8") api.update_status(status=status, media_ids=media_ids) ###Output _____no_output_____

01_Getting_&_Knowing_Your_Data/World Food Facts/Exercises_with_solutions.ipynb

###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the csv file and assign it to a dataframe called food ###Code food = pd.read_csv('/Users/guilhermeoliveira/Desktop/world-food-facts/FoodFacts.csv') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2723: DtypeWarning: Columns (0,3,5,27,36) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print food.shape #will give you both (observations/rows, columns) print food.shape[1] #will give you only the columns number #OR food.info() #Columns: 159 entries ###Output (65503, 159) 159 <class 'pandas.core.frame.DataFrame'> RangeIndex: 65503 entries, 0 to 65502 Columns: 159 entries, code to nutrition_score_uk_100g dtypes: float64(103), object(56) memory usage: 79.5+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown 연습1 단계1 https://www.kaggle.com/openfoodfacts/world-food-facts/data로 간다. Step 2. 데이터를 다운 받아서 압축을 푼다. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown 단계 3. tsv파일을 불러와서 food라는 이름의 데이터 프레임에 저장한다. (잊지 말고 넘파이와 판다스를 import한다) ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown 단계 4. 처음 5개 열(column)을 본다. ###Code food.head() ###Output _____no_output_____ ###Markdown 단계 5. 데이터 셋에 있는 관측치는 모두 몇 개인가? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown 단계 6. 데이터 셋에 있는 열의 수는 몇 개인가? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown 단계 7. 모든 열의 이름을 출력해본다 ###Code food.columns ###Output _____no_output_____ ###Markdown 단계 8. 105번째 열의 이름name은 무엇인가? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown 단계 9. 105번째 열의 타입은 무엇인가? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown 단계 10. 데이터는 어떻게 색인 되어 있는가? ###Code food.index ###Output _____no_output_____ ###Markdown 단계 11. 19번째 관측치(observation)의 상품명(product name)은 무엇인가? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output _____no_output_____ ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output _____no_output_____ ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output _____no_output_____ ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output _____no_output_____ ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your DataCheck out [World Food Facts Exercises Video Tutorial](https://youtu.be/_jCSK4cMcVw) to watch a data scientist go through the exercises Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of ~~observations~~ rows in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____ ###Markdown Ex1 - Getting and knowing your Data Step 1. Go to https://www.kaggle.com/openfoodfacts/world-food-facts/data Step 2. Download the dataset to your computer and unzip it. ###Code import pandas as pd import numpy as np ###Output _____no_output_____ ###Markdown Step 3. Use the tsv file and assign it to a dataframe called food ###Code food = pd.read_csv('~/Desktop/en.openfoodfacts.org.products.tsv', sep='\t') ###Output //anaconda/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (0,3,5,19,20,24,25,26,27,28,36,37,38,39,48) have mixed types. Specify dtype option on import or set low_memory=False. interactivity=interactivity, compiler=compiler, result=result) ###Markdown Step 4. See the first 5 entries ###Code food.head() ###Output _____no_output_____ ###Markdown Step 5. What is the number of observations in the dataset? ###Code food.shape #will give you both (observations/rows, columns) food.shape[0] #will give you only the observations/rows number ###Output _____no_output_____ ###Markdown Step 6. What is the number of columns in the dataset? ###Code print(food.shape) #will give you both (observations/rows, columns) print(food.shape[1]) #will give you only the columns number #OR food.info() #Columns: 163 entries ###Output (356027, 163) 163 <class 'pandas.core.frame.DataFrame'> RangeIndex: 356027 entries, 0 to 356026 Columns: 163 entries, code to water-hardness_100g dtypes: float64(107), object(56) memory usage: 442.8+ MB ###Markdown Step 7. Print the name of all the columns. ###Code food.columns ###Output _____no_output_____ ###Markdown Step 8. What is the name of 105th column? ###Code food.columns[104] ###Output _____no_output_____ ###Markdown Step 9. What is the type of the observations of the 105th column? ###Code food.dtypes['-glucose_100g'] ###Output _____no_output_____ ###Markdown Step 10. How is the dataset indexed? ###Code food.index ###Output _____no_output_____ ###Markdown Step 11. What is the product name of the 19th observation? ###Code food.values[18][7] ###Output _____no_output_____

Data wrangling .ipynb

###Markdown **Space X Falcon 9 First Stage Landing Prediction** Lab 2: Data wrangling Estimated time needed: **60** minutes In this lab, we will perform some Exploratory Data Analysis (EDA) to find some patterns in the data and determine what would be the label for training supervised models.In the data set, there are several different cases where the booster did not land successfully. Sometimes a landing was attempted but failed due to an accident; for example, True Ocean means the mission outcome was successfully landed to a specific region of the ocean while False Ocean means the mission outcome was unsuccessfully landed to a specific region of the ocean. True RTLS means the mission outcome was successfully landed to a ground pad False RTLS means the mission outcome was unsuccessfully landed to a ground pad.True ASDS means the mission outcome was successfully landed on a drone ship False ASDS means the mission outcome was unsuccessfully landed on a drone ship.In this lab we will mainly convert those outcomes into Training Labels with `1` means the booster successfully landed `0` means it was unsuccessful. Falcon 9 first stage will land successfully  Several examples of an unsuccessful landing are shown here:  ObjectivesPerform exploratory Data Analysis and determine Training Labels* Exploratory Data Analysis* Determine Training Labels *** Import Libraries and Define Auxiliary Functions We will import the following libraries. ###Code # Pandas is a software library written for the Python programming language for data manipulation and analysis. import pandas as pd #NumPy is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays import numpy as np ###Output _____no_output_____ ###Markdown Data Analysis Load Space X dataset, from last section. ###Code df=pd.read_csv("https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBM-DS0321EN-SkillsNetwork/datasets/dataset_part_1.csv") df.head(10) ###Output _____no_output_____ ###Markdown Identify and calculate the percentage of the missing values in each attribute ###Code df.isnull().sum()/df.count()*100 ###Output _____no_output_____ ###Markdown Identify which columns are numerical and categorical: ###Code df.dtypes ###Output _____no_output_____ ###Markdown TASK 1: Calculate the number of launches on each siteThe data contains several Space X launch facilities: Cape Canaveral Space Launch Complex 40 VAFB SLC 4E , Vandenberg Air Force Base Space Launch Complex 4E (SLC-4E), Kennedy Space Center Launch Complex 39A KSC LC 39A .The location of each Launch Is placed in the column LaunchSite Next, let's see the number of launches for each site.Use the method value_counts() on the column LaunchSite to determine the number of launches on each site: ###Code # Apply value_counts() on column LaunchSite df["LaunchSite"].value_counts() ###Output _____no_output_____ ###Markdown Each launch aims to an dedicated orbit, and here are some common orbit types: * LEO: Low Earth orbit (LEO)is an Earth-centred orbit with an altitude of 2,000 km (1,200 mi) or less (approximately one-third of the radius of Earth),\[1] or with at least 11.25 periods per day (an orbital period of 128 minutes or less) and an eccentricity less than 0.25.\[2] Most of the manmade objects in outer space are in LEO \[1].* VLEO: Very Low Earth Orbits (VLEO) can be defined as the orbits with a mean altitude below 450 km. Operating in these orbits can provide a number of benefits to Earth observation spacecraft as the spacecraft operates closer to the observation\[2].* GTO A geosynchronous orbit is a high Earth orbit that allows satellites to match Earth's rotation. Located at 22,236 miles (35,786 kilometers) above Earth's equator, this position is a valuable spot for monitoring weather, communications and surveillance. Because the satellite orbits at the same speed that the Earth is turning, the satellite seems to stay in place over a single longitude, though it may drift north to south,” NASA wrote on its Earth Observatory website \[3] .* SSO (or SO): It is a Sun-synchronous orbit also called a heliosynchronous orbit is a nearly polar orbit around a planet, in which the satellite passes over any given point of the planet's surface at the same local mean solar time \[4] .* ES-L1 :At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies. L1 is one such point between the sun and the earth \[5] .* HEO A highly elliptical orbit, is an elliptic orbit with high eccentricity, usually referring to one around Earth \[6].* ISS A modular space station (habitable artificial satellite) in low Earth orbit. It is a multinational collaborative project between five participating space agencies: NASA (United States), Roscosmos (Russia), JAXA (Japan), ESA (Europe), and CSA (Canada) \[7] * MEO Geocentric orbits ranging in altitude from 2,000 km (1,200 mi) to just below geosynchronous orbit at 35,786 kilometers (22,236 mi). Also known as an intermediate circular orbit. These are "most commonly at 20,200 kilometers (12,600 mi), or 20,650 kilometers (12,830 mi), with an orbital period of 12 hours \[8] * HEO Geocentric orbits above the altitude of geosynchronous orbit (35,786 km or 22,236 mi) \[9] * GEO It is a circular geosynchronous orbit 35,786 kilometres (22,236 miles) above Earth's equator and following the direction of Earth's rotation \[10] * PO It is one type of satellites in which a satellite passes above or nearly above both poles of the body being orbited (usually a planet such as the Earth \[11] some are shown in the following plot:  TASK 2: Calculate the number and occurrence of each orbit Use the method .value_counts() to determine the number and occurrence of each orbit in the column Orbit ###Code # Apply value_counts on Orbit column df["Orbit"].value_counts() ###Output _____no_output_____ ###Markdown TASK 3: Calculate the number and occurence of mission outcome per orbit type Use the method value_counts() to determine the number and occurrence of each orbit in the column Outcome , then assign it to the variable landing_outcomes: ###Code # landing_outcomes = values on Outcome column landing_outcomes = df["Outcome"].value_counts() landing_outcomes ###Output _____no_output_____ ###Markdown True Ocean means the mission outcome was successfully landed to a specific region of the ocean while False Ocean means the mission outcome was unsuccessfully landed to a specific region of the ocean. True RTLS means the mission outcome was successfully landed to a ground pad False RTLS means the mission outcome was unsuccessfully landed to a ground pad.True ASDS means the mission outcome was successfully landed to a drone ship False ASDS means the mission outcome was unsuccessfully landed to a drone ship. None ASDS and None None these represent a failure to land. ###Code for i,outcome in enumerate(landing_outcomes.keys()): print(i,outcome) ###Output 0 True ASDS 1 None None 2 True RTLS 3 False ASDS 4 True Ocean 5 False Ocean 6 None ASDS 7 False RTLS ###Markdown We create a set of outcomes where the second stage did not land successfully: ###Code bad_outcomes=set(landing_outcomes.keys()[[1,3,5,6,7]]) bad_outcomes ###Output _____no_output_____ ###Markdown TASK 4: Create a landing outcome label from Outcome column Using the Outcome, create a list where the element is zero if the corresponding row in Outcome is in the set bad_outcome; otherwise, it's one. Then assign it to the variable landing_class: ###Code # landing_class = 0 if bad_outcome # landing_class = 1 otherwise def onehot(item): if item in bad_outcomes: return 0 else: return 1 landing_class = df["Outcome"].apply(onehot) landing_class ###Output _____no_output_____ ###Markdown This variable will represent the classification variable that represents the outcome of each launch. If the value is zero, the first stage did not land successfully; one means the first stage landed Successfully ###Code df['Class']=landing_class df[['Class']].head(8) df.head(5) ###Output _____no_output_____ ###Markdown We can use the following line of code to determine the success rate: ###Code df["Class"].mean() ###Output _____no_output_____ ###Markdown **Space X Falcon 9 First Stage Landing Prediction** Lab 2: Data wrangling Estimated time needed: **60** minutes In this lab, we will perform some Exploratory Data Analysis (EDA) to find some patterns in the data and determine what would be the label for training supervised models.In the data set, there are several different cases where the booster did not land successfully. Sometimes a landing was attempted but failed due to an accident; for example, True Ocean means the mission outcome was successfully landed to a specific region of the ocean while False Ocean means the mission outcome was unsuccessfully landed to a specific region of the ocean. True RTLS means the mission outcome was successfully landed to a ground pad False RTLS means the mission outcome was unsuccessfully landed to a ground pad.True ASDS means the mission outcome was successfully landed on a drone ship False ASDS means the mission outcome was unsuccessfully landed on a drone ship.In this lab we will mainly convert those outcomes into Training Labels with `1` means the booster successfully landed `0` means it was unsuccessful. Falcon 9 first stage will land successfully  Several examples of an unsuccessful landing are shown here:  ObjectivesPerform exploratory Data Analysis and determine Training Labels* Exploratory Data Analysis* Determine Training Labels *** Import Libraries and Define Auxiliary Functions We will import the following libraries. ###Code # Pandas is a software library written for the Python programming language for data manipulation and analysis. import pandas as pd #NumPy is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays import numpy as np ###Output _____no_output_____ ###Markdown Data Analysis Load Space X dataset, from last section. ###Code df=pd.read_csv("https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBM-DS0321EN-SkillsNetwork/datasets/dataset_part_1.csv") df.head(10) ###Output _____no_output_____ ###Markdown Identify and calculate the percentage of the missing values in each attribute ###Code df.isnull().sum()/df.count()*100 ###Output _____no_output_____ ###Markdown Identify which columns are numerical and categorical: ###Code df.dtypes ###Output _____no_output_____ ###Markdown TASK 1: Calculate the number of launches on each siteThe data contains several Space X launch facilities: Cape Canaveral Space Launch Complex 40 VAFB SLC 4E , Vandenberg Air Force Base Space Launch Complex 4E (SLC-4E), Kennedy Space Center Launch Complex 39A KSC LC 39A .The location of each Launch Is placed in the column LaunchSite Next, let's see the number of launches for each site.Use the method value_counts() on the column LaunchSite to determine the number of launches on each site: ###Code # Apply value_counts() on column LaunchSite df["LaunchSite"].value_counts() ###Output _____no_output_____ ###Markdown Each launch aims to an dedicated orbit, and here are some common orbit types: * LEO: Low Earth orbit (LEO)is an Earth-centred orbit with an altitude of 2,000 km (1,200 mi) or less (approximately one-third of the radius of Earth),\[1] or with at least 11.25 periods per day (an orbital period of 128 minutes or less) and an eccentricity less than 0.25.\[2] Most of the manmade objects in outer space are in LEO \[1].* VLEO: Very Low Earth Orbits (VLEO) can be defined as the orbits with a mean altitude below 450 km. Operating in these orbits can provide a number of benefits to Earth observation spacecraft as the spacecraft operates closer to the observation\[2].* GTO A geosynchronous orbit is a high Earth orbit that allows satellites to match Earth's rotation. Located at 22,236 miles (35,786 kilometers) above Earth's equator, this position is a valuable spot for monitoring weather, communications and surveillance. Because the satellite orbits at the same speed that the Earth is turning, the satellite seems to stay in place over a single longitude, though it may drift north to south,” NASA wrote on its Earth Observatory website \[3] .* SSO (or SO): It is a Sun-synchronous orbit also called a heliosynchronous orbit is a nearly polar orbit around a planet, in which the satellite passes over any given point of the planet's surface at the same local mean solar time \[4] .* ES-L1 :At the Lagrange points the gravitational forces of the two large bodies cancel out in such a way that a small object placed in orbit there is in equilibrium relative to the center of mass of the large bodies. L1 is one such point between the sun and the earth \[5] .* HEO A highly elliptical orbit, is an elliptic orbit with high eccentricity, usually referring to one around Earth \[6].* ISS A modular space station (habitable artificial satellite) in low Earth orbit. It is a multinational collaborative project between five participating space agencies: NASA (United States), Roscosmos (Russia), JAXA (Japan), ESA (Europe), and CSA (Canada) \[7] * MEO Geocentric orbits ranging in altitude from 2,000 km (1,200 mi) to just below geosynchronous orbit at 35,786 kilometers (22,236 mi). Also known as an intermediate circular orbit. These are "most commonly at 20,200 kilometers (12,600 mi), or 20,650 kilometers (12,830 mi), with an orbital period of 12 hours \[8] * HEO Geocentric orbits above the altitude of geosynchronous orbit (35,786 km or 22,236 mi) \[9] * GEO It is a circular geosynchronous orbit 35,786 kilometres (22,236 miles) above Earth's equator and following the direction of Earth's rotation \[10] * PO It is one type of satellites in which a satellite passes above or nearly above both poles of the body being orbited (usually a planet such as the Earth \[11] some are shown in the following plot:  TASK 2: Calculate the number and occurrence of each orbit Use the method .value_counts() to determine the number and occurrence of each orbit in the column Orbit ###Code # Apply value_counts on Orbit column df["Orbit"].value_counts() ###Output _____no_output_____ ###Markdown TASK 3: Calculate the number and occurence of mission outcome per orbit type Use the method value_counts() to determine the number and occurrence of each orbit in the column Outcome , then assign it to the variable landing_outcomes: ###Code # landing_outcomes = values on Outcome column landing_outcomes = df["Outcome"].value_counts() landing_outcomes ###Output _____no_output_____ ###Markdown True Ocean means the mission outcome was successfully landed to a specific region of the ocean while False Ocean means the mission outcome was unsuccessfully landed to a specific region of the ocean. True RTLS means the mission outcome was successfully landed to a ground pad False RTLS means the mission outcome was unsuccessfully landed to a ground pad.True ASDS means the mission outcome was successfully landed to a drone ship False ASDS means the mission outcome was unsuccessfully landed to a drone ship. None ASDS and None None these represent a failure to land. ###Code for i,outcome in enumerate(landing_outcomes.keys()): print(i,outcome) ###Output 0 True ASDS 1 None None 2 True RTLS 3 False ASDS 4 True Ocean 5 False Ocean 6 None ASDS 7 False RTLS ###Markdown We create a set of outcomes where the second stage did not land successfully: ###Code bad_outcomes=set(landing_outcomes.keys()[[1,3,5,6,7]]) bad_outcomes ###Output _____no_output_____ ###Markdown TASK 4: Create a landing outcome label from Outcome column Using the Outcome, create a list where the element is zero if the corresponding row in Outcome is in the set bad_outcome; otherwise, it's one. Then assign it to the variable landing_class: ###Code # landing_class = 0 if bad_outcome # landing_class = 1 otherwise def onehot(item): if item in bad_outcomes: return 0 else: return 1 landing_class = df["Outcome"].apply(onehot) landing_class ###Output _____no_output_____ ###Markdown This variable will represent the classification variable that represents the outcome of each launch. If the value is zero, the first stage did not land successfully; one means the first stage landed Successfully ###Code df['Class']=landing_class df[['Class']].head(8) df.head(5) ###Output _____no_output_____ ###Markdown We can use the following line of code to determine the success rate: ###Code df["Class"].mean() ###Output _____no_output_____

notebooks/Computer Vision/blob-detection-using-opencv.ipynb

###Markdown Blob Detection Using OpenCV ###Code # Standard imports import cv2 import numpy as np; # images ROOT = "/home/jeff/Jupyter-Notebooks/DataSets/Images/" IMAGE = "vending_machine.png" # Read image im = cv2.imread(ROOT + IMAGE, cv2.IMREAD_GRAYSCALE) # Setup SimpleBlobDetector parameters. params = cv2.SimpleBlobDetector_Params() # Change thresholds params.minThreshold = 10; params.maxThreshold = 200; # Filter by Area params.filterByArea = True params.minArea = 1500 # Filter by Circularity params.filterByCircularity = True params.minCircularity = 0.1 # Filter by Convexity params.filterByConvexity = True params.minConvexity = 0.87 # Filter by Inertia params.filterByInertia = True params.minInertiaRatio = 0.01 # Create a detector with the parameters ver = (cv2.__version__).split('.') if int(ver[0]) < 3 : detector = cv2.SimpleBlobDetector(params) else : detector = cv2.SimpleBlobDetector_create(params) # Detect blobs keypoints = detector.detect(im) # Draw detected blobs as red circles. # cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS ensures the size of the circle corresponds to the size of blob im_with_keypoints = cv2.drawKeypoints(im, keypoints, np.array([]), (0,0,255), cv2.DRAW_MATCHES_FLAGS_DRAW_RICH_KEYPOINTS) # Show keypoints cv2.imshow("Keypoints", im_with_keypoints) # wait for key entry of ESC or 'q' to exit while True: k = cv2.waitKey(20) & 0xFF if k == 27 or k == ord('q'): break # clean up cv2.destroyAllWindows() ###Output _____no_output_____

nb/01_data-acquisition.ipynb

###Markdown Data aquisitionDownload data from https://coinmarketcap.com/ and store it into a CSV. ###Code # import needed modules # standard modules import os import sys import asyncio import datetime import re import json import codecs import io import concurrent.futures import csv from pprint import pprint # pypy modules import requests import lxml.html ###Output _____no_output_____ ###Markdown Constants ###Code # main url of coinmarketcap COINMARKETCAP_URL = "https://coinmarketcap.com" # url to download the currencies (coins/tokens) CURRENCY_URL = COINMARKETCAP_URL + "/{}/views/all" # url to get historical data per coin SLUG_URL = COINMARKETCAP_URL + "/currencies/{}/historical-data/?start={}&end={}" # directory of this projects root, jupyter must be started accordingly ROOT_DIR = os.path.abspath(os.path.join(os.getcwd(), "..")) # directory for the cache CACHE_DIR = os.path.join(ROOT_DIR, "cache") # resulting csv file holding **all** data DATA_CSV = os.path.join(ROOT_DIR, "coinmarketcap.csv") ###Output _____no_output_____ ###Markdown Functions from third-party modules Parse the coin/token list returned as HTML codeSource: https://github.com/prouast/coinmarketcap-scraper ###Code def parseCoinTokenList(html, type): """Parse the information returned by requestList for view 'all'.""" data = [] docRoot = lxml.html.fromstring(html) rows = docRoot.cssselect( "table#{0}-all > tbody > tr".format(type)) for row in rows: datum = {} fields = row.cssselect("td") # Name and slug nameField = fields[1].cssselect("a")[0] datum['name'] = nameField.text_content().strip() datum['slug'] = nameField.attrib['href'].replace( '/currencies/', '').replace('/', '').strip() # Symbol datum['symbol'] = fields[2].text_content().strip() # Explorer link supplyFieldPossible = fields[5].cssselect("a") if len(supplyFieldPossible) > 0: datum['explorer_link'] = supplyFieldPossible[0].attrib['href'] else: datum['explorer_link'] = '' data.append(datum) return data ###Output _____no_output_____ ###Markdown Parse the historical dataSource: https://github.com/jhogan4288/coinmarketcap-history ###Code def parseHistoricalData(html): """ Extract the price history from the HTML. The CoinMarketCap historical data page has just one HTML table. This table contains the data we want. It's got one header row with the column names. We need to derive the "average" price for the provided data. """ head = re.search(r'<thead>(.*)</thead>', html, re.DOTALL).group(1) header = re.findall(r'<th .*>([\w ]+)</th>', head) body = re.search(r'<tbody>(.*)</tbody>', html, re.DOTALL).group(1) raw_rows = re.findall(r'<tr[^>]*>' + r'\s*<td[^>]*>([^<]+)</td>'*7 + r'\s*</tr>', body) # strip commas rows = [] for row in raw_rows: row = [ re.sub(",", "", field) for field in row ] row = [ re.sub("-", "0", field) for field in row ] # convert date row[0]= datetime.datetime.strptime(row[0], "%b %d %Y").strftime("%Y%m%d") rows.append(row) return header, rows ###Output _____no_output_____ ###Markdown Helper functions ###Code # convert between datetime object and string representation "YYYYMMDD" string2datetime = lambda s: datetime.datetime.strptime(s, "%Y%m%d") datetime2string = lambda dt: dt.strftime("%Y%m%d") # create directory if it does not exist def mkdir(path): if not os.path.exists(path): os.makedirs(path) ###Output _____no_output_____ ###Markdown Next, a cache is introduced. Data downloaded from *coinmarketcap.com* are stored in this cache.With the cache it is not needed to download every time all historical data. ###Code # load cached data def loadCache(path): path = os.path.abspath(path) try: with codecs.open(path, "r", encoding="UTF8") as fp: return fp.read() except OSError: pass return "" # save cached data def saveCache(path, content): path = os.path.abspath(path) mkdir(os.path.dirname(path)) with codecs.open(path, "w", encoding="UTF8") as fp: fp.write(content) ###Output _____no_output_____ ###Markdown Provide a `main` method for asyncio. This function downloads the *urls* parallel and stores the *responses* for further processing. ###Code async def main(urls, responses): with concurrent.futures.ThreadPoolExecutor(max_workers=20) as executor: loop = asyncio.get_event_loop() futures = [ loop.run_in_executor( None, requests.get, url, ) for url in urls ] for response in await asyncio.gather(*futures): responses.append(response) ###Output _____no_output_____ ###Markdown Download function for coins/tokens ###Code # use the cache, encode currency data with json def decodeJson(rawData): try: return json.loads(rawData) except json.decoder.JSONDecodeError: pass return [] def encodeJson(pythonDict): return json.dumps(pythonDict, indent=4) # download coins and tokens from the cache def getCoinsAndTokens(forceUpdate=False): # forceUpdate: do not use the cache # cache path for coins cacheCoins = os.path.join(CACHE_DIR, "coins.json") # cache path for tokens cacheTokens = os.path.join(CACHE_DIR, "tokens.json") coins, tokens = [], [] if not forceUpdate: # load coins and tokens from the cache coins = decodeJson(loadCache(cacheCoins)) tokens = decodeJson(loadCache(cacheTokens)) # early return, coins/tokens loaded from the cache if coins and tokens: print("Cached: Coins: {}, Tokens: {}".format(len(coins), len(tokens))) return coins, tokens # load coins/tokens from the web # initalize asyncio loop = asyncio.get_event_loop() # get urls to be downloaded urls = [CURRENCY_URL.format(type) for type in ["coins", "tokens"]] responses = [] # download urls in parallel loop.run_until_complete(main(urls, responses)) # parse the responses coins = parseCoinTokenList(responses[0].content, "currencies") tokens = parseCoinTokenList(responses[1].content, "assets") # update cache saveCache(cacheCoins, encodeJson(coins)) saveCache(cacheTokens, encodeJson(tokens)) print("Coins: {}, Tokens: {}".format(len(coins), len(tokens))) return coins, tokens ###Output _____no_output_____ ###Markdown Download function for historical data ###Code # construct/generate the currency url based on the slug # start/end may be provided, otherwise, the whole history is downloaded def genCurrencySlugUrl(slug, start=None, end=None): start = start or string2datetime("20100101") end = end or datetime.datetime.utcnow() + datetime.timedelta(days=1) return SLUG_URL.format(slug, datetime2string(start), datetime2string(end)) # get the cache path for a given slug def getSlugCache(slug): return os.path.join(CACHE_DIR, "{}.csv".format(slug)) # encode historical data with csv def encodeCsv(data): fp = io.StringIO() writer = csv.writer(fp) writer.writerows(data) return fp.getvalue() def decodeCsv(raw): reader = csv.reader(raw.splitlines()) return list(reader) # only keep the date part of the datetime object striptime = lambda dt: datetime.datetime.combine(dt.date(), datetime.time()) # parse response for a slug and save the data to the cache def parseResponseSaveCache(slug, response): # parse historical data _, rawData = parseHistoricalData(response.content.decode("UTF8")) # get the cache file path = getSlugCache(slug) # load the cache rows = decodeCsv(loadCache(path)) # append new date rows.extend(rawData) # sort by date rows = sorted(rows, key=lambda r: int(r[0])) # update the cache saveCache(path, encodeCsv(rows)) # download **all** historical data of **all** slugs # use a cache to make it faster on successive runs # the function returns the number of updated histories def getHistories(slugs): # build requests requests = [] # keep track which request belongs to which slug slugRequestMap = {} # current utc time, historical data are update on UTC 00:00:00 utcnow = striptime(datetime.datetime.utcnow()) # for all slugs, prepare the url for slug in slugs: path = getSlugCache(slug) dtCache = None if os.path.exists(path): # get the timestamp of the cached file of the slug st = os.stat(path) dtCache = datetime.datetime.utcfromtimestamp(st.st_mtime) dtCache = striptime(dtCache) # load the cached file rows = decodeCsv(loadCache(path)) # find the date of the next entry start = None if rows: # get latest date start = string2datetime(rows[-1][0]) # add one day start += datetime.timedelta(days=1) if start: # if start lies in the future, skip if start >= utcnow: continue # if the cache date current, skip if dtCache and dtCache >= utcnow: continue # build the url for the slug url = genCurrencySlugUrl(slug, start) # append to requests requests.append(url) # add to inverse mapping slugRequestMap[url] = slug # nothing to download, return if not slugRequestMap: return 0 # prepare asyncio loop = asyncio.get_event_loop() responses = [] while requests: print("\rRequest to process: {}{}".format(len(requests), " "*20), flush=True, end="") # download all requests loop.run_until_complete(main(requests, responses)) # check responses, try again if it failed requests = [] for r in responses: # remove responses responses.remove(r) if r.ok: parseResponseSaveCache(slugRequestMap[r.url], r) else: # print("Failed: {}".format(url)) pass responses = [] print("") # add newline feed ###Output _____no_output_____ ###Markdown Function to build the final CSV file holding all currency dataThis function reads all cached coin/token data and merges it into a single *csv* file. ###Code # merge all cached csv into a single csv def buildAllCurrenciesCsv(allCurrencies): # count rows rowCnt = 0 with codecs.open(DATA_CSV, "w", encoding="UTF8") as fp: writer = csv.writer(fp) writer.writerow([ "date", "slug", "name", "open", "high", "low", "close", "volume", "marketcap"]) # for each currency append to the data file # and insert *slug* and *name* as column for currency in allCurrencies: slug = currency["slug"] name = currency["name"] path = getSlugCache(slug) rows = decodeCsv(loadCache(path)) print("\r{}/{}{}".format(slug, len(rows), " "*20), end="", flush=True) for row in rows: writer.writerow([row[0]] + [slug, name] + row[1:]) rowCnt += 1 print("\rCurrencies: {}, rows: {}".format(len(allCurrencies), rowCnt)) print("CACHE: {}".format(CACHE_DIR)) print("DATA: {}".format(DATA_CSV)) # download coins and tokens coins, tokens = getCoinsAndTokens(forceUpdate=True) allCurrencies = coins + tokens # get the slug name from the dicts slugs = [x["slug"] for x in allCurrencies] # download historical data getHistories(slugs) # always build CSV buildAllCurrenciesCsv(allCurrencies) ###Output CACHE: /home/dahuebi/PML/cas-pml-prj/cache DATA: /home/dahuebi/PML/cas-pml-prj/coinmarketcap.csv Coins: 917, Tokens: 677 Request to process: 1594 Currencies: 1594, rows: 750954

labs/07_analisis_supervisado_regresion/laboratorio_07.ipynb

###Markdown MAT281 - Laboratorios N°01 Objetivos del laboratorio* Reforzar conceptos básicos de regresión lineal. Contenidos* [Problema 01](p1) I.- Problema 01 El **cuarteto de Anscombe** comprende cuatro conjuntos de datos que tienen las mismas propiedades estadísticas, pero que evidentemente son distintas al inspeccionar sus gráficos respectivos.Cada conjunto consiste de once puntos (x, y) y fueron construidos por el estadístico F. J. Anscombe. El cuarteto es una demostración de la importancia de mirar gráficamente un conjunto de datos antes de analizarlos. ###Code import os import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns %matplotlib inline sns.set_palette("deep", desat=.6) sns.set(rc={'figure.figsize':(11.7,8.27)}) # cargar datos df = pd.read_csv(os.path.join("data","anscombe.csv"), sep=",") df.head() ###Output _____no_output_____ ###Markdown Basado en la información presentada responda las siguientes preguntas:1. Gráfique mediante un gráfico tipo **scatter** cada grupo. A simple vista, ¿ los grupos son muy distintos entre si?.2. Realice un resumen de las medidas estadísticas más significativas ocuapando el comando **describe** para cada grupo. Interprete.3. Realice un ajuste lineal para cada grupo. Además, grafique los resultados de la regresión lineal para cada grupo. Interprete.4. Calcule los resultados de las métricas para cada grupo. Interprete.5. Es claro que el ajuste lineal para algunos grupos no es el correcto. Existen varias formas de solucionar este problema (eliminar outliers, otros modelos, etc.). Identifique una estrategia para que el modelo de regresión lineal ajuste de mejor manera e implemente otros modelos en los casos que encuentre necesario. 1. Gráfique mediante un gráfico tipo scatter cada grupo. A simple vista, ¿Los grupos son muy distintos entre si? ###Code fig = plt.figure(figsize=(12, 8)) #esta es la ventana sobre donde se va a plottear plt.subplot(2,2,1) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_1']) plt.xlabel('$x_1$') plt.ylabel('$y_1$') plt.subplot(2,2,2) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_2']) plt.xlabel('$x_2$') plt.ylabel('$y_2$') plt.subplot(2,2,3) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_3']) plt.xlabel('$x_3$') plt.ylabel('$y_3$') plt.subplot(2,2,4) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_4']) plt.xlabel('$x_4$') plt.ylabel('$y_4$') plt.show() ###Output _____no_output_____ ###Markdown 2. Realice un resumen de las medidas estadísticas más significativas ocuapando el comando describe para cada grupo. Interprete. ###Code df.groupby(['grupo']).describe() ###Output _____no_output_____ ###Markdown Se ve que en principio, los estadísticos son similares, la media y la desviación estandar se acercan bastante. Sin embargo, se ve en los gráficos que no son muy parecidos, tal vez el grupo 1 y el 3 se parecen, pero los otros 2 no se acercan a lo que podría ser un modelo lineal, se van a ver casi igual, pero los R^2 cambiarán bastante dependiendo del grupo. El 4to podría tomarse como un x=8 con un outlayer, y el 2do como una suerte de función polinómica. 3. Realice un ajuste lineal para cada grupo. Además, grafique los resultados de la regresión lineal para cada grupo. Interprete. ###Code #Se importan las librerías a utilizar de modelos lineales from sklearn.linear_model import LinearRegression from sklearn.model_selection import train_test_split #Se crean los 4 modelos con linear regression: #Modelo 1: model_rl1 = LinearRegression() x1 = df[df['grupo'] == 'Grupo_1'][['x']] y1 = df[df['grupo'] == 'Grupo_1']['y'] X1_train, X1_test, y1_train, y1_test = train_test_split(x1, y1, test_size=0.33, random_state=42) model_rl1.fit(X1_train,y1_train) #Modelo 2: model_rl2 = LinearRegression() x2 = df[df['grupo'] == 'Grupo_2'][['x']] y2 = df[df['grupo'] == 'Grupo_2']['y'] X2_train, X2_test, y2_train, y2_test = train_test_split(x2, y2, test_size=0.33, random_state=42) model_rl2.fit(X2_train,y2_train) #Modelo 3: model_rl3 = LinearRegression() x3 = df[df['grupo'] == 'Grupo_3'][['x']] y3 = df[df['grupo'] == 'Grupo_3']['y'] X3_train, X3_test, y3_train, y3_test = train_test_split(x3, y3, test_size=0.33, random_state=42) model_rl3.fit(X3_train,y3_train) #Modelo 4: model_rl4 = LinearRegression() x4 = df[df['grupo'] == 'Grupo_4'][['x']] y4 = df[df['grupo'] == 'Grupo_4']['y'] X4_train, X4_test, y4_train, y4_test = train_test_split(x4, y4, test_size=0.33, random_state=42) model_rl4.fit(X4_train,y4_train) # Lista de coeficientes beta para cada modelo: beta_1_0 = round(model_rl1.intercept_,4) beta_1_1 = round(model_rl1.coef_[0],4) beta_2_0 = round(model_rl2.intercept_,4) beta_2_1 = round(model_rl2.coef_[0],4) beta_3_0 = round(model_rl3.intercept_,4) beta_3_1 = round(model_rl3.coef_[0],4) beta_4_0 = round(model_rl4.intercept_,4) beta_4_1 = round(model_rl4.coef_[0],4) #Se definen los arreglos para graficar: x1_range = np.arange(2,21,1) y1_range=[beta_1_0 + beta_1_1*n for n in x1_range] y2_range=[beta_2_0 + beta_2_1*n for n in x1_range] y3_range=[beta_3_0 + beta_3_1*n for n in x1_range] y4_range=[beta_4_0 + beta_4_1*n for n in x1_range] #Aqui los dataframes: df_plot1 = pd.DataFrame({'x':x1_range, 'y':y1_range}) df_plot2 = pd.DataFrame({'x':x1_range, 'y':y2_range}) df_plot3 = pd.DataFrame({'x':x1_range, 'y':y3_range}) df_plot4 = pd.DataFrame({'x':x1_range, 'y':y4_range}) fig = plt.figure(figsize=(12, 8)) #Esta es la ventana, tal como antes #Grafico 1: plt.subplot(2,2,1) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_1']) sns.lineplot(x='x', y='y', data=df_plot1,color="red") plt.xlabel('$x_1$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_1$') #Grafico 2: plt.subplot(2,2,2) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_2']) sns.lineplot(x='x', y='y', data=df_plot2,color="red") plt.xlabel('$x_2$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_2$') #Grafico 3: plt.subplot(2,2,3) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_3']) sns.lineplot(x='x', y='y', data=df_plot3,color="red") plt.xlabel('$x_3$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_3$') #Grafico 4: plt.subplot(2,2,4) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_4']) sns.lineplot(x='x', y='y', data=df_plot4,color="red") plt.xlabel('$x_4$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_4$') plt.show() ###Output _____no_output_____ ###Markdown Pasó la hipótesis que se dio en el item 2, las regresiones son similares, pero claramente no se ajustan bien al 2do y al 4to.Se ve también una pendiente bastante mala en el 3ro por el outlayer. 4. Calcule los resultados de las métricas para cada grupo. Interprete. ###Code from metrics_regression import * from sklearn.metrics import r2_score #Metricas del grupo 1: df_temp = pd.DataFrame({ 'y':y1_test, 'yhat': model_rl1.predict(X1_test) }) df_metrics= summary_metrics(df_temp) #Se crea el dataframe de metricas ahora solo con el grupo 1 df_metrics['r2'] = round(r2_score(y1_test, model_rl1.predict(X1_test)),4) #Metricas del grupo 2: df_temp = pd.DataFrame({ 'y':y2_test, 'yhat': model_rl2.predict(X2_test) }) df_metrics_temp = summary_metrics(df_temp) df_metrics_temp['r2'] = round(r2_score(y2_test, model_rl2.predict(X2_test)),4) df_metrics=pd.concat([df_metrics,df_metrics_temp]) #Se agrega el dataframe de metricas del grupo 2 al ya existente #Metricas del grupo 3: df_temp = pd.DataFrame({ 'y':y3_test, 'yhat': model_rl3.predict(X3_test) }) df_metrics_temp = summary_metrics(df_temp) df_metrics_temp['r2'] = round(r2_score(y3_test, model_rl3.predict(X3_test)),4) df_metrics=pd.concat([df_metrics,df_metrics_temp]) #Se agrega el dataframe de metricas del grupo 3 al ya existente #Metricas del grupo 4: df_temp = pd.DataFrame({ 'y':y4_test, 'yhat': model_rl4.predict(X4_test) }) df_metrics_temp = summary_metrics(df_temp) df_metrics_temp['r2'] = round(r2_score(y4_test, model_rl4.predict(X4_test)),4) df_metrics=pd.concat([df_metrics,df_metrics_temp]) #Se agrega el dataframe de metricas del grupo 4 al ya existente grupos = pd.Series(['Grupo_1','Grupo_2','Grupo_3', 'Grupo_4']) #Se cambia el indice para mostrar cada grupo df_metrics.set_index(keys=grupos) df_metrics ###Output _____no_output_____ ###Markdown MAT281 - Laboratorios N°01 Objetivos del laboratorio* Reforzar conceptos básicos de regresión lineal. Contenidos* [Problema 01](p1) I.- Problema 01 El **cuarteto de Anscombe** comprende cuatro conjuntos de datos que tienen las mismas propiedades estadísticas, pero que evidentemente son distintas al inspeccionar sus gráficos respectivos.Cada conjunto consiste de once puntos (x, y) y fueron construidos por el estadístico F. J. Anscombe. El cuarteto es una demostración de la importancia de mirar gráficamente un conjunto de datos antes de analizarlos. ###Code import os import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns %matplotlib inline sns.set_palette("deep", desat=.6) sns.set(rc={'figure.figsize':(11.7,8.27)}) # cargar datos df = pd.read_csv(os.path.join("data","anscombe.csv"), sep=",") df.head() ###Output _____no_output_____ ###Markdown Basado en la información presentada responda las siguientes preguntas:1. Gráfique mediante un gráfico tipo **scatter** cada grupo. A simple vista, ¿ los grupos son muy distintos entre si?.2. Realice un resumen de las medidas estadísticas más significativas ocuapando el comando **describe** para cada grupo. Interprete.3. Realice un ajuste lineal para cada grupo. Además, grafique los resultados de la regresión lineal para cada grupo. Interprete.4. Calcule los resultados de las métricas para cada grupo. Interprete.5. Es claro que el ajuste lineal para algunos grupos no es el correcto. Existen varias formas de solucionar este problema (eliminar outliers, otros modelos, etc.). Identifique una estrategia para que el modelo de regresión lineal ajuste de mejor manera e implemente otros modelos en los casos que encuentre necesario. 1. Gráfique mediante un gráfico tipo **scatter** cada grupo. A simple vista, ¿ los grupos son muy distintos entre si?. ###Code # tamano del grafico fig = plt.figure(figsize=(12, 8)) # ventana plt.subplot(2,2,1) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_1']) plt.xlabel('$x_1$') plt.ylabel('$y_1$') plt.subplot(2,2,2) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_2']) plt.xlabel('$x_2$') plt.ylabel('$y_2$') plt.subplot(2,2,3) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_3']) plt.xlabel('$x_3$') plt.ylabel('$y_3$') plt.subplot(2,2,4) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_4']) plt.xlabel('$x_4$') plt.ylabel('$y_4$') plt.show() ###Output _____no_output_____ ###Markdown Se observa de los graficos que las distribuciones de los datos de cada grupo son notoriamente diferentes 2. Realice un resumen de las medidas estadísticas más significativas ocuapando el comando **describe** para cada grupo. Interprete. ###Code df.groupby(['grupo']).describe() ###Output _____no_output_____ ###Markdown Notamos que aunque los graficos eran distintos, las estadisticas de los 4 grupos son sumamente parecidas, lo que hará que los ajustes lineales sean muy parecidos para cada grupo. Aun así, los valores de datos minimos, maximos y como se distribuyen los datos son claramente distintos. 3. Realice un ajuste lineal para cada grupo. Además, grafique los resultados de la regresión lineal para cada grupo. Interprete. ###Code # importando el modelo de regresión lineal from sklearn.linear_model import LinearRegression from sklearn.model_selection import train_test_split #Crecion de 4 modelos, uno para cada grupo: #Modelo 1: model_rl1 = LinearRegression() # Creando el modelo. x1 = df[df['grupo'] == 'Grupo_1'][['x']] y1 = df[df['grupo'] == 'Grupo_1']['y'] X1_train, X1_test, y1_train, y1_test = train_test_split(x1, y1, test_size=0.33, random_state=42) model_rl1.fit(X1_train,y1_train) #Modelo 2: model_rl2 = LinearRegression() # Creando el modelo. x2 = df[df['grupo'] == 'Grupo_2'][['x']] y2 = df[df['grupo'] == 'Grupo_2']['y'] X2_train, X2_test, y2_train, y2_test = train_test_split(x2, y2, test_size=0.33, random_state=42) model_rl2.fit(X2_train,y2_train) #Modelo 3: model_rl3 = LinearRegression() # Creando el modelo. x3 = df[df['grupo'] == 'Grupo_3'][['x']] y3 = df[df['grupo'] == 'Grupo_3']['y'] X3_train, X3_test, y3_train, y3_test = train_test_split(x3, y3, test_size=0.33, random_state=42) model_rl3.fit(X3_train,y3_train) #Modelo 4: model_rl4 = LinearRegression() # Creando el modelo. x4 = df[df['grupo'] == 'Grupo_4'][['x']] y4 = df[df['grupo'] == 'Grupo_4']['y'] X4_train, X4_test, y4_train, y4_test = train_test_split(x4, y4, test_size=0.33, random_state=42) model_rl4.fit(X4_train,y4_train) # Lista de coeficientes beta para cada modelo: beta_1_0 = round(model_rl1.intercept_,4) beta_1_1 = round(model_rl1.coef_[0],4) beta_2_0 = round(model_rl2.intercept_,4) beta_2_1 = round(model_rl2.coef_[0],4) beta_3_0 = round(model_rl3.intercept_,4) beta_3_1 = round(model_rl3.coef_[0],4) beta_4_0 = round(model_rl4.intercept_,4) beta_4_1 = round(model_rl4.coef_[0],4) #Defincion de arreglos para fraficar cada ajuste: x1_range = np.arange(2,21,1) y1_range=[beta_1_0 + beta_1_1*n for n in x1_range] y2_range=[beta_2_0 + beta_2_1*n for n in x1_range] y3_range=[beta_3_0 + beta_3_1*n for n in x1_range] y4_range=[beta_4_0 + beta_4_1*n for n in x1_range] #Definición de dataFrames para graficar cada ajuste: df_plot1 = pd.DataFrame({'x':x1_range, 'y':y1_range}) df_plot2 = pd.DataFrame({'x':x1_range, 'y':y2_range}) df_plot3 = pd.DataFrame({'x':x1_range, 'y':y3_range}) df_plot4 = pd.DataFrame({'x':x1_range, 'y':y4_range}) #Se grafica: fig = plt.figure(figsize=(12, 8)) # ventana #Grafico 1: plt.subplot(2,2,1) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_1']) sns.lineplot(x='x', y='y', data=df_plot1,color="red") plt.xlabel('$x_1$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_1$') #Grafico 2: plt.subplot(2,2,2) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_2']) sns.lineplot(x='x', y='y', data=df_plot2,color="red") plt.xlabel('$x_2$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_2$') #Grafico 3: plt.subplot(2,2,3) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_3']) sns.lineplot(x='x', y='y', data=df_plot3,color="red") plt.xlabel('$x_3$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_3$') #Grafico 4: plt.subplot(2,2,4) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_4']) sns.lineplot(x='x', y='y', data=df_plot4,color="red") plt.xlabel('$x_4$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_4$') plt.show() ###Output _____no_output_____ ###Markdown Se observa que aunque la distribucion de los datos de cada grupo es claramente distinta, los ajustes lineales de los 4 grupos resultaron practicamente iguales. 4. Calcule los resultados de las métricas para cada grupo. Interprete. ###Code from metrics_regression import * from sklearn.metrics import r2_score #Metricas del grupo 1: df_temp = pd.DataFrame({ 'y':y1_test, 'yhat': model_rl1.predict(X1_test) }) df_metrics= summary_metrics(df_temp) #Se crea el dataframe de metricas ahora solo con el grupo 1 df_metrics['r2'] = round(r2_score(y1_test, model_rl1.predict(X1_test)),4) #Metricas del grupo 2: df_temp = pd.DataFrame({ 'y':y2_test, 'yhat': model_rl2.predict(X2_test) }) df_metrics_temp = summary_metrics(df_temp) df_metrics_temp['r2'] = round(r2_score(y2_test, model_rl2.predict(X2_test)),4) df_metrics=pd.concat([df_metrics,df_metrics_temp]) #Se agrega el dataframe de metricas del grupo 2 al ya existente #Metricas del grupo 3: df_temp = pd.DataFrame({ 'y':y3_test, 'yhat': model_rl3.predict(X3_test) }) df_metrics_temp = summary_metrics(df_temp) df_metrics_temp['r2'] = round(r2_score(y3_test, model_rl3.predict(X3_test)),4) df_metrics=pd.concat([df_metrics,df_metrics_temp]) #Se agrega el dataframe de metricas del grupo 3 al ya existente #Metricas del grupo 4: df_temp = pd.DataFrame({ 'y':y4_test, 'yhat': model_rl4.predict(X4_test) }) df_metrics_temp = summary_metrics(df_temp) df_metrics_temp['r2'] = round(r2_score(y4_test, model_rl4.predict(X4_test)),4) df_metrics=pd.concat([df_metrics,df_metrics_temp]) #Se agrega el dataframe de metricas del grupo 4 al ya existente grupos = pd.Series(['Grupo_1','Grupo_2','Grupo_3', 'Grupo_4']) #Se cambia el indice para mostrar cada grupo df_metrics.set_index(keys=grupos) df_metrics ###Output _____no_output_____ ###Markdown Grupo:1 Notamos que los errores se notan normales y no muy alejados del 0. El factor $r^2$ en este caso no está muy cercano al 0. Así, en mi opinión el ajuste correspondiente al grupo 1 es correcto. Grupo:2 Notamos que los errores absolutos son mayores a los del grupo 1, aunque los porcentuales no son muy diferentes. Lo que se destaca es que el factor $r^2$ es mucho menor que el del grupo 1 y además se encuentra cercno al 0, lo que se puede interpretar como que el ajuste lineal de los datos de este grupo no está bien hecho. Grupo:3 Al igual que en 2 los errores absolutos son mayores que en 1 y los porcentuales son cercanos 0. En este caso el factor $r^2$ es aun más bajo que en 2, el ajuste está aun más mal hecho. Grupo:4 Para este grupo los errores absolutos no son muy malos al igual que los porcentuales, pero el factor $r^2$ resultó negativo, lo que indica que la regresión lineal está completamente mal hecha, el ajuste no representa para nada la distribución de los datos. 5. Es claro que el ajuste lineal para algunos grupos no es el correcto. Existen varias formas de solucionar este problema (eliminar outliers, otros modelos, etc.). Identifique una estrategia para que el modelo de regresión lineal ajuste de mejor manera e implemente otros modelos en los casos que encuentre necesario. Grupo 1: Para este grupo de datos podemos ver visualmente que el ajuste parece ser bueno. Al analizar las metricas para este grupo también se observa que el factor $r^2$ por ejemplo tiene un valor de aprox 0,7 y los errores porcentuales también no estan muy alejados del 0. Así, a mi opinión, el ajuste parece ser correcto para este grupo. Grupo 2: Observando el gráfico de este grupo se puede notar claramente que la distribución de los datos no es lineal. Por esto, propongo una regresión polinomica para aproximar los datos de mejor manera: ###Code from sklearn.preprocessing import PolynomialFeatures from sklearn.pipeline import make_pipeline degree=2 #grado del polinomio de regresion polyreg=make_pipeline(PolynomialFeatures(degree),LinearRegression()) #Creacion del modelo polyreg.fit(X2_train,y2_train) #Se usan los datos train creados en Pregunta 3 #Definiciones para graficar el ajuste X_seq = np.linspace(2,18,300).reshape(-1,1) #Se grafica: plt.figure(figsize=(8,5)) sns.scatterplot(x='x', y='y', data=df[df['grupo'] == 'Grupo_2']) plt.plot(X_seq,polyreg.predict(X_seq),color="red") plt.title("Regresión polinómica de grado "+str(degree)) plt.show() #Se presentan las nuevas metricas con el ajuste cuadrático df_temp = pd.DataFrame({ 'y':y2_test, 'yhat': polyreg.predict(X2_test) }) df_metrica2 = summary_metrics(df_temp) df_metrica2['r2'] = round(r2_score(y2_test, polyreg.predict(X2_test)),4) df_metrica2.set_index(pd.Series({'Grupo_2':'Grupo_2'})) ###Output _____no_output_____ ###Markdown Se observa que con el nuevo ajuste, las metricas resultaron perfectas, resulataba ser que la distribucion de los datos correspondia a una función cuadratica. Grupo 3: Observando el comportamiento del ajuste lineal de este grupo se puede notar que hay un outlier que hace que la pendiente del ajuste lineal se aleje de la distribución de los datos del Grupo_3. Con esto, propondgo una estrategia de eliminar el dato anómalo y hacer el ajuste con el resto de datos bien distribuidos: ###Code #Se elimina el dato anómalo: df_nuevo = df[df['grupo'] == 'Grupo_3'].drop(24) #Se crea un nuevo ajuste ahora para los datos sin el outlier: model_rl3 = LinearRegression() x3 = df_nuevo[['x']] y3 = df_nuevo['y'] X3_train, X3_test, y3_train, y3_test = train_test_split(x3, y3, test_size=0.33, random_state=42) model_rl3.fit(X3_train,y3_train) #Definición de los coef del ajuste beta_3_0 = round(model_rl3.intercept_,4) beta_3_1 = round(model_rl3.coef_[0],4) #Definciones para Graficar el ajuste: x_range = np.arange(2,21,1) y3_range=[beta_3_0 + beta_3_1*n for n in x_range] df_plot3 = pd.DataFrame({'x':x_range, 'y':y3_range}) #Grafico con el ajuste y los datos de df_nuevo: fig = plt.figure(figsize=(8, 5)) # ventana sns.scatterplot(x='x', y='y', data=df_nuevo) #Datos originales sin el outlier sns.lineplot(x='x', y='y', data=df_plot3,color="red") #Ajuste lineal plt.xlabel('$x_3$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_3$') plt.show() #Se presentan las nuevas metricas con los datos actualizados quitando el outlier df_temp = pd.DataFrame({ 'y':y3_test, 'yhat': model_rl3.predict(X3_test) }) df_metrica3= summary_metrics(df_temp) df_metrica3['r2'] = round(r2_score(y3_test, model_rl3.predict(X3_test)),4) df_metrica3.set_index(pd.Series({'Grupo_3':'Grupo_3'})) ###Output _____no_output_____ ###Markdown Se observa que al quitar el oulier, el ajuste resulta sumamente bueno visualmente y además contiene errores muy cercanos a 0 y un factor $r^2=1$. Grupo 4: Para este grupo de datos se observa en el grafico que existe una distribucion de datos muy particular, hay un outlier y todos los demás datos se encuentran concentrados en una linea vertical correspondiente a $x=8$. Así, propongo el eliminar el outlier y realizar un ajuste intercambiando los ejes (para obtener un ajuste de pendiente 0 y no $\infty$): ###Code #Definicion del dataframe sin el outlier df_nuevo4 = df[df['grupo'] == 'Grupo_4'].drop(40) #Defincion del nuevo modelo model_rl4_nuevo = LinearRegression() # Creando el modelo. x4 = df_nuevo4['x'] y4 = df_nuevo4[['y']] X4_train, X4_test, y4_train, y4_test = train_test_split(y4, x4, test_size=0.33, random_state=42) model_rl4_nuevo.fit(X4_train,y4_train) #Definición de los coef del nuevo ajuste: beta_4_0_nuevo = round(model_rl4_nuevo.intercept_,4) beta_4_1_nuevo = round(model_rl4_nuevo.coef_[0],4) #Definiciones para graficar el ajuste x_range = np.arange(4,10,1) y4_range=[beta_4_0_nuevo + beta_4_1_nuevo*n for n in x_range] df_plot4_nuevo = pd.DataFrame({'x':x_range, 'y':y4_range}) #Se grafica: plt.figure(figsize=(8,5)) sns.scatterplot(x='x', y='y', data=df_nuevo4) plt.plot(y4_range, x_range,'r') plt.xlabel('$x_4$') plt.xticks([2*x for x in range(1,10)]) plt.ylabel('$y_4$') plt.show() #Se presentan las nuevas metricas con los datos actualizados quitando el outlier df_temp = pd.DataFrame( { 'y':y4_test, 'yhat': model_rl4_nuevo.predict(X4_test) } ) df_metrica4 = summary_metrics(df_temp) df_metrica4['r2'] = round(r2_score(y4_test, model_rl4_nuevo.predict(X4_test)),4) df_metrica4.set_index(pd.Series({'Grupo_4':'Grupo_4'})) df_metrica4 ###Output _____no_output_____

LinkedIn/LinkedIn_Send_connections_from_network_to_gsheet.ipynb

###Markdown LinkedIn - Send connections from network to gsheet **Tags:** linkedin network connections naas_drivers csv automation content googlesheets **Author:** [Florent Ravenel](https://www.linkedin.com/in/florent-ravenel/) Input Import libraries ###Code from naas_drivers import linkedin, gsheet import naas import pandas as pd ###Output _____no_output_____ ###Markdown Setup LinkedIn👉 How to get your cookies ? ###Code # Lindekin cookies LI_AT = "AQEDARCNSioDe6wmAAABfqF-HR4AAAF-xYqhHlYAtSu7EZZEpFer0UZF-GLuz2DNSz4asOOyCRxPGFjenv37irMObYYgxxxxxxx" JSESSIONID = "ajax:12XXXXXXXXXXXXXXXXX" ###Output _____no_output_____ ###Markdown Setup your Google Sheet👉 Get your spreadsheet URL👉 Share your gsheet with our service account to connect : [email protected]👉 Create your sheet before sending data into it ###Code # Spreadsheet URL SPREADSHEET_URL = "https://docs.google.com/spreadsheets/d/XXXXXXXXXXXXXXXXXXXX" # Sheet name SHEET_NAME = "LK_CONNECTIONS" ###Output _____no_output_____ ###Markdown Setup Naas ###Code naas.scheduler.add(cron="0 8 * * *") #-> To delete your scheduler, please uncomment the line below and execute this cell # naas.scheduler.delete() ###Output _____no_output_____ ###Markdown Model Get connections from Google Sheet ###Code df_gsheet = gsheet.connect(SPREADSHEET_URL).get(sheet_name=SHEET_NAME) df_gsheet ###Output _____no_output_____ ###Markdown Get new connections ###Code def get_new_connections(df_gsheet, key="PROFILE_URN"): profiles = [] if len(df_gsheet) > 0: profiles = df_gsheet[key].unique() else: df = linkedin.connect(LI_AT, JSESSIONID).network.get_connections(limit=-1) return df # Get new df_new = pd.DataFrame() update = True while update: start = 0 df = linkedin.connect(LI_AT, JSESSIONID).network.get_connections(start=start, count=100, limit=100) new_profiles = df[key].unique() for i, p in enumerate(new_profiles): if p in profiles: update = False df = df[:i] break start += 100 df_new = pd.concat([df_new, df]) return df_new df_new = get_new_connections(df_gsheet, key="PROFILE_URN") df_new ###Output _____no_output_____ ###Markdown Output Send to Google Sheet ###Code gsheet.connect(SPREADSHEET_URL).send(df_new, sheet_name=SHEET_NAME, append=True) ###Output _____no_output_____ ###Markdown LinkedIn - Send connections from network to gsheet **Tags:** linkedin network connections naas_drivers csv automation content googlesheets **Author:** [Florent Ravenel](https://www.linkedin.com/in/florent-ravenel/) Input Import libraries ###Code from naas_drivers import linkedin, gsheet import naas import pandas as pd ###Output _____no_output_____ ###Markdown Setup LinkedIn👉 How to get your cookies ? ###Code # Lindekin cookies LI_AT = "AQEDARCNSioDe6wmAAABfqF-HR4AAAF-xYqhHlYAtSu7EZZEpFer0UZF-GLuz2DNSz4asOOyCRxPGFjenv37irMObYYgxxxxxxx" JSESSIONID = "ajax:12XXXXXXXXXXXXXXXXX" ###Output _____no_output_____ ###Markdown Setup your Google Sheet👉 Get your spreadsheet URL👉 Share your gsheet with our service account to connect : [email protected]👉 Create your sheet before sending data into it ###Code # Spreadsheet URL SPREADSHEET_URL = "https://docs.google.com/spreadsheets/d/XXXXXXXXXXXXXXXXXXXX" # Sheet name SHEET_NAME = "LK_CONNECTIONS" ###Output _____no_output_____ ###Markdown Setup Naas ###Code naas.scheduler.add(cron="0 8 * * *") #-> To delete your scheduler, please uncomment the line below and execute this cell # naas.scheduler.delete() ###Output _____no_output_____ ###Markdown Model Get connections from Google Sheet ###Code df_gsheet = gsheet.connect(SPREADSHEET_URL).get(sheet_name=SHEET_NAME) df_gsheet ###Output _____no_output_____ ###Markdown Get new connections ###Code def get_new_connections(df_gsheet, key="PROFILE_URN"): profiles = [] if len(df_gsheet) > 0: profiles = df_gsheet[key].unique() else: df = linkedin.connect(LI_AT, JSESSIONID).network.get_connections(limit=-1) return df # Get new df_new = pd.DataFrame() update = True while update: start = 0 df = linkedin.connect(LI_AT, JSESSIONID).network.get_connections(start=start, count=100, limit=100) new_profiles = df[key].unique() for i, p in enumerate(new_profiles): if p in profiles: update = False df = df[:i] break start += 100 df_new = pd.concat([df_new, df]) return df_new df_new = get_new_connections(df_gsheet, key="PROFILE_URN") df_new ###Output _____no_output_____ ###Markdown Output Send to Google Sheet ###Code gsheet.connect(SPREADSHEET_URL).send(df_new, sheet_name=SHEET_NAME, append=True) ###Output _____no_output_____ ###Markdown LinkedIn - Send connections from network to gsheet **Tags:** linkedin network connections naas_drivers csv automation **Author:** [Florent Ravenel](https://www.linkedin.com/in/florent-ravenel/) Input Import libraries ###Code from naas_drivers import linkedin, gsheet import naas import pandas as pd ###Output _____no_output_____ ###Markdown Setup LinkedIn👉 How to get your cookies ? ###Code # Lindekin cookies LI_AT = "AQEDARCNSioDe6wmAAABfqF-HR4AAAF-xYqhHlYAtSu7EZZEpFer0UZF-GLuz2DNSz4asOOyCRxPGFjenv37irMObYYgxxxxxxx" JSESSIONID = "ajax:12XXXXXXXXXXXXXXXXX" ###Output _____no_output_____ ###Markdown Setup your Google Sheet👉 Get your spreadsheet URL👉 Share your gsheet with our service account to connect : [email protected]👉 Create your sheet before sending data into it ###Code # Spreadsheet URL SPREADSHEET_URL = "https://docs.google.com/spreadsheets/d/XXXXXXXXXXXXXXXXXXXX" # Sheet name SHEET_NAME = "LK_CONNECTIONS" ###Output _____no_output_____ ###Markdown Setup Naas ###Code naas.scheduler.add(cron="0 8 * * *") #-> To delete your scheduler, please uncomment the line below and execute this cell # naas.scheduler.delete() ###Output _____no_output_____ ###Markdown Model Get connections from Google Sheet ###Code df_gsheet = gsheet.connect(SPREADSHEET_URL).get(sheet_name=SHEET_NAME) df_gsheet ###Output _____no_output_____ ###Markdown Get new connections ###Code def get_new_connections(df_gsheet, key="PROFILE_URN"): profiles = [] if len(df_gsheet) > 0: profiles = df_gsheet[key].unique() else: df = linkedin.connect(LI_AT, JSESSIONID).network.get_connections(limit=-1) return df # Get new df_new = pd.DataFrame() update = True while update: start = 0 df = linkedin.connect(LI_AT, JSESSIONID).network.get_connections(start=start, count=100, limit=100) new_profiles = df[key].unique() for i, p in enumerate(new_profiles): if p in profiles: update = False df = df[:i] break start += 100 df_new = pd.concat([df_new, df]) return df_new df_new = get_new_connections(df_gsheet, key="PROFILE_URN") df_new ###Output _____no_output_____ ###Markdown Output Send to Google Sheet ###Code gsheet.connect(SPREADSHEET_URL).send(df_new, sheet_name=SHEET_NAME, append=True) ###Output _____no_output_____

OneHotEncoder/OneHotEncoder.ipynb

###Markdown Preprocessing ###Code # Import our dependencies from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler, OneHotEncoder import pandas as pd import tensorflow as tf # Import and read the charity_data.csv. import pandas as pd application_df = pd.read_csv("../Resources/charity_data.csv") application_df.head() # Drop the non-beneficial ID columns, 'EIN' and 'NAME'. application_df = application_df.drop(["EIN","NAME"], axis = 1) application_df # Determine the number of unique values in each column. application_df.nunique() # Look at APPLICATION_TYPE value counts for binning value_count = application_df["APPLICATION_TYPE"].value_counts() value_count_df = value_count.to_frame() value_count_df # Choose a cutoff value and create a list of application types to be replaced # use the variable name `application_types_to_replace` application_types_to_replace = value_count_df.loc[value_count_df['APPLICATION_TYPE'] <= 500].index.tolist() # Replace in dataframe for app in application_types_to_replace: application_df['APPLICATION_TYPE'] = application_df['APPLICATION_TYPE'].replace(app,"Other") # Check to make sure binning was successful application_df['APPLICATION_TYPE'].value_counts() # Look at CLASSIFICATION value counts for binning application_df["CLASSIFICATION"].value_counts() # You may find it helpful to look at CLASSIFICATION value counts >1 application_df["CLASSIFICATION"].value_counts()[application_df["CLASSIFICATION"].value_counts()>1] # Choose a cutoff value and create a list of classifications to be replaced # use the variable name `classifications_to_replace` classifications_to_replace = application_df["CLASSIFICATION"].value_counts()[application_df["CLASSIFICATION"].value_counts()<1000].index.tolist() # Replace in dataframe for cls in classifications_to_replace: application_df['CLASSIFICATION'] = application_df['CLASSIFICATION'].replace(cls,"Other") # Check to make sure binning was successful application_df['CLASSIFICATION'].value_counts() application_df # Generate our categorical variable lists attrition_cat = application_df.dtypes[application_df.dtypes == "object"].index.tolist() # Check the number of unique values in each column application_df[attrition_cat].nunique() # Create a OneHotEncoder instance enc = OneHotEncoder(sparse=False) # Fit and transform the OneHotEncoder using the categorical variable list encode_df = pd.DataFrame(enc.fit_transform(application_df[attrition_cat])) # Add the encoded variable names to the dataframe encode_df.columns = enc.get_feature_names(attrition_cat) encode_df.head() # Merge one-hot encoded features and drop the originals application_df = application_df.merge(encode_df,left_index=True, right_index=True) application_df = application_df.drop(attrition_cat,1) application_df.head() # Split our preprocessed data into our features and target arrays y = application_df['IS_SUCCESSFUL'].values X = application_df.drop(columns='IS_SUCCESSFUL').values # Split the preprocessed data into a training and testing dataset X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=78, stratify=y) # Create a StandardScaler instances scaler = StandardScaler() # Fit the StandardScaler X_scaler = scaler.fit(X_train) # Scale the data X_train_scaled = X_scaler.transform(X_train) X_test_scaled = X_scaler.transform(X_test) ###Output _____no_output_____ ###Markdown Compile, Train and Evaluate the Model ###Code # Create a method that creates a new Sequential model with hyperparameter options def create_model(hp): nn_model = tf.keras.models.Sequential() # Allow kerastuner to decide which activation function to use in hidden layers activation = hp.Choice('activation',['relu','tanh','sigmoid']) # Allow kerastuner to decide number of neurons in first layer nn_model.add(tf.keras.layers.Dense(units=hp.Int('first_units', min_value=1, max_value=120, step=2), activation=activation, input_dim=43)) # Allow kerastuner to decide number of hidden layers and neurons in hidden layers for i in range(hp.Int('num_layers', 1, 15)): nn_model.add(tf.keras.layers.Dense(units=hp.Int('units_' + str(i), min_value=1, max_value=120, step=2), activation=activation)) nn_model.add(tf.keras.layers.Dense(units=1, activation="sigmoid")) # Compile the model nn_model.compile(loss="binary_crossentropy", optimizer='adam', metrics=["accuracy"]) return nn_model # Import the kerastuner library import keras_tuner as kt tuner = kt.Hyperband( create_model, objective="val_accuracy", max_epochs=50, hyperband_iterations=2) # Run the kerastuner search for best hyperparameters tuner.search(X_train_scaled,y_train,epochs=20,validation_data=(X_test_scaled,y_test)) # Get best model hyperparameters best_hyper = tuner.get_best_hyperparameters(1)[0] best_hyper.values # Evaluate best model against full test data best_model = tuner.get_best_models(1)[0] model_loss, model_accuracy = best_model.evaluate(X_test_scaled,y_test,verbose=2) print(f"Loss: {model_loss}, Accuracy: {model_accuracy}") # Export our model to HDF5 file best_model.save('AlphabetSoupCharity.h5') ###Output _____no_output_____

scripts/examples/Make a calcsfh input parameter file.ipynb

###Markdown Make CALCSFH input parameter fileThis notebook will go through how to use calcsfh_input_parameter to programatically write calcsfh input parameter files. ###Code from match.scripts.fileio import calcsfh_input_parameter ###Output /Users/rosenfield/anaconda/lib/python2.7/site-packages/IPython/kernel/__init__.py:13: ShimWarning: The `IPython.kernel` package has been deprecated. You should import from ipykernel or jupyter_client instead. "You should import from ipykernel or jupyter_client instead.", ShimWarning) ###Markdown The default dictionary for calcsfh is accessible via fileio.calcsfh_dict() and is stored in templates/calcsfh_input_parameter.jsonTo use all the default values (it won't actually work when running calcsfh (Notice the CMD limits are all -99,99 and the filters as stupidly called filter1, filter2.): ###Code print(calcsfh_input_parameter()) ###Output 1.35 10.000 10.000 0.050 0.000 0.000 0.050 -2.30 0.10 0.10 0.35 0.000001 0.000001 1 0.10 0.05 5 -99.00 99.00 filter1,filter2 -99.00 99.00 filter1 -99.00 99.00 filter2 0 0 71 6.60 6.65 6.65 6.70 6.70 6.75 6.75 6.80 6.80 6.85 6.85 6.90 6.90 6.95 6.95 7.00 7.00 7.05 7.05 7.10 7.10 7.15 7.15 7.20 7.20 7.25 7.25 7.30 7.30 7.35 7.35 7.40 7.40 7.45 7.45 7.50 7.50 7.55 7.55 7.60 7.60 7.65 7.65 7.70 7.70 7.75 7.75 7.80 7.80 7.85 7.85 7.90 7.90 7.95 7.95 8.00 8.00 8.05 8.05 8.10 8.10 8.15 8.15 8.20 8.20 8.25 8.25 8.30 8.30 8.35 8.35 8.40 8.40 8.45 8.45 8.50 8.50 8.55 8.55 8.60 8.60 8.65 8.65 8.70 8.70 8.75 8.75 8.80 8.80 8.85 8.85 8.90 8.90 8.95 8.95 9.00 9.00 9.05 9.05 9.10 9.10 9.15 9.15 9.20 9.20 9.25 9.25 9.30 9.30 9.35 9.35 9.40 9.40 9.45 9.45 9.50 9.50 9.55 9.55 9.60 9.60 9.65 9.65 9.70 9.70 9.75 9.75 9.80 9.80 9.85 9.85 9.90 9.90 9.95 9.95 10.00 10.00 10.05 10.05 10.10 10.10 10.15 ###Markdown If you will be running calcsfh with -zinc, -kroupa, or -chabrier, the input file format changes (line 2 for zinc, line 1 for IMF). Access the options as arguments. ###Code print(calcsfh_input_parameter(zinc=True)) print(calcsfh_input_parameter(zinc=True, power_law_imf=False)) ###Output 10.000 10.000 0.050 0.000 0.000 0.050 -2.30 0.10 0.10 -2.30 -1.00 -0.10 -1.30 0.35 0.000001 0.000001 1 0.10 0.05 5 -99.00 99.00 filter1,filter2 -99.00 99.00 filter1 -99.00 99.00 filter2 0 0 71 6.60 6.65 6.65 6.70 6.70 6.75 6.75 6.80 6.80 6.85 6.85 6.90 6.90 6.95 6.95 7.00 7.00 7.05 7.05 7.10 7.10 7.15 7.15 7.20 7.20 7.25 7.25 7.30 7.30 7.35 7.35 7.40 7.40 7.45 7.45 7.50 7.50 7.55 7.55 7.60 7.60 7.65 7.65 7.70 7.70 7.75 7.75 7.80 7.80 7.85 7.85 7.90 7.90 7.95 7.95 8.00 8.00 8.05 8.05 8.10 8.10 8.15 8.15 8.20 8.20 8.25 8.25 8.30 8.30 8.35 8.35 8.40 8.40 8.45 8.45 8.50 8.50 8.55 8.55 8.60 8.60 8.65 8.65 8.70 8.70 8.75 8.75 8.80 8.80 8.85 8.85 8.90 8.90 8.95 8.95 9.00 9.00 9.05 9.05 9.10 9.10 9.15 9.15 9.20 9.20 9.25 9.25 9.30 9.30 9.35 9.35 9.40 9.40 9.45 9.45 9.50 9.50 9.55 9.55 9.60 9.60 9.65 9.65 9.70 9.70 9.75 9.75 9.80 9.80 9.85 9.85 9.90 9.90 9.95 9.95 10.00 10.00 10.05 10.05 10.10 10.10 10.15 ###Markdown To adjust the time bins, pass a dictionary as params. * set ntbins, the number of time bins, to calculate the time bin sizes using tmin and tmax.* set tbins, the time bin size, to calculate the number of time bins using tmin and tmax. ###Code params = {'ntbins': 5} print(calcsfh_input_parameter(**params)) params = {'tmax': 9.5, 'tmin': 7.5, 'tbin': 0.1} print(calcsfh_input_parameter(**params)) ###Output 1.35 10.000 10.000 0.050 0.000 0.000 0.050 -2.30 0.10 0.10 0.35 0.000001 0.000001 1 0.10 0.05 5 -99.00 99.00 filter1,filter2 -99.00 99.00 filter1 -99.00 99.00 filter2 0 0 20 7.50 7.60 7.60 7.70 7.70 7.80 7.80 7.90 7.90 8.00 8.00 8.10 8.10 8.20 8.20 8.30 8.30 8.40 8.40 8.50 8.50 8.60 8.60 8.70 8.70 8.80 8.80 8.90 8.90 9.00 9.00 9.10 9.10 9.20 9.20 9.30 9.30 9.40 9.40 9.50 ###Markdown Set the CMD limits using the same nomenclature as found in the MATCH README file. You could also add a background file. ###Code params = {'tmax': 9.5, 'tmin': 7.5, 'tbin': 0.1, 'vmin': 16, 'vmax': 24, 'imin': 18, 'imax': 27, 'v-imin': -0.5, 'v-imax': 2.5, 'v': 'F555W', 'i': 'F814W', 'bg_file': 'bg.dat'} print(calcsfh_input_parameter(**params)) ###Output 1.35 10.000 10.000 0.050 0.000 0.000 0.050 -2.30 0.10 0.10 0.35 0.000001 0.000001 1 0.10 0.05 5 -0.50 2.50 F555W,F814W 16.00 24.00 F555W 18.00 24.00 F814W 0 0 20 7.50 7.60 7.60 7.70 7.70 7.80 7.80 7.90 7.90 8.00 8.00 8.10 8.10 8.20 8.20 8.30 8.30 8.40 8.40 8.50 8.50 8.60 8.60 8.70 8.70 8.80 8.80 8.90 8.90 9.00 9.00 9.10 9.10 9.20 9.20 9.30 9.30 9.40 9.40 9.50 -1 1 -1bg.dat ###Markdown To use this in your own script, do something like: ###Code with open('match.param', 'w') as outputfile: outputfile.write(calcsfh_input_parameter(**params)) ! cat match.param ###Output 1.35 10.000 10.000 0.050 0.000 0.000 0.050 -2.30 0.10 0.10 0.35 0.000001 0.000001 1 0.10 0.05 5 -0.50 2.50 F555W,F814W 16.00 24.00 F555W 18.00 24.00 F814W 0 0 20 7.50 7.60 7.60 7.70 7.70 7.80 7.80 7.90 7.90 8.00 8.00 8.10 8.10 8.20 8.20 8.30 8.30 8.40 8.40 8.50 8.50 8.60 8.60 8.70 8.70 8.80 8.80 8.90 8.90 9.00 9.00 9.10 9.10 9.20 9.20 9.30 9.30 9.40 9.40 9.50 -1 1 -1bg.dat ###Markdown Using different values of tbinSet tbreak to be the value where a different tbin value should be used. tbin should be an array lenth tbreak + 1 * Have 6.6-9.0 at dt=0.1 and 9.0-10.15 at dt=0.05 ###Code params['tmin'] = 6.6 params['tmax'] = 10.15 params['tbreak'] = [9.0] params['tbin'] = [0.1, 0.05] print(calcsfh_input_parameter(**params)) ###Output 1.35 10.000 10.000 0.050 0.000 0.000 0.050 -2.30 0.10 0.10 0.35 0.000001 0.000001 1 0.10 0.05 5 -0.50 2.50 F555W,F814W 16.00 24.00 F555W 18.00 24.00 F814W 0 0 49 6.60 6.70 6.70 6.80 6.80 6.90 6.90 7.00 7.00 7.10 7.10 7.20 7.20 7.30 7.30 7.40 7.40 7.50 7.50 7.60 7.60 7.70 7.70 7.80 7.80 7.90 7.90 8.00 8.00 8.10 8.10 8.20 8.20 8.30 8.30 8.40 8.40 8.50 8.50 8.60 8.60 8.70 8.70 8.80 8.80 8.90 8.90 9.00 9.00 9.05 9.05 9.10 9.10 9.15 9.15 9.20 9.20 9.25 9.25 9.30 9.30 9.35 9.35 9.40 9.40 9.45 9.45 9.50 9.50 9.55 9.55 9.60 9.60 9.65 9.65 9.70 9.70 9.75 9.75 9.80 9.80 9.85 9.85 9.90 9.90 9.95 9.95 10.00 10.00 10.05 10.05 10.10 10.10 10.15 10.15 10.20 -1 1 -1bg.dat ###Markdown * Have 6.6-7.0 at dt=0.1 and 8.0-9.0 at dt=0.05 and 9.0-10.0 at dt=0.05 ###Code params['tmin'] = 7.0 params['tmax'] = 10.0 params['tbreak'] = [8.0, 9.0] params['tbin'] = [0.1, 0.05, 0.02] print(calcsfh_input_parameter(**params)) calcsfh_input_parameter? from match.scripts.fileio import calcsfh_dict calcsfh_dict().keys() ###Output _____no_output_____

Daniel.ipynb

###Markdown ###Code # EDA ANALYSIS # research problem # Figure out how we can predict which individuals are most likely to have or use a bank account. # Your solution will help provide an indication of the state of financial inclusion in Kenya, Rwanda, Tanzania, and Uganda, # while providing insights into some of the key demographic factors that might drive individuals’ financial outcomes. # Import libraries import numpy as np import pandas as pd from matplotlib import pyplot as plt import seaborn as sns %matplotlib inline # Import dataset # Load the firts 5 records # shape of the data print(fd.shape) fd = pd.read_csv('/content/Financial Dataset - 1.csv') fd.head(5) # Renaming columns fd.columns= fd.columns.str.replace(" ","_",) fd.columns = map(str.lower,fd.columns) fd # Missing data fd.isnull().sum() # fd # since we interested in data that has bank account, the null values can be dropped fd1 = fd.dropna(subset=['has_a_bank_account'],axis=0,how='all') fd1.isnull().sum() # # perform interpolation for the household and age columns # fd.iloc[0:6, 6:8].head(10) # fd.interpolate().iloc[0:6, 6:8] # fd.isnull().sum() # use forward ffill for the other categorical columns fd2['level_of_educuation'] = fd2['level_of_educuation'].replace(6,'NaN') # fd1 = fd.fillna(method='ffill') fd1.isnull().sum() # Overview of the data fd1.describe() # we can see the household size mean is 3 and age is 38 years # Std for household being 2 and age being 16 # One can tell that the sample population size has an average age of 38 which covers almost 50% of the data # number of unique elements in the dataset print(fd1.nunique()) # We see that the year has 6 unique elements instead of 4 thus showing some anomalies # Drop years not within 2016 -2018 value_list = ['2016', '2017', '2018'] fd2 = fd1[fd1.year.isin(value_list)] print(fd1.shape) print(fd2.shape) # fd2.drop_duplicates(['uniqueid'], keep='first') # data["Number_of_households"] < 50,000 fd_kenya = fd2['country'] == 'Kenya' print(fd2[fd_kenya].shape) fd_uganda = fd2['country'] == 'Uganda' print(fd2[fd_uganda].shape) fd_tz = fd2['country'] == 'Tanzania' print(fd2[fd_tz].shape) fd_rw = fd2['country'] == 'Rwanda' print(fd2[fd_rw].shape) fd2[fd_rw].duplicated(subset=['uniqueid']).sum() # fd2[fd_kenya].drop_duplicates(['uniqueid'], keep=False) # print(fd2.shape) # fd2[fd_uganda].drop_duplicates(['uniqueid'], keep=False, inplace=True) # print(fd2.shape) # fd2[fd_tz].drop_duplicates(['uniqueid'], keep='last', inplace=True) # print(fd2.shape) # fd2[fd_rw].drop_duplicates(['uniqueid'], inplace=True) # print(fd2.shape) fd2.info() # Outliers # Univariate analysis fd2['country'].value_counts().plot.bar(title='Freq dist of accounts per country ') fd2['the_relathip_with_head'].value_counts().plot.bar(title='Freq dist of accounts per rshp household ') fd2['marital_status'].value_counts().plot.bar(title='Freq dist of accounts on marital status') fd2['level_of_educuation'].value_counts().plot.bar(title='Freq dist of accounts on level of education') sns.boxplot(y=fd2['respondent_age']) sns.boxplot(y=fd2['household_size']) # coorelation matrix f, ax = plt.subplots(figsize=(10, 8)) corr = fd2.corr() sns.heatmap(corr, xticklabels=corr.columns.values, yticklabels=corr.columns.values) fd2 # Frequency table for accounts fd2.has_a_bank_account.value_counts() fd2.country.value_counts() plt.hist(fd2['has_a_bank_account'], bin = 10, histtype ='bar',rwidth = 0.9) ###Output _____no_output_____

math-data-cleanup.ipynb

###Markdown Load in data saved from scraping notebook - At this point we have a csv with the text and other various information from each video lecture. - The data still isn't labeled ###Code lectures1 = pd.read_csv('math2019.csv') lectures2 = pd.read_csv('math20192.csv') lectures = pd.concat([lectures1.reset_index(drop=True),lectures2.reset_index(drop=True)], axis=0) lectures.playlist_id.unique() ###Output _____no_output_____ ###Markdown add labels to data - we are going to use our list of playlist Ids and match them with their subject, then create a new target column based of playlist id ###Code #load playlist csv playlist_ids = pd.read_csv('playlists_math.csv') playlist_ids.iloc[17].PlaylistID = 'PLUl4u3cNGP61hsJNdULdudlRL493b-XZf' playlist_ids #we need some consolidation in terms of target subjects #we will create a dictionary with the playlist as a key and the subject as the value subject_keys = playlist_ids.PlaylistID subject_values = ['Probability','Statistics','CS','Algorithms','AI','Calculus','Calculus','Linear Algebra','Diff. Eq.', 'Linear Algebra','CS','Probability','CS','Algorithms','Robotics','Math for Eng.','Statistics', 'Data Structures','Probability','NLP','CS','Statistics','Algebraic Geometry','Calculus','Calculus', 'Calculus','AI','Various'] subject_lookup = {i:j for i,j in zip(subject_keys,subject_values)} #function to label a subject for a given videos PL id subject_re = re.compile('(%s)' % '|'.join(subject_lookup.keys())) def label_subjects(s, subject_lookup=subject_lookup): def replace(match): return subject_lookup[match.group(0)] return subject_re.sub(replace, s) lectures['Subject'] = [ label_subjects(i) for i in lectures.playlist_id] lectures.head() lectures[lectures.playlist_id == 'PL8_xPU5epJddl1dmAZWlERA0zplgD0W4E'] import matplotlib.pyplot as plt import seaborn as sns subject_counts = lectures.Subject.value_counts().reset_index() len(subject_counts) sns.barplot(x='Subject', y='index', data=subject_counts, palette='mako') chan_cnt = lectures.channelid.value_counts().reset_index() sns.barplot(x='channelid',y='index',data=chan_cnt, palette='mako') lectures.isnull().sum() #correct description for harvard CS50 lectures lectures['description'] = np.where(pd.isnull(lectures.description) == True,'HAR_CS50',lectures.description) lectures ###Output _____no_output_____ ###Markdown Cleaning, tokenizing the text - The text is pretty messy - we need to clean it up a bit. we do a clean up for the doc2vec model and another for the tfidf model This intro is tricky as the '\n's are not always in the same spot, so we can't use regex. My preference is to remove the first 300 characters of each lecture. Not all of the lectures start with a long intro like the MIT lectures, however this approach should not affect the integry of any one lecture's content. ###Code lectures.head(2) #for the doc2vec model, we wont remove the stop words def make_d2v_data(lectures): clean_lectures = [] #iterate over the text by lecture for lecture in lectures: #skip intro lecture = lecture[295:] #tokenize punctuation for key, token in punt_dict.items(): lecture = lecture.replace(key, ' {} '.format(token)) #expand contractions for key, expan in contract_dict.items(): lecture = lecture.replace(key, ' {} '.format(expan)) #append clean lecture to list of lectures clean_lectures.append(lecture) return clean_lectures orig_text = pd.read_csv('all_lectures.csv') d2v_df = pd.read_csv('all_lecture_text.csv') new_df = pd.concat([orig_text.reset_index(drop=True),d2v_df],axis=1) new_df.isnull().sum().sum() new = pd.DataFrame() new['text'] = orig_text.lecture_text new['label'] = d2v_df.Subject new.dropna(inplace=True) new.head() new.isnull().sum() new.shape new.to_csv('raw_text.csv',index=False) ###Output _____no_output_____

Modeling/ModelingExamples.ipynb

###Markdown The Stingray Modeling API ExplainedSome more in-depth explanations of how the Stingray modeling API works.Who should be using this API?Basically, anyone who wants to model power spectral products with parametric functions. The purpose of this API is two-fold:(1) provide convenient methods and classes in order to model a large range of typical data representations implemented in Stingray(2) provide a more general framework for users to build their own modelsA note on terminology: in this tutorial, we largely use _model_ to denote both the parametric model describing the underlying process that generated the data, and the statistical model used to account for uncertainties in the measurement process. The `modeling` subpackage defines a wider range of classes for typical statistical models than most standard modelling packages in X-ray astronomy, including likelihoods for Gaussian-distributed uncertainties (what astronomers call the $\chi^2$ likelihood), Poisson-distributed data (e.g. light curves) and $\chi^2$-distributed data (confusingly, *not* what astronomers call the $\chi^2$ likelihood, but the likelihood of data with $\chi^2$-distributed uncertainties appropriate for power spectra). It also defines a superclass `LogLikelihood` that make extending the framework to other types of data uncertainties straightforward. It supports Bayesian modelling via the `Posterior` class and its subclasses (for different types of data, equivalent to the likelihood classes) and provides support for defining priors. The class `ParameterEstimation` and its data type-specific subclasses implement a range of operations usually done with power spectra and other products, including optimization (fitting), sampling (via Markov-Chain Monte Carlo), calibrating models comparison metrics (particularly likelihood ratio tests) and outlier statistics (for finding periodic signal candidates).Overall, it is designed to be as modular as possible and extensible to new data types and problems in many places, though we do explicitly *not* aim to provide a fully general modelling framework (for example, at the moment, we have given no thought to modeling multi-variate data, though this may change in the future). Some backgroundModeling power spectra and light curves with parametric models is a fairly standard task. Stingray aims to make solving these problems as easy as possible. We aim to integrate our existing code with `astropy.modeling` for for maximum compatibility. Please note, however, that we are only using the models, not the fitting interface, which is too constrained for our purposes. ###Code %load_ext autoreload %autoreload 2 # ignore warnings to make notebook easier to see online # COMMENT OUT THESE LINES FOR ACTUAL ANALYSIS import warnings warnings.filterwarnings("ignore") %matplotlib inline import matplotlib.pyplot as plt try: import seaborn as sns sns.set_palette("colorblind") except ImportError: print("Install seaborn. It help you make prettier figures!") import numpy as np from astropy.modeling import models ###Output _____no_output_____ ###Markdown The models and API of `astropy.modeling.models` is explained in the [astropy documentation](http://docs.astropy.org/en/stable/modeling/) in more detail.Here's how you instantiate a simple 1-D Gaussian: ###Code g = models.Gaussian1D() # Generate fake data np.random.seed(0) x = np.linspace(-5., 5., 200) y = 3 * np.exp(-0.5 * (x - 1.3)**2 / 0.8**2) y += np.random.normal(0., 0.2, x.shape) yerr = 0.2 plt.figure(figsize=(8,5)) plt.errorbar(x, y, yerr=yerr, fmt='ko') ###Output _____no_output_____ ###Markdown Likelihoods and PosteriorsIn general, model fitting will happen either in a frequentist (Maximum Likelihood) or Bayesian framework. Stingray's strategy is to let the user define a posterior in both cases, but ignore the prior in the former case. Let's first make some fake data: ###Code # define power law component pl = models.PowerLaw1D() # fix x_0 of power law component pl.x_0.fixed = True # define constant c = models.Const1D() # make compound model plc = pl + c ###Output _____no_output_____ ###Markdown We're going to pick some fairly standard parameters for our data: ###Code # parameters for fake data. alpha = 2.0 amplitude = 5.0 white_noise = 2.0 ###Output _____no_output_____ ###Markdown And now a frequency array: ###Code freq = np.linspace(0.01, 10.0, int(10.0/0.01)) ###Output _____no_output_____ ###Markdown Now we can set the parameters in the model: ###Code from astropy.modeling.fitting import _fitter_to_model_params _fitter_to_model_params(plc, [amplitude, alpha, white_noise]) psd_shape = plc(freq) ###Output _____no_output_____ ###Markdown As a last step, we need to add noise by picking from a chi-square distribution with 2 degrees of freedom: ###Code powers = psd_shape*np.random.chisquare(2, size=psd_shape.shape[0])/2.0 ###Output _____no_output_____ ###Markdown Let's plot the result: ###Code plt.figure(figsize=(12,7)) plt.loglog(freq, powers, ds="steps-mid", label="periodogram realization") plt.loglog(freq, psd_shape, label="power spectrum") plt.legend() ###Output _____no_output_____ ###Markdown Maximum Likelihood FittingLet's assume we've observed this periodogram from our source. We would now like to estimate the parameters. This requires the definition of *likelihood*, which describes the probability of observing the data plotted above given some underlying model with a specific set of parameters. To say it differently, the likelihood encodes what we know about the underlying model (here a power law and a constant) and the statistical properties of the data (power spectra generally follow a chi-square distribution) and then allows us to compare data and model for various parameters under the assumption of the statistical uncertainties.In order to find the best parameter set, one generally maximizes the likelihood function using an optimization algorithm. Because optimization algorithms generally *minimize* functions, they effectively minimize the log-likelihood, which comes out to be the same as maximizing the likelihood itself.Below is an implementation of the $\chi^2$ likelihood as appropriate for power spectral analysis, with comments for easier understanding. The same is also implemented in `posterior.py` in Stingray: ###Code logmin = -1e16 class PSDLogLikelihood(object): def __init__(self, freq, power, model, m=1): """ A Chi-square likelihood as appropriate for power spectral analysis. Parameters ---------- freq : iterable x-coordinate of the data power : iterable y-coordinte of the data model: an Astropy Model instance The model to use in the likelihood. m : int 1/2 of the degrees of freedom, i.e. the number of powers that were averaged to obtain the power spectrum input into this routine. """ self.x = ps.freq # the x-coordinate of the data (frequency array) self.y = ps.power # the y-coordinate of the data (powers) self.model = model # an astropy.models instance self.m = m self.params = [k for k,l in self.model.fixed.items() if not l] self.npar = len(self.params) # number of free parameters def evaluate(self, pars, neg=False): """ Evaluate the log-likelihood. Parameters ---------- pars : iterable The list of parameters for which to evaluate the model. neg : bool, default False If True, compute the *negative* log-likelihood, otherwise compute the *positive* log-likelihood. Returns ------- loglike : float The log-likelihood of the model """ # raise an error if the length of the parameter array input into # this method doesn't match the number of free parameters in the model if np.size(pars) != self.npar: raise Exception("Input parameters must" + " match model parameters!") # set parameters in self.model to the parameter set to be used for # evaluation _fitter_to_model_params(self.model, pars) # compute the values of the model at the positions self.x mean_model = self.model(self.x) # if the power spectrum isn't averaged, compute simple exponential # likelihood (chi-square likelihood for 2 degrees of freedom) if self.m == 1: loglike = -np.sum(np.log(mean_model)) - \ np.sum(self.y/mean_model) # otherwise use chi-square distribution to compute likelihood else: loglike = -2.0*self.m*(np.sum(np.log(mean_model)) + np.sum(self.y/mean_model) + np.sum((2.0 / (2. * self.m) - 1.0) * np.log(self.y))) if not np.isfinite(loglike): loglike = logmin if neg: return -loglike else: return loglike def __call__(self, parameters, neg=False): return self.evaluate(parameters, neg) ###Output _____no_output_____ ###Markdown Let's make an object and see what it calculates if we put in different parameter sets. First, we have to make our sample PSD into an actual `Powerspectrum` object: ###Code from stingray import Powerspectrum ps = Powerspectrum() ps.freq = freq ps.power = powers ps.df = ps.freq[1] - ps.freq[0] ps.m = 1 loglike = PSDLogLikelihood(ps.freq, ps.power, plc, m=ps.m) test_pars = [1, 5, 100] loglike(test_pars) test_pars = [4.0, 10, 2.5] loglike(test_pars) test_pars = [2.0, 5.0, 2.0] loglike(test_pars) ###Output _____no_output_____ ###Markdown Something close to the parameters we put in should yield the largest log-likelihood. Feel free to play around with the test parameters to verify that this is true.You can similarly import the `PSDLogLikelihood` class from `stingray.modeling` and do the same: ###Code from stingray.modeling import PSDLogLikelihood loglike = PSDLogLikelihood(ps.freq, ps.power, plc, m=ps.m) loglike(test_pars) ###Output _____no_output_____ ###Markdown To estimate the parameters, we can use an optimization routine, such as those implemented in `scipy.optimize.minimize`.We have wrapped some code around that, to make your lives easier. We will not reproduce the full code here, just demonstrate its functionality.Now we can instantiate the `PSDParEst` (for PSD Parameter Estimation) object. This can do more than simply optimize a single model, but we'll get to that later.The `PSDParEst` object allows one to specify the fit method to use (however, this must be one of the optimizers in `scipy.optimize`). The parameter `max_post` allows for doing maximum-a-posteriori fits on the Bayesian posterior rather than maximum likelihood fits (see below for more details). We'll set it to `False` for now, since we haven't defined any priors: ###Code from stingray.modeling import PSDParEst parest = PSDParEst(ps, fitmethod="L-BFGS-B", max_post=False) ###Output _____no_output_____ ###Markdown In order to fit a model, make an instance of the appropriate `LogLikelihood` or `Posterior` subclass, andsimply call the `fit` method with that instance and starting parameters you would like to fit. ###Code loglike = PSDLogLikelihood(ps.freq, ps.power, plc, m=ps.m) loglike.model.parameters loglike.npar starting_pars = [3.0, 1.0, 2.4] res = parest.fit(loglike, starting_pars) ###Output _____no_output_____ ###Markdown The result is an `OptimizationResults` object, which computes various summaries and useful quantities.For example, here's the value of the likelihood function at the maximum the optimizer found: ###Code res.result ###Output _____no_output_____ ###Markdown **Note**: Optimizers routinely get stuck in *local* minima (corresponding to local maxima of the likelihood function). It is usually useful to run an optimizer several times with different starting parameters in order to get close to the global maximum.Most useful are the estimates of the parameters at the maximum likelihood and their uncertainties: ###Code print(res.p_opt) print(res.err) ###Output [4.72916493 2.09193061 2.10372265] [3.78311696 0.7300253 0.55312843] ###Markdown **Note**: uncertainties are estimated here via the covariance matrix between parameters, i.e. the inverse of the Hessian at the maximum. This only represents the true uncertainties for specific assumptions about the likelihood function (Gaussianity), so use with care!It also computes Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC) for model comparison purposes: ###Code print("AIC: " + str(res.aic)) print("BIC: " + str(res.bic)) ###Output AIC: 2189.789677035487 BIC: 2204.512942872433 ###Markdown Finally, it also produces the values of the mean function for the parameters at the maximum. Let's plot that and compare with the power spectrum we put in: ###Code plt.figure(figsize=(12,8)) plt.loglog(ps.freq, psd_shape, label="true power spectrum",lw=3) plt.loglog(ps.freq, ps.power, label="simulated data") plt.loglog(ps.freq, res.mfit, label="best fit", lw=3) plt.legend() ###Output _____no_output_____ ###Markdown That looks pretty good!You can print a summary of the fitting results by calling `print_summary`: ###Code res.print_summary(loglike) ###Output The best-fit model parameters plus errors are: 0) Parameter amplitude_0 : 4.72916 +/- 3.78312 [ None None] 1) Parameter x_0_0 : 1.00000 (Fixed) 2) Parameter alpha_0 : 2.09193 +/- 0.73003 [ None None] 3) Parameter amplitude_1 : 2.10372 +/- 0.55313 [ None None] Fitting statistics: -- number of data points: 1000 -- Deviance [-2 log L] D = 4367.579354.3 -- The Akaike Information Criterion of the model is: 2189.789677035487. -- The Bayesian Information Criterion of the model is: 2204.512942872433. -- The figure-of-merit function for this model is: 1079.682849.5f and the fit for 997 dof is 1.082932.3f -- Summed Residuals S = 69267.121618.5f -- Expected S ~ 6000.000000.5 +/- 109.544512.5 ###Markdown Likelihood RatiosThe parameter estimation code has more functionality than act as a simple wrapper around `scipy.optimize`. For example, it allows for easy computation of likelihood ratios. Likelihood ratios are a standard way to perform comparisons between two models (though they are not always statistically meaningful, and should be used with caution!).To demonstrate that, let's make a broken power law model ###Code # broken power law model bpl = models.BrokenPowerLaw1D() # add constant bplc = bpl + c bplc.param_names # define starting parameters bplc_start_pars = [2.0, 1.0, 3.0, 1.0, 2.5] loglike_bplc = PSDLogLikelihood(ps.freq, ps.power, bplc, m=ps.m) pval, plc_opt, bplc_opt = parest.compute_lrt(loglike, starting_pars, loglike_bplc, bplc_start_pars) print("Likelihood Ratio: " + str(pval)) ###Output Likelihood Ratio: 2.2374827070098036 ###Markdown Bayesian Parameter EstimationFor Bayesian parameter estimation, we require a prior along with the likelihood defined above. Together, they form the *posterior*, the probability of the parameters given the data, which is what we generally want to compute in science.Since there are no universally accepted priors for a model (they depend on the problem at hand and your physical knowledge about the system), they cannot be easily hard-coded in stingray. Consequently, setting priors is slightly more complex. Analogously to the `LogLikelihood` above, we can also define a `Posterior` object. Each posterior object has three methods: `logprior`, `loglikelihood` and `logposterior`. We have pre-defined some `Posterior` objects in `posterior.py` for common problems, including power spectral analysis. We start by making a `PSDPosterior` object: ###Code from stingray.modeling import PSDPosterior lpost = PSDPosterior(ps.freq, ps.power, plc, m=ps.m) ###Output _____no_output_____ ###Markdown The priors are set as a dictionary of functions: ###Code import scipy.stats # flat prior for the power law index p_alpha = lambda alpha: ((-1. <= alpha) & (alpha <= 5.)) # flat prior for the power law amplitude p_amplitude = lambda amplitude: ((0.01 <= amplitude) & (amplitude <= 10.0)) # normal prior for the white noise parameter p_whitenoise = lambda white_noise: scipy.stats.norm(2.0, 0.1).pdf(white_noise) priors = {} priors["alpha_0"] = p_alpha priors["amplitude_0"] = p_amplitude priors["amplitude_1"] = p_whitenoise ###Output _____no_output_____ ###Markdown There's a function `set_logprior` in `stingray.modeling` that sets the prior correctly: ###Code from stingray.modeling import set_logprior lpost.logprior = set_logprior(lpost, priors) ###Output _____no_output_____ ###Markdown You can also set the priors when you instantiate the posterior object: ###Code lpost = PSDPosterior(ps.freq, ps.power, plc, priors=priors, m=ps.m) ###Output _____no_output_____ ###Markdown Much like before with the log-likelihood, we can now also compute the log-posterior for various test parameter sets: ###Code test_pars = [1.0, 2.0, 4.0] print("log-prior: " + str(lpost.logprior(test_pars))) print("log-likelihood: " + str(lpost.loglikelihood(test_pars))) print("log-posterior: " + str(lpost(test_pars))) ###Output log-prior: -198.61635344021062 log-likelihood: -2412.2493594640564 log-posterior: -2610.865712904267 ###Markdown When the prior is zero (so the log-prior is -infinity), it automatically gets set to a very small value in order to avoid problems when doing the optimization: ###Code test_pars = [6, 6, 3.0] print("log-prior: " + str(lpost.logprior(test_pars))) print("log-likelihood: " + str(lpost.loglikelihood(test_pars))) print("log-posterior: " + str(lpost(test_pars))) test_pars = [5.0, 2.0, 2.0] print("log-prior: " + str(lpost.logprior(test_pars))) print("log-likelihood: " + str(lpost.loglikelihood(test_pars))) print("log-posterior: " + str(lpost(test_pars))) ###Output log-prior: 1.383646559789373 log-likelihood: -2184.6739536386162 log-posterior: -2183.290307078827 ###Markdown We can do the same parameter estimation as above, except now it's called maximum-a-posteriori instead of maximum likelihood and includes the prior (notice we set `max_post=True`): ###Code parest = PSDParEst(ps, fitmethod='BFGS', max_post=True) res = parest.fit(lpost, starting_pars) print("best-fit parameters:") for p,e in zip(res.p_opt, res.err): print("%.4f +/- %.4f"%(p,e)) ###Output best-fit parameters: 4.8949 +/- 0.0762 2.0690 +/- 0.0636 2.0547 +/- 0.0149 ###Markdown The same outputs exist as for the Maximum Likelihood case: ###Code res.print_summary(lpost) ###Output The best-fit model parameters plus errors are: 0) Parameter amplitude_0 : 4.89491 +/- 0.07623 [ None None] 1) Parameter x_0_0 : 1.00000 (Fixed) 2) Parameter alpha_0 : 2.06898 +/- 0.06363 [ None None] 3) Parameter amplitude_1 : 2.05471 +/- 0.01489 [ None None] Fitting statistics: -- number of data points: 1000 -- Deviance [-2 log L] D = 4367.845867.3 -- The Akaike Information Criterion of the model is: 2188.688941098666. -- The Bayesian Information Criterion of the model is: 2203.412206935612. -- The figure-of-merit function for this model is: 1104.686605.5f and the fit for 997 dof is 1.108011.3f -- Summed Residuals S = 75870.935552.5f -- Expected S ~ 6000.000000.5 +/- 109.544512.5 ###Markdown Unlike in the maximum likelihood case, we can also *sample* from the posterior probability distribution. The method `sample` uses the [emcee](http://dfm.io/emcee/current/) package to do MCMC. **Important**: Do *not* sample from the likelihood function. This is formally incorrect and can lead to incorrect inferences about the problem, because there is no guarantee that a posterior with improper (flat, infinite) priors will be bounded!**Important**: emcee has had a major upgrade to version 3, which came with a number of API changes. To ensure compatibility with stingray, please update emcee to the latest version, if you haven't already.Much like the optimizer, the sampling method requires a model and a set of starting parameters `t0`. Optionally, it can be useful to also input a covariance matrix, for example from the output of the optimizer.Finally, the user should specify the number of walkers as well as the number of steps to use for both burn-in and sampling: ###Code sample = parest.sample(lpost, res.p_opt, cov=res.cov, nwalkers=400, niter=100, burnin=300, namestr="psd_modeling_test") ###Output Chains too short to compute autocorrelation lengths. -- The acceptance fraction is: 0.640200.5 R_hat for the parameters is: [0.33858822 0.00779588 0.00477259] -- Posterior Summary of Parameters: parameter mean sd 5% 95% --------------------------------------------- theta[0] 4.92699673203164 0.5826084748010877 4.001167475075788 5.916405947428704 theta[1] 2.0850162824299567 0.08840420643721274 1.945198565812 2.236054242762929 theta[2] 2.059927524015745 0.06916995745141118 1.944976347964247 2.172179088048585 ###Markdown The sampling method returns an object with various attributes that are useful for further analysis, for example the acceptance fraction: ###Code sample.acceptance ###Output _____no_output_____ ###Markdown Or the mean and confidence intervals of the parameters: ###Code sample.mean sample.ci ###Output _____no_output_____ ###Markdown The method `print_results` prints the results: ###Code sample.print_results() ###Output -- The acceptance fraction is: 0.640200.5 R_hat for the parameters is: [0.33858822 0.00779588 0.00477259] -- Posterior Summary of Parameters: parameter mean sd 5% 95% --------------------------------------------- theta[0] 4.92699673203164 0.5826084748010877 4.001167475075788 5.916405947428704 theta[1] 2.0850162824299567 0.08840420643721274 1.945198565812 2.236054242762929 theta[2] 2.059927524015745 0.06916995745141118 1.944976347964247 2.172179088048585 ###Markdown Similarly, the method `plot_results` produces a bunch of plots: ###Code fig = sample.plot_results(nsamples=1000, fig=None, save_plot=True, filename="modeling_tutorial_mcmc_corner.pdf") ###Output _____no_output_____ ###Markdown Calibrating Likelihood Ratio TestsIn order to use likelihood ratio tests for model comparison, one must compute the p-value of obtaining a likelihood ratio at least as high as that observed given that the null hypothesis (the simpler model) is true. The distribution of likelihood ratios under that assumption will only follow an analytical distribution if* the models are nested, i.e. the simpler model is a special case of the more complex model *and** the parameter values that transform the complex model into the simple one do not lie on the boundary of parameter space. Imagine e.g. a simple model without a QPO, and a complex model with a QPO, where in order to make the simpler model out of the more complex one you would set the QPO amplitude to zero. However, the amplitude cannot go below zero, thus the critical parameter value transforming the complex into the simple model lie on the boundary of parameter space.If these two conditions are not given, the observed likelihood ratio must be calibrated via simulations of the simpler model. In general, one should *not* simulate from the best-fit model alone: this ignores the uncertainty in the model parameters, and thus may artificially inflate the significance of the result.In the purely frequentist (maximum likelihood case), one does not know the shape of the probability distribution for the parameters. A rough approximation can be obtained by assuming the likelihood surface to be a multi-variate Gaussian, with covariances given by the inverse Fisher information. One may sample from that distribution and then simulate fake data sets using the sampled parameters. Each simulated data set will be fit with both models to compute a likelihood ratio, which is then used to build a distribution of likelihood ratios from the simpler model to compare the observed likelihood ratio to.In the Bayesian case, one may sample from the posterior for the parameters directly and then use these samples as above to create fake data sets in order to derive a posterior probability distribution for the likelihood ratios and thus a posterior predictive p-value.For the statistical background of much of this, see [Protassov et al, 2002](http://adsabs.harvard.edu/abs/2002ApJ...571..545P).Below, we set up code that will do exactly that, for both the frequentist and Bayesian case. ###Code import copy def _generate_model(lpost, pars): """ Helper function that generates a fake PSD similar to the one in the data, but with different parameters. Parameters ---------- lpost : instance of a Posterior or LogLikelihood subclass The object containing the relevant information about the data and the model pars : iterable A list of parameters to be passed to lpost.model in oder to generate a model data set. Returns: -------- model_data : numpy.ndarray An array of model values for each bin in lpost.x """ # get the model m = lpost.model # reset the parameters _fitter_to_model_params(m, pars) # make a model spectrum model_data = lpost.model(lpost.x) return model_data def _generate_psd(ps, lpost, pars): """ Generate a fake power spectrum from a model. Parameters: ---------- lpost : instance of a Posterior or LogLikelihood subclass The object containing the relevant information about the data and the model pars : iterable A list of parameters to be passed to lpost.model in oder to generate a model data set. Returns: -------- sim_ps : stingray.Powerspectrum object The simulated Powerspectrum object """ model_spectrum = _generate_model(lpost, pars) # use chi-square distribution to get fake data model_powers = model_spectrum*np.random.chisquare(2*ps.m, size=model_spectrum.shape[0])/(2.*ps.m) sim_ps = copy.copy(ps) sim_ps.powers = model_powers return sim_ps def _compute_pvalue(obs_val, sim): """ Compute the p-value given an observed value of a test statistic and some simulations of that same test statistic. Parameters ---------- obs_value : float The observed value of the test statistic in question sim: iterable A list or array of simulated values for the test statistic Returns ------- pval : float [0, 1] The p-value for the test statistic given the simulations. """ # cast the simulations as a numpy array sim = np.array(sim) # find all simulations that are larger than # the observed value ntail = sim[sim > obs_val].shape[0] # divide by the total number of simulations pval = ntail/sim.shape[0] return pval def calibrate_lrt(ps, lpost1, t1, lpost2, t2, sample=None, neg=True, max_post=False, nsim=1000, niter=200, nwalker=500, burnin=200, namestr="test"): # set up the ParameterEstimation object parest = PSDParEst(ps, fitmethod="L-BFGS-B", max_post=False) # compute the observed likelihood ratio lrt_obs, res1, res2 = parest.compute_lrt(lpost1, t1, lpost2, t2, neg=neg, max_post=max_post) # simulate parameter sets from the simpler model if not max_post: # using Maximum Likelihood, so I'm going to simulate parameters # from a multivariate Gaussian # set up the distribution mvn = scipy.stats.multivariate_normal(mean=res1.p_opt, cov=res1.cov) # sample parameters s_all = mvn.rvs(size=nsim) else: if sample is None: # sample the posterior using MCMC sample = parest.sample(lpost, res1.p_opt, cov=res1.cov, nwalkers=nwalker, niter=niter, burnin=burnin, namestr=namestr) # pick nsim samples out of the posterior sample s_all = sample[np.random.choice(sample.shape[0], nsim, replace=False)] lrt_sim = np.zeros(nsim) # now I can loop over all simulated parameter sets to generate a PSD for i,s in enumerate(s_all): # generate fake PSD sim_ps = _generate_psd(ps, lpost1, s) # make LogLikelihood objects for both: if not max_post: sim_lpost1 = PSDLogLikelihood(sim_ps.freq, sim_ps.power, model=lpost1.model, m=sim_ps.m) sim_lpost2 = PSDLogLikelihood(sim_ps.freq, sim_ps.power, model=lpost2.model, m=sim_ps.m) else: # make a Posterior object sim_lpost1 = PSDPosterior(sim_ps.freq, sim_ps.power, lpost1.model, m=sim_ps.m) sim_lpost1.logprior = lpost1.logprior sim_lpost2 = PSDPosterior(sim_ps.freq, sim_ps.power, lpost2.model, m=sim_ps.m) sim_lpost2.logprior = lpost2.logprior parest_sim = PSDParEst(sim_ps, max_post=max_post) lrt_sim[i], _, _ = parest_sim.compute_lrt(sim_lpost1, t1, sim_lpost2, t2, neg=neg, max_post=max_post) # now I can compute the p-value: pval = _compute_pvalue(lrt_obs, lrt_sim) return pval pval = calibrate_lrt(ps, loglike, starting_pars, loglike_bplc, bplc_start_pars, max_post=False, nsim=100) print("The p-value for rejecting the simpler model is: " + str(pval)) ###Output The p-value for rejecting the simpler model is: 0.97 ###Markdown As expected, the p-value for rejecting the powerlaw model is fairly large: since we simulated from that model, we would be surprised if it generated a small p-value, causing us to reject this model (note, however, that if the null hypothesis is true, the p-value will be uniformely distributed between 0 and 1. By definition, then, you will get a p-value smaller or equal to 0.01 in approximately one out of a hundred cases)We can do the same with the Bayesian model, in which case the result is called a *posterior predictive p-value*, which, in turn, is often used in posterior model checking (not yet implemented!).We have not yet defined a `PSDPosterior` object for the bent power law model, so let's do that. First, let's define some priors: ###Code import scipy.stats # flat prior for the power law indices p_alpha1 = lambda alpha: ((-1. <= alpha) & (alpha <= 5.)) p_alpha2 = lambda alpha: ((-1. <= alpha) & (alpha <= 5.)) # flat prior for the break frequency p_x_break = lambda xbreak: ((0.01 <= xbreak) & (10.0 >= xbreak)) # flat prior for the power law amplitude p_amplitude = lambda amplitude: ((0.01 <= amplitude) & (amplitude <= 10.0)) # normal prior for the white noise parameter p_whitenoise = lambda white_noise: scipy.stats.norm(2.0, 0.1).pdf(white_noise) priors = {} priors["alpha_1_0"] = p_alpha priors["alpha_2_0"] = p_alpha priors["amplitude_0"] = p_amplitude priors["amplitude_1"] = p_whitenoise priors["x_break_0"] = p_x_break ###Output _____no_output_____ ###Markdown Now we can set up the `PSDPosterior` object: ###Code lpost_bplc = PSDPosterior(ps.freq, ps.power, bplc, priors=priors, m=ps.m) lpost_bplc(bplc_start_pars) ###Output _____no_output_____ ###Markdown And do the posterior predictive p-value. Since we've already sampled from the simple model, we can pass that sample to the `calibrate_lrt` function, in order to cut down on computation time (if the keyword `sample` is not given, it will automatically run MCMC: ###Code pval = calibrate_lrt(ps, lpost, starting_pars, lpost_bplc, bplc_start_pars, sample=sample.samples, max_post=True, nsim=100) print("The posterior predictive p-value is: p = " + str(pval)) ###Output The posterior predictive p-value is: p = 1.0 ###Markdown Again, we find that the p-value does not suggest rejecting the powerlaw model.Of course, a slightly modified version is implemented in `stingray` as a subclass of the `PSDParEst` class: ###Code from stingray.modeling import PSDParEst parest = PSDParEst(ps, fitmethod="BFGS") pval = parest.calibrate_lrt(lpost, starting_pars, lpost_bplc, bplc_start_pars, sample=sample.samples, nsim=100, max_post=True, seed=200) print(pval) ###Output 0.2 ###Markdown Bayesian-ish QPO SearchesWhen searching for quasi-periodic oscillations (QPOs) in light curves that are not constant (for example because they are bursts or have other types of variability), one must take care that the variable background is accurately modelled (most standard tools assume that the light curve is constant). In [Vaughan et al, 2010](http://adsabs.harvard.edu/abs/2010MNRAS.402..307V), a method was introduced to search for QPOs in the presence of red noise (stochastic variability), and in [Huppenkothen et al, 2013](http://adsabs.harvard.edu/abs/2013ApJ...768...87H) it was extended to magnetar bursts, and in [Inglis et al, 2015](http://adsabs.harvard.edu/abs/2015ApJ...798..108I) and [Inglis et al, 2016](http://adsabs.harvard.edu/abs/2016ApJ...833..284I) a similar approach was used to find QPOs in solar flares.Based on a model for the broadband spectral noise, the algorithm finds the highest outlier in a test statistic based on the data-model residuals (under the assumption that if the broadband model is correct, the test statistic $T_R = \max_j(2 D_j/m_j)$ for $j$ power spectral bins with powers $D_j$ and model powers $m_j$ will be distributed following a $\chi^2$ distribution with two degrees of freedom). The observed test statistic $T_R$ is then compared to a theoretical distribution based on simulated power spectra without an outlier in order to compute a posterior predictive p-value as above for the likelihood ratio.Since the concept is very similar to that above, we do not show the full code here. Instead, the p-value can be calculated using the method `calibrate_highest_outlier`, which belongs to the `PSDParEst` class: ###Code # compute highest outlier in the data, and the frequency and index # where that power occurs max_power, max_freq, max_ind = parest._compute_highest_outlier(lpost, res) max_power pval = parest.calibrate_highest_outlier(lpost, starting_pars, sample=sample, max_post=True, nsim=100, niter=200, nwalkers=500, burnin=200, namestr="test") pval ###Output _____no_output_____ ###Markdown Convenience FunctionsFor convenience, we have implemented some simple functions to reduce overhead with having to instantiate objects of the various classes.Note that these convenience function use similar approaches and guesses in all cases; this might work for some simple quicklook analysis, but when preparing publication-ready results, one should approach the analysis with more care and make sure the options chosen are appropriate for the problem at hand. Fitting a power spectrum with some modelThe code above allows for a lot of freedom in building an appropriate model for your application. However, in everyday life, one might occasionally want to do a quick fit for various applications, without having to go too much into details. Below is a convenience function written for exactly that purpose.Please note that while this aims to use reasonable defaults, this is unlikely to produce publication-ready results!So let's fit a power law and a constant to some data, which we'll create below: ###Code from stingray import Powerspectrum m = 1 nfreq = 100000 freq = np.linspace(1, 1000, nfreq) np.random.seed(100) # set the seed for the random number generator noise = np.random.exponential(size=nfreq) model = models.PowerLaw1D() + models.Const1D() model.x_0_0.fixed = True alpha_0 = 2.0 amplitude_0 = 100.0 amplitude_1 = 2.0 model.alpha_0 = alpha_0 model.amplitude_0 = amplitude_0 model.amplitude_1 = amplitude_1 p = model(freq) power = noise * p ps = Powerspectrum() ps.freq = freq ps.power = power ps.m = m ps.df = freq[1] - freq[0] ps.norm = "leahy" ###Output _____no_output_____ ###Markdown What does this data set look like? ###Code plt.figure() plt.loglog(ps.freq, ps.power, ds="steps-mid", lw=2, color="black") ###Output _____no_output_____ ###Markdown In order to fit this, we'll write a convenience function that can take the power spectrum, a model, some starting parameters and just run with it: ###Code from stingray.modeling import PSDLogLikelihood, PSDPosterior, PSDParEst def fit_powerspectrum(ps, model, starting_pars, max_post=False, priors=None, fitmethod="L-BFGS-B"): if priors: lpost = PSDPosterior(ps, model, priors=priors) else: lpost = PSDLogLikelihood(ps.freq, ps.power, model, m=ps.m) parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post) res = parest.fit(lpost, starting_pars, neg=True) return parest, res ###Output _____no_output_____ ###Markdown Let's see if it works. We've already defined our model above, but to be explicit, let's define it again: ###Code model_to_test = models.PowerLaw1D() + models.Const1D() model_to_test.x_0_0.fixed = True ###Output _____no_output_____ ###Markdown Now we just need some starting parameters: ###Code t0 = [80, 1.5, 2.5] parest, res = fit_powerspectrum(ps, model_to_test, t0) res.p_opt ###Output _____no_output_____ ###Markdown Looks like it worked! Let's plot the result, too: ###Code plt.figure() plt.figure() plt.loglog(ps.freq, ps.power, ds="steps-mid", lw=2, color="black") plt.plot(ps.freq, res.mfit, lw=3, color="red") ###Output _____no_output_____ ###Markdown You can find the function in the `scripts` sub-module: ###Code from stingray.modeling.scripts import fit_powerspectrum parest, res = fit_powerspectrum(ps, model_to_test, t0) res.p_opt ###Output _____no_output_____ ###Markdown Fitting LorentziansFitting Lorentzians to power spectra is a routine task for most astronomers working with power spectra, hence there is a function that can produce either Maximum Likelihood or Maximum-A-Posteriori fits of the data. ###Code l = models.Lorentz1D l.param_names def fit_lorentzians(ps, nlor, starting_pars, fit_whitenoise=True, max_post=False, priors=None, fitmethod="L-BFGS-B"): model = models.Lorentz1D() if nlor > 1: for i in range(nlor-1): model += models.Lorentz1D() if fit_whitenoise: model += models.Const1D() parest = PSDParEst(ps, fitmethod=fitmethod, max_post=max_post) lpost = PSDPosterior(ps.freq, ps.power, model, priors=priors, m=ps.m) res = parest.fit(lpost, starting_pars, neg=True) return parest, res ###Output _____no_output_____ ###Markdown Let's make a dataset so we can test it! ###Code np.random.seed(400) nlor = 3 x_0_0 = 0.5 x_0_1 = 2.0 x_0_2 = 7.5 amplitude_0 = 150.0 amplitude_1 = 50.0 amplitude_2 = 15.0 fwhm_0 = 0.1 fwhm_1 = 1.0 fwhm_2 = 0.5 whitenoise = 2.0 model = models.Lorentz1D(amplitude_0, x_0_0, fwhm_0) + \ models.Lorentz1D(amplitude_1, x_0_1, fwhm_1) + \ models.Lorentz1D(amplitude_2, x_0_2, fwhm_2) + \ models.Const1D(whitenoise) p = model(ps.freq) noise = np.random.exponential(size=len(ps.freq)) power = p*noise plt.figure() plt.loglog(ps.freq, power, lw=1, ds="steps-mid", c="black") plt.loglog(ps.freq, p, lw=3, color="red") ###Output _____no_output_____ ###Markdown Let's make this into a `Powerspectrum` object: ###Code import copy ps_new = copy.copy(ps) ps_new.power = power ###Output _____no_output_____ ###Markdown So now we can fit this model with our new function, but first, we need to define the starting parameters for our fit. The starting parameters will be `[amplitude, x_0, fwhm]` for each component plus the white noise component at the end: ###Code t0 = [150, 0.4, 0.2, 50, 2.3, 0.6, 20, 8.0, 0.4, 2.1] parest, res = fit_lorentzians(ps_new, nlor, t0) ###Output _____no_output_____ ###Markdown Let's look at the output: ###Code res.p_opt ###Output _____no_output_____ ###Markdown Cool, that seems to work! For convenience `PSDParEst` also has a plotting function: ###Code parest.plotfits(res, save_plot=False, namestr="lorentzian_test") ###Output _____no_output_____ ###Markdown The function exists in the library as well for ease of use: ###Code from stingray.modeling import fit_lorentzians parest, res = fit_lorentzians(ps_new, nlor, t0) res.p_opt ###Output _____no_output_____

01 Data Analysis and Pre-processing/Visualization/04 Plotly Tutorial for Beginners.ipynb

###Markdown 1. Line Charts Line Charts Example: Citation and Teaching vs World Rank of Top 100 Universities * Import graph_objs as *go* * Creating traces * x = x axis * y = y axis * mode = type of plot like marker, line or line + markers * name = name of the plots * marker = marker is used with dictionary. * color = color of lines. It takes RGB (red, green, blue) and opacity (alpha) * text = The hover text (hover is curser) * data = is a list that we add traces into it * layout = it is dictionary. * title = title of layout * x axis = it is dictionary * title = label of x axis * ticklen = length of x axis ticks * zeroline = showing zero line or not * fig = it includes data and layout* iplot() = plots the figure(fig) that is created by data and layout ###Code # prepare data frame df = timesData.iloc[:100,:] # import graph objects as "go" import plotly.graph_objs as go # Creating trace1 trace1 = go.Scatter( x = df.world_rank, y = df.citations, mode = "lines", name = "citations", marker = dict(color = 'rgba(16, 112, 2, 0.8)'), text= df.university_name) # Creating trace2 trace2 = go.Scatter( x = df.world_rank, y = df.teaching, mode = "lines+markers", name = "teaching", marker = dict(color = 'rgba(80, 26, 80, 0.8)'), text= df.university_name) data = [trace1, trace2] layout = dict(title = 'Citation and Teaching vs World Rank of Top 100 Universities', xaxis= dict(title= 'World Rank',ticklen= 5,zeroline= False) ) fig = dict(data = data, layout = layout) iplot(fig) ###Output _____no_output_____ ###Markdown ScatterScatter Example: Citation vs world rank of top 100 universities with 2014, 2015 and 2016 years* Import graph_objs as *go** Creating traces * x = x axis * y = y axis * mode = type of plot like marker, line or line + markers * name = name of the plots * marker = marker is used with dictionary. * color = color of lines. It takes RGB (red, green, blue) and opacity (alpha) * text = The hover text (hover is curser)* data = is a list that we add traces into it* layout = it is dictionary. * title = title of layout * x axis = it is dictionary * title = label of x axis * ticklen = length of x axis ticks * zeroline = showing zero line or not * y axis = it is dictionary and same with x axis* fig = it includes data and layout* iplot() = plots the figure(fig) that is created by data and layout ###Code # prepare data frames df2014 = timesData[timesData.year == 2014].iloc[:100,:] df2015 = timesData[timesData.year == 2015].iloc[:100,:] df2016 = timesData[timesData.year == 2016].iloc[:100,:] import plotly.graph_objs as go # creating trace1 trace1 =go.Scatter( x = df2014.world_rank, y = df2014.citations, mode = "markers", name = "2014", marker = dict(color = 'rgba(255, 128, 255, 0.8)'), text= df2014.university_name) # creating trace2 trace2 =go.Scatter( x = df2015.world_rank, y = df2015.citations, mode = "markers", name = "2015", marker = dict(color = 'rgba(255, 128, 2, 0.8)'), text= df2015.university_name) # creating trace3 trace3 =go.Scatter( x = df2016.world_rank, y = df2016.citations, mode = "markers", name = "2016", marker = dict(color = 'rgba(0, 255, 200, 0.8)'), text= df2016.university_name) data = [trace1, trace2, trace3] layout = dict(title = 'Citation vs world rank of top 100 universities with 2014, 2015 and 2016 years', xaxis= dict(title= 'World Rank',ticklen= 5,zeroline= False), yaxis= dict(title= 'Citation',ticklen= 5,zeroline= False) ) fig = dict(data = data, layout = layout) iplot(fig) ###Output _____no_output_____ ###Markdown Bar ChartsFirst Bar Charts Example: citations and teaching of top 3 universities in 2014 (style1)* Import graph_objs as *go** Creating traces * x = x axis * y = y axis * mode = type of plot like marker, line or line + markers * name = name of the plots * marker = marker is used with dictionary. * color = color of lines. It takes RGB (red, green, blue) and opacity (alpha) * line = It is dictionary. line between bars * color = line color around bars * text = The hover text (hover is curser)* data = is a list that we add traces into it* layout = it is dictionary. * barmode = bar mode of bars like grouped* fig = it includes data and layout* iplot() = plots the figure(fig) that is created by data and layout ###Code # prepare data frames df2014 = timesData[timesData.year == 2014].iloc[:10,:] import plotly.graph_objs as go # create trace1 trace1 = go.Bar( x = df2014.university_name, y = df2014.citations, name = "citations", marker = dict(color = 'rgba(255, 174, 255, 0.5)', line=dict(color='rgb(0,0,0)',width=1.5)), text = df2014.country) # create trace2 trace2 = go.Bar( x = df2014.university_name, y = df2014.teaching, name = "teaching", marker = dict(color = 'rgba(255, 255, 128, 0.5)', line=dict(color='rgb(0,0,0)',width=1.5)), text = df2014.country) data = [trace1, trace2] layout = go.Layout(barmode = "group") fig = go.Figure(data = data, layout = layout) iplot(fig) ###Output _____no_output_____ ###Markdown Second Bar Charts Example: citations and teaching of top 3 universities in 2014 (style2) Actually, if you change only the barmode from *group* to *relative* in previous example, you achieve what we did here. However, for diversity I use different syntaxes. * Import graph_objs as *go** Creating traces * x = x axis * y = y axis * name = name of the plots * type = type of plot like bar plot* data = is a list that we add traces into it* layout = it is dictionary. * xaxis = label of x axis * barmode = bar mode of bars like grouped( previous example) or relative * title = title of layout* fig = it includes data and layout* iplot() = plots the figure(fig) that is created by data and layout ###Code # prepare data frames df2014 = timesData[timesData.year == 2014].iloc[:10,:] import plotly.graph_objs as go x = df2014.university_name trace1 = { 'x': x, 'y': df2014.citations, 'name': 'citation', 'type': 'bar' }; trace2 = { 'x': x, 'y': df2014.teaching, 'name': 'teaching', 'type': 'bar' }; data = [trace1, trace2]; layout = { 'xaxis': {'title': 'Top 10 universities'}, 'barmode': 'relative', 'title': 'citations and teaching of top 10 universities in 2014' }; fig = go.Figure(data = data, layout = layout) iplot(fig) ###Output _____no_output_____ ###Markdown Third Bar Charts Example: Horizontal bar charts. (style3) Citation vs income for universities* Import graph_objs as *go* and importing tools * Tools: used for subplots* Creating trace1 * bar: bar plot * x = x axis * y = y axis * marker * color: color of bars * line: bar line color and width * name: name of bar * orientation: orientation like horizontal * creating trace2 * scatter: scatter plot * x = x axis * y = y axis * mode: scatter type line line + markers or only markers * line: properties of line * color: color of line * name: name of scatter plot * layout: axis, legend, margin, paper and plot properties * ###Code import plotly.graph_objs as go from plotly import tools df2016 = timesData[timesData.year == 2016].iloc[:7,:] y_saving = [each for each in df2016.research] y_net_worth = [float(each) for each in df2016.income] x_saving = [each for each in df2016.university_name] x_net_worth = [each for each in df2016.university_name] trace0 = go.Bar( x=y_saving, y=x_saving, marker=dict(color='rgba(171, 50, 96, 0.6)',line=dict(color='rgba(171, 50, 96, 1.0)',width=1)), name='research', orientation='h', ) trace1 = go.Scatter( x=y_net_worth, y=x_net_worth, mode='lines+markers', line=dict(color='rgb(63, 72, 204)'), name='income', ) layout = dict( title='Citations and income', yaxis=dict(showticklabels=True, domain=[0, 0.85]), yaxis2=dict(showline=True, showticklabels=False, linecolor='rgba(102, 102, 102, 0.8)', linewidth=2, domain=[0, 0.85]), xaxis=dict(zeroline=False, showline=False, showticklabels=True, showgrid=True, domain=[0, 0.42]), xaxis2=dict(zeroline=False, showline=False, showticklabels=True, showgrid=True, domain=[0.47, 1], side='top', dtick=25), legend=dict(x=0.029, y=1.038, font=dict(size=10) ), margin=dict(l=200, r=20, t=70, b=70), paper_bgcolor='rgb(248, 248, 255)', plot_bgcolor='rgb(248, 248, 255)', ) annotations = [] y_s = np.round(y_saving, decimals=2) y_nw = np.rint(y_net_worth) # Adding labels for ydn, yd, xd in zip(y_nw, y_s, x_saving): # labeling the scatter savings annotations.append(dict(xref='x2', yref='y2', y=xd, x=ydn - 4,text='{:,}'.format(ydn), font=dict(family='Arial', size=12, color='rgb(63, 72, 204)'), showarrow=False)) # labeling the bar net worth annotations.append(dict(xref='x1', yref='y1', y=xd, x=yd + 3,text=str(yd), font=dict(family='Arial', size=12, color='rgb(171, 50, 96)'), showarrow=False)) layout['annotations'] = annotations # Creating two subplots fig = tools.make_subplots(rows=1, cols=2, specs=[[{}, {}]], shared_xaxes=True, shared_yaxes=False, vertical_spacing=0.001) fig.append_trace(trace0, 1, 1) fig.append_trace(trace1, 1, 2) fig['layout'].update(layout) iplot(fig) ###Output C:\anaconda3\envs\keras\lib\site-packages\plotly\tools.py:465: DeprecationWarning: plotly.tools.make_subplots is deprecated, please use plotly.subplots.make_subplots instead ###Markdown Pie ChartsPie Charts Example: Students rate of top 7 universities in 2016* fig: create figures * data: plot type * values: values of plot * labels: labels of plot * name: name of plots * hoverinfo: information in hover * hole: hole width * type: plot type like pie * layout: layout of plot * title: title of layout * annotations: font, showarrow, text, x, y ###Code # data preparation df2016 = timesData[timesData.year == 2016].iloc[:7,:] pie1 = df2016.num_students pie1_list = [float(each.replace(',', '.')) for each in df2016.num_students] # str(2,4) => str(2.4) = > float(2.4) = 2.4 labels = df2016.university_name # figure fig = { "data": [ { "values": pie1_list, "labels": labels, "domain": {"x": [0, .5]}, "name": "Number Of Students Rates", "hoverinfo":"label+percent+name", "hole": .3, "type": "pie" },], "layout": { "title":"Universities Number of Students rates", "annotations": [ { "font": { "size": 20}, "showarrow": False, "text": "Number of Students", "x": 0.1, "y": 1.1, }, ] } } iplot(fig) ###Output _____no_output_____ ###Markdown Bubble ChartsBubble Charts Example: University world rank (first 20) vs teaching score with number of students(size) and international score (color) in 2016* x = x axis* y = y axis* mode = markers(scatter)* marker = marker properties * color = third dimension of plot. Internaltional score * size = fourth dimension of plot. Number of students* text: university names ###Code # data preparation df2016 = timesData[timesData.year == 2016].iloc[:20,:] num_students_size = [float(each.replace(',', '.')) for each in df2016.num_students] international_color = [float(each) for each in df2016.international] data = [ { 'y': df2016.teaching, 'x': df2016.world_rank, 'mode': 'markers', 'marker': { 'color': international_color, 'size': num_students_size, 'showscale': True }, "text" : df2016.university_name } ] iplot(data) ###Output _____no_output_____ ###Markdown HistogramLets look at histogram of students-staff ratio in 2011 and 2012 years. * trace1 = first histogram * x = x axis * y = y axis * opacity = opacity of histogram * name = name of legend * marker = color of histogram* trace2 = second histogram* layout = layout * barmode = mode of histogram like overlay. Also you can change it with *stack* ###Code # prepare data x2011 = timesData.student_staff_ratio[timesData.year == 2011] x2012 = timesData.student_staff_ratio[timesData.year == 2012] trace1 = go.Histogram( x=x2011, opacity=0.75, name = "2011", marker=dict(color='rgba(171, 50, 96, 0.6)')) trace2 = go.Histogram( x=x2012, opacity=0.75, name = "2012", marker=dict(color='rgba(12, 50, 196, 0.6)')) data = [trace1, trace2] layout = go.Layout(barmode='overlay', title=' students-staff ratio in 2011 and 2012', xaxis=dict(title='students-staff ratio'), yaxis=dict( title='Count'), ) fig = go.Figure(data=data, layout=layout) iplot(fig) ###Output _____no_output_____ ###Markdown Word CloudNot a pyplot but learning it is good for visualization. Lets look at which country is mentioned most in 2011.* WordCloud = word cloud library that I import at the beginning of kernel * background_color = color of back ground * generate = generates the country name list(x2011) a word cloud ###Code # data prepararion x2011 = timesData.country[timesData.year == 2011] plt.subplots(figsize=(8,8),dpi=300) wordcloud = WordCloud( background_color='white', width=512, height=384 ).generate(" ".join(x2011)) plt.imshow(wordcloud) plt.axis('off') plt.savefig('graph.png') plt.show() ###Output _____no_output_____ ###Markdown Box Plots* Box Plots * Median (50th percentile) = middle value of the data set. Sort and take the data in the middle. It is also called 50% percentile that is 50% of data are less that median(50th quartile)(quartile) * 25th percentile = quartile 1 (Q1) that is lower quartile * 75th percentile = quartile 3 (Q3) that is higher quartile * height of box = IQR = interquartile range = Q3-Q1 * Whiskers = 1.5 * IQR from the Q1 and Q3 * Outliers = being more than 1.5*IQR away from median commonly. * trace = box * y = data we want to visualize with box plot * marker = color ###Code # data preparation x2015 = timesData[timesData.year == 2015] trace0 = go.Box( y=x2015.total_score, name = 'total score of universities in 2015', marker = dict( color = 'rgb(12, 12, 140)', ) ) trace1 = go.Box( y=x2015.research, name = 'research of universities in 2015', marker = dict( color = 'rgb(12, 128, 128)', ) ) data = [trace0, trace1] iplot(data) ###Output _____no_output_____ ###Markdown Scatter Matrix PlotsScatter Matrix = it helps us to see covariance and relation between more than 2 features* import figure factory as ff* create_scatterplotmatrix = creates scatter plot * data2015 = prepared data. It includes research, international and total scores with index from 1 to 401 * colormap = color map of scatter plot * colormap_type = color type of scatter plot * height and weight ###Code import plotly.figure_factory as ff dataframe = timesData[timesData.year == 2015] data2015 = dataframe.loc[:,["research","international", "total_score"]] data2015["index"] = np.arange(1,len(data2015)+1) # scatter matrix fig = ff.create_scatterplotmatrix(data2015, diag='box', index='index', colormap='Portland', colormap_type='cat', height=700, width=700) iplot(fig) ###Output _____no_output_____ ###Markdown Inset Plots ###Code # first line plot trace1 = go.Scatter( x=dataframe.world_rank, y=dataframe.teaching, name = "teaching", marker = dict(color = 'rgba(16, 112, 2, 0.8)'), ) # second line plot trace2 = go.Scatter( x=dataframe.world_rank, y=dataframe.income, xaxis='x2', yaxis='y2', name = "income", marker = dict(color = 'rgba(160, 112, 20, 0.8)'), ) data = [trace1, trace2] layout = go.Layout( xaxis2=dict( domain=[0.6, 0.95], anchor='y2', ), yaxis2=dict( domain=[0.6, 0.95], anchor='x2', ), title = 'Income and Teaching vs World Rank of Universities' ) fig = go.Figure(data=data, layout=layout) iplot(fig) ###Output _____no_output_____ ###Markdown 3D Scatter Plot with Colorscaling3D Scatter: Sometimes 2D is not enough to understand data. Therefore adding one more dimension increase the intelligibility of the data. Even we will add color that is actually 4th dimension.* go.Scatter3d: create 3d scatter plot* x,y,z: axis of plots* mode: market that is scatter* size: marker size* color: axis of colorscale* colorscale: actually it is 4th dimension ###Code # create trace 1 that is 3d scatter trace1 = go.Scatter3d( x=dataframe.world_rank, y=dataframe.research, z=dataframe.citations, mode='markers', marker=dict( size=10, color='rgb(255,0,0)', # set color to an array/list of desired values ) ) data = [trace1] layout = go.Layout( margin=dict( l=0, r=0, b=0, t=0 ) ) fig = go.Figure(data=data, layout=layout) iplot(fig) ###Output _____no_output_____ ###Markdown Multiple SubplotsMultiple Subplots: While comparing more than one features, multiple subplots can be useful. ###Code trace1 = go.Scatter( x=dataframe.world_rank, y=dataframe.research, name = "research" ) trace2 = go.Scatter( x=dataframe.world_rank, y=dataframe.citations, xaxis='x2', yaxis='y2', name = "citations" ) trace3 = go.Scatter( x=dataframe.world_rank, y=dataframe.income, xaxis='x3', yaxis='y3', name = "income" ) trace4 = go.Scatter( x=dataframe.world_rank, y=dataframe.total_score, xaxis='x4', yaxis='y4', name = "total_score" ) data = [trace1, trace2, trace3, trace4] layout = go.Layout( xaxis=dict( domain=[0, 0.45] ), yaxis=dict( domain=[0, 0.45] ), xaxis2=dict( domain=[0.55, 1] ), xaxis3=dict( domain=[0, 0.45], anchor='y3' ), xaxis4=dict( domain=[0.55, 1], anchor='y4' ), yaxis2=dict( domain=[0, 0.45], anchor='x2' ), yaxis3=dict( domain=[0.55, 1] ), yaxis4=dict( domain=[0.55, 1], anchor='x4' ), title = 'Research, citation, income and total score VS World Rank of Universities' ) fig = go.Figure(data=data, layout=layout) iplot(fig) ###Output _____no_output_____

notebooks/exploratory/rdnfn-1-geopandas.ipynb

###Markdown Comparison between Biotope and Vegetation dataCompares the two different shape files found in the Chernobyl data set. ###Code import geopandas as gpd import pathlib import matplotlib.pyplot as plt # from src.constants import GWS_DATA_DIR GWS_DATA_DIR = pathlib.Path("/gws/nopw/j04/ai4er/guided-team-challenge/2021/biodiversity") # Getting biotope data bio_path = GWS_DATA_DIR / "chernobyl_habitat_data" / "Biotope_EUNIS_ver1.shp" bio_data = gpd.read_file(bio_path) # getting vegetation data veg_path = GWS_DATA_DIR / "chernobyl_habitat_data" / "Vegetation_mape.shp" veg_data = gpd.read_file(veg_path) fig, (ax1,ax2) = plt.subplots(1,2, figsize=(10,4)) ax1.set_title("bio_data") bio_data.plot(ax=ax1) ax2.set_title("veg_data") veg_data.plot(ax=ax2) import folium # TODO: fix coordinates to actual location m2 = folium.Map([51.386998452, 30.092666296], zoom_start=8, tiles='cartodbpositron') # This block adds the data provided by Tom and Adham # This adds a number for each category for color coding bio_data['Eunis_name_num'] = bio_data.Eunis_name.astype('category').cat.codes.astype('int64') # Adding the colored polygons for both datasets bio_choropleth = folium.Choropleth(bio_data, data=bio_data, key_on='feature.properties.OBJECTID', columns=['OBJECTID','Eunis_name_num'], fill_color= 'YlOrBr', name="bio_data") bio_choropleth.add_to(m2) # Adding the labels folium.features.GeoJsonPopup(fields=['Eunis_name'], labels=True ).add_to(bio_choropleth.geojson) veg_data['index'] = veg_data.index veg_choropleth = folium.Choropleth(veg_data, data=veg_data, key_on='feature.properties.index', columns=['index','Vegetation'], fill_color='YlOrBr', name="veg_data") veg_choropleth.add_to(m2) # Adding more layers (satellite and openstreetmap) folium.TileLayer(tiles='OpenStreetMap').add_to(m2) folium.TileLayer( tiles = 'https://server.arcgisonline.com/ArcGIS/rest/services/World_Imagery/MapServer/tile/{z}/{y}/{x}', attr = 'Esri', name = 'Esri Satellite', overlay = False, control = True ).add_to(m2) # Adding geojson files of exclusion zone from Simon Mathis exclusion_json_path = GWS_DATA_DIR / "chernobyl_exclusion_zone_v1.geojson" exc_data = gpd.read_file(exclusion_json_path) def get_style_function(color = '#ff0000'): return lambda x: {'fillColor': color, 'color': color} colors = ['#000000','#ffff99','#ff9933','#990000','#ff0000','#000000'] for index, row in exc_data.iterrows(): folium.GeoJson(row['geometry'], name=row['name'], style_function=get_style_function(colors[index])).add_to(m2) # Adding layer control legend # (needs to be after all layers added) folium.LayerControl().add_to(m2) m2 # Btw this is probably where EUNIS comes from: # https://eunis.eea.europa.eu/ display("Bio_data", bio_data.head(3)) display("Veg_data", veg_data.head(3)) # Get a list of the Eunis labels bio_data.Eunis_name.unique().tolist() #print("Number of polygons:", len(bio_data)) len(veg_data) len(bio_data) merged_data = veg_data.merge(bio_data, on='AREA') # validate="one_to_one") print(len(merged_data)) merged_data.head() # Number of double area occurances len(veg_data) - len(veg_data.AREA.value_counts()) len(bio_data) - len(bio_data.AREA.value_counts()) ###Output _____no_output_____

notebooks/RNAseq_SNV_WF_DEV.ipynb

###Markdown Create example bash calls from workflowWorks best with non-restarted WF ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" task_id = "9aeaeaf3-0e59-4c92-a709-c6bd37431294" out_file = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-06-22_VEP.tsv", "w") # task_id = "3c20cc8e-18d7-43f2-bc2c-4a76d38a88f8" task = api.tasks.get(task_id) jobs = {} temp = {} for job in task.get_execution_details().jobs: if job.status == "COMPLETED": check = job.name.split('_') cmd = job.command_line if job.command_line == None: # pdb.set_trace() cmd = "embedded script or task retry" sys.stderr.write("WARN: Job " + job.name + " had null cmd\n") if check[-1] == "s": key = "_".join(check[:-2]) if key not in temp: jobs[job.start_time] = {} jobs[job.start_time][key] = cmd temp[key] = 1 else: temp[key] += 1 else: jobs[job.start_time] = {} jobs[job.start_time][job.name] = cmd out_file.write("Step\tType\tNum scatter\tCommand\n") for rtime in sorted(jobs.keys()): for key in jobs[rtime]: rtype = "run step" sct = "NA" if key in temp and temp[key] > 1: rtype = "scatter" sct = str(temp[key]) cmds = jobs[rtime][key].split('\n') for cmd in cmds: out_file.write(key + "\t" + rtype + "\t" + sct + "\t" + cmd + "\n") out_file.close() ###Output _____no_output_____ ###Markdown Convert tsv to markdown table ###Code import sys # max desired col width max_w = 200 tsv_in = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-06-22_VEP.tsv") out_md = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-06-22_VEP.md", "w") data = [] max_len = [] for line in tsv_in: info = line.rstrip('\n').split('\t') data.append(info) if len(max_len) == 0: for item in info: max_len.append(len(item)) else: for i in range(len(max_len)): if len(info[i]) > max_w: max_len[i] = max_w elif len(info[i]) > max_len[i]: max_len[i] = len(info[i]) # print header first d_ct = [] for i in range(len(data[0])): d_ct.append(len(data[0][i])) out_md.write(" | " + data[0][i] + "".join([" "] * max_len[i])) d_ct[i] += max_len[i] out_md.write(" |\n") for i in range(len(data[0])): out_md.write(" | " + "".join(["-"] * d_ct[i])) out_md.write(" |\n") # pdb.set_trace() for i in range(1, len(data), 1): for j in range(len(data[i])): d_ct = len(data[i][j]) + 2 out_md.write(" | " + data[i][j] + "".join([" "] * max_len[j])) d_ct += max_len[j] out_md.write(" |\n") out_md.close() ###Output _____no_output_____ ###Markdown Get run times Get run times by step ###Code def get_job_run_time(task, phrase): data = [] if re.search(phrase, task.name): try: for job in task.get_execution_details().jobs: if job.status != "COMPLETED": sys.stderr.write("Skipping job likely killed due to spot instance kill for " + job.name + " from task " + task.id + "\n") else: data.append([job.name, str((job.end_time-job.start_time).seconds/3600)]) # pdb.set_trace() hold=1 return task.id, task.name, str(task.price.amount), str((task.end_time - task.start_time).seconds/3600), data except Exception as e: return [e, task.id] else: return [] project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" phrase = "VEP R100 ANNOTATE" tasks = api.tasks.query(project=project, status="COMPLETED").all() actual_out = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/cost_est/VEP_cov-irt-actual_cost.txt", "w") actual_out.write("Task name\tTask ID\tCost\tRun Time in hours\n") step_run = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/cost_est/VEP_cov-irt_step_run_times.txt", "w") step_run.write("Run step\tRun time in hours\n") # for task in tasks: # result = get_job_run_time(task, phrase) # if len(result) > 0: # pdb.set_trace() # actual_out.write("\t".join(result[0:4]) + "\n") # for step in result[4]: # step_run.write("\t".join(step) + "\n") x = 0 m = 100 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(get_job_run_time, task, phrase): task for task in tasks} for result in concurrent.futures.as_completed(results): if len(result.result()) > 2: if x % m == 0: sys.stderr.write("Processed " + str(x) + " valid tasks\n") actual_out.write("\t".join(result.result()[0:4]) + "\n") for step in result.result()[4]: step_run.write("\t".join(step) + "\n") x += 1 elif len(result.result()) == 2: sys.stderr.write(str(result.result()[0]) + "\tFailed processing task ID " + result.result()[1] + "\n") exit(1) actual_out.close() step_run.close() ###Output Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task fc616f63-b3b1-4c5e-af7b-ff7320eee644 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task f5090a20-6c22-4797-be41-7d358a7db164 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task 8a02e36f-e613-4d0d-a0f3-f1038463cca1 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task 2622d457-209a-466b-84db-1abdb677d7e6 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task cd1d9077-c5a2-4433-bc16-b74e44f02c05 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task b43b42bf-6cb2-4d08-84b3-9cd1e30d875b Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task ead6d714-32dd-4975-9272-182f5b857ca5 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task 92e3dfad-a4d7-4a31-8d01-48009bff1e76 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task f88487a0-5dc5-4169-b454-6aafbacf4f77 Skipping job likely killed due to spot instance kill for vep-1oo-annotate from task 1fb00414-01c8-4355-886b-d22f9723f3ac Processed 0 valid tasks Processed 100 valid tasks Processed 200 valid tasks Processed 300 valid tasks Processed 400 valid tasks Processed 500 valid tasks Processed 600 valid tasks Processed 700 valid tasks ###Markdown Tag source files ###Code def tag_file(info, header): try: meta = info.rstrip('\n').split('\t') f_obj = api.files.get(meta[0]) metadata = {} for i in range(3, len(header), 1): metadata[header[i]] = meta[i] f_obj.metadata = metadata f_obj.save() except Exception as e: sys.stderr.write(str(e) + "\n") sys.stderr.write("Could not process " + info) exit(1) project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/manifests/covwc_to_tag.txt") head = next(manifest) header = head.rstrip("\n").split("\t") x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(tag_file, line, header): line for line in manifest} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' files\n') sys.stderr.flush() ###Output No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb671e4b0a6d31133e684 COVWC-20200312-P2-E02-P.all-reads_Aligned.sortedByCoord.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb672e4b0a6d31133e6a7 COVWC-20200312-P2-E02-P.all-reads_ReadsPerGene.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb672e4b0a6d31133e693 COVWC-20200312-P2-E02-P.all-reads_Chimeric.out.junction d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb673e4b0a6d31133e6e2 COVWC-20200313-P4-C01-P.all-reads_Log.final.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive Could not process 5eebb672e4b0a6d31133e6a2 COVWC-20200312-P2-E02-P.all-reads_Log.progress.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb673e4b0a6d31133e6d3 COVWC-20200313-P4-C01-P.all-reads_Aligned.sortedByCoord.out.bam.bai d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb672e4b0a6d31133e698 COVWC-20200312-P2-E02-P.all-reads_Log.final.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb672e4b0a6d31133e69d COVWC-20200312-P2-E02-P.all-reads_Log.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb671e4b0a6d31133e689 COVWC-20200312-P2-E02-P.all-reads_Aligned.sortedByCoord.out.bam.bai d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive Could not process 5eebb673e4b0a6d31133e6e7 COVWC-20200313-P4-C01-P.all-reads_Log.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb674e4b0a6d31133e6f6 COVWC-20200313-P4-C01-P.all-reads_SJ.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb674e4b0a6d31133e6f1 COVWC-20200313-P4-C01-P.all-reads_ReadsPerGene.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb673e4b0a6d31133e6dd COVWC-20200313-P4-C01-P.all-reads_Chimeric.out.junction d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb673e4b0a6d31133e6d8 COVWC-20200313-P4-C01-P.all-reads_Aligned.toTranscriptome.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive Could not process 5eebb674e4b0a6d31133e6ec COVWC-20200313-P4-C01-P.all-reads_Log.progress.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb673e4b0a6d31133e6ce COVWC-20200313-P4-C01-P.all-reads_Aligned.sortedByCoord.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-C01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb672e4b0a6d31133e6ac COVWC-20200312-P2-E02-P.all-reads_SJ.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb676e4b0a6d31133e740 COVWC-20200313-P4-D01-P.all-reads_SJ.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb671e4b0a6d31133e68e COVWC-20200312-P2-E02-P.all-reads_Aligned.toTranscriptome.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200312-P2-E02-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb676e4b0a6d31133e72c COVWC-20200313-P4-D01-P.all-reads_Log.final.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive Could not process 5eebb675e4b0a6d31133e722 COVWC-20200313-P4-D01-P.all-reads_Aligned.toTranscriptome.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb677e4b0a6d31133e762 COVWC-20200313-P4-F01-N.all-reads_Aligned.sortedByCoord.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb678e4b0a6d31133e771 COVWC-20200313-P4-F01-N.all-reads_Chimeric.out.junction d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb678e4b0a6d31133e77b COVWC-20200313-P4-F01-N.all-reads_Log.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative Could not process 5eebb678e4b0a6d31133e776 COVWC-20200313-P4-F01-N.all-reads_Log.final.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative Could not process 5eebb677e4b0a6d31133e76c COVWC-20200313-P4-F01-N.all-reads_Aligned.toTranscriptome.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative Could not process 5eebb677e4b0a6d31133e767 COVWC-20200313-P4-F01-N.all-reads_Aligned.sortedByCoord.out.bam.bai d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb676e4b0a6d31133e731 COVWC-20200313-P4-D01-P.all-reads_Log.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive Could not process 5eebb675e4b0a6d31133e718 COVWC-20200313-P4-D01-P.all-reads_Aligned.sortedByCoord.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb678e4b0a6d31133e78a COVWC-20200313-P4-F01-N.all-reads_SJ.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ae4b0a6d31133e7c7 COVWC-20200313-P4-G01-N.all-reads_Log.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb679e4b0a6d31133e7ae COVWC-20200313-P4-G01-N.all-reads_Aligned.sortedByCoord.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb679e4b0a6d31133e7bd COVWC-20200313-P4-G01-N.all-reads_Chimeric.out.junction d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ae4b0a6d31133e7c2 COVWC-20200313-P4-G01-N.all-reads_Log.final.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ae4b0a6d31133e7cc COVWC-20200313-P4-G01-N.all-reads_Log.progress.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb676e4b0a6d31133e727 COVWC-20200313-P4-D01-P.all-reads_Chimeric.out.junction d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb679e4b0a6d31133e7b8 COVWC-20200313-P4-G01-N.all-reads_Aligned.toTranscriptome.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative Could not process 5eebb679e4b0a6d31133e7b3 COVWC-20200313-P4-G01-N.all-reads_Aligned.sortedByCoord.out.bam.bai d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative Could not process 5eebb676e4b0a6d31133e736 COVWC-20200313-P4-D01-P.all-reads_Log.progress.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive Could not process 5eebb678e4b0a6d31133e780 COVWC-20200313-P4-F01-N.all-reads_Log.progress.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb678e4b0a6d31133e785 COVWC-20200313-P4-F01-N.all-reads_ReadsPerGene.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-F01-N Negative Could not process 5eebb676e4b0a6d31133e73b COVWC-20200313-P4-D01-P.all-reads_ReadsPerGene.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb675e4b0a6d31133e71d COVWC-20200313-P4-D01-P.all-reads_Aligned.sortedByCoord.out.bam.bai d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-D01-P Positive No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ae4b0a6d31133e7d6 COVWC-20200313-P4-G01-N.all-reads_SJ.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-G01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ce4b0a6d31133e80c COVWC-20200313-P4-H01-N.all-reads_Log.final.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ce4b0a6d31133e816 COVWC-20200313-P4-H01-N.all-reads_Log.progress.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67be4b0a6d31133e802 COVWC-20200313-P4-H01-N.all-reads_Aligned.toTranscriptome.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative Could not process 5eebb67be4b0a6d31133e7fd COVWC-20200313-P4-H01-N.all-reads_Aligned.sortedByCoord.out.bam.bai d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ce4b0a6d31133e81b COVWC-20200313-P4-H01-N.all-reads_ReadsPerGene.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ce4b0a6d31133e820 COVWC-20200313-P4-H01-N.all-reads_SJ.out.tab d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ce4b0a6d31133e807 COVWC-20200313-P4-H01-N.all-reads_Chimeric.out.junction d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative No relevant changes were detected in order to update the resource on the server. No relevant changes were detected in order to update the resource on the server. Could not process 5eebb67ce4b0a6d31133e811 COVWC-20200313-P4-H01-N.all-reads_Log.out d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative Could not process 5eebb67be4b0a6d31133e7f8 COVWC-20200313-P4-H01-N.all-reads_Aligned.sortedByCoord.out.bam d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study COVWC-20200313-P4-H01-N Negative ###Markdown Set up GATK4 RNAseq WF Tasks ###Code def get_gatk_refs(api, project): try: ref_dict = {} ref_dict['reference_fasta'] = api.files.get('5eebc5d1e4b0a6d311357eb9') ref_dict['reference_dict'] = api.files.get('5eecb14ae4b0efd899f474da') known_sites = [] known_sites.append(api.files.get('5eecd8c3e4b0efd899f4ae44')) known_sites.append(api.files.get('5eecd846e4b0efd899f4ae27')) known_sites.append(api.files.get('5eecd846e4b0efd899f4ae26')) known_sites.append(api.files.get('5eecd846e4b0efd899f4ae21')) ref_dict['knownsites'] = known_sites ref_dict['call_bed_file'] = api.files.get('5eebdeece4b0efd899f43eaa') ref_dict['dbsnp_vcf'] = api.files.get('5eecd846e4b0efd899f4ae24') ref_dict['tool_name'] = 'STAR_GATK4' except Exception as e: sys.stderr.write(str(e) + "\nFailed to get REFS\n") exit(1) return ref_dict def draft_task(in_file): try: input_dict = {} for key in ref_obj: input_dict[key] = ref_obj[key] info = in_file.rstrip('\n').split('\t') input_dict['STAR_sorted_genomic_bam'] = api.files.get(info[0]) task_name = "GATK RNAseq SNV: " + info[3] task = api.tasks.create(name=task_name, project=project, app=app_name, inputs=input_dict, run=False) task.inputs['output_basename'] = task.id task.save() except Exception as e: sys.stderr.write(str(e) + "\nfailed to set up task for " + in_file) exit(1) project = 'd3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study' app_name = project + "/d3b-gatk-rnaseq-snv-wf" manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/manifests/bams_for_gatk_to_run.tsv") head = next(manifest) ref_obj = get_gatk_refs(api, project) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(draft_task, line ): line for line in manifest} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' tasks\n') sys.stderr.flush() ###Output _____no_output_____ ###Markdown Run VEP ###Code def get_vep_refs(api, project): try: ref_dict = {} ref_dict['reference'] = api.files.get('5eebc5d1e4b0a6d311357eb9') ref_dict['cache'] = api.files.get('5eed0f54e4b0efd899f4afda') ref_dict['merged_cache'] = True ref_dict['tool_name'] = 'STAR_GATK4' except Exception as e: sys.stderr.write(str(e) + "\nFailed to get REFS\n") exit(1) return ref_dict def draft_vep_task(in_file): try: input_dict = {} for key in ref_obj: input_dict[key] = ref_obj[key] info = in_file.rstrip('\n').split(',') input_dict['input_vcf'] = api.files.get(info[0]) task_name = "VEP R100 ANNOTATE: " + info[3] task = api.tasks.create(name=task_name, project=project, app=app_name, inputs=input_dict, run=False) task.inputs['output_basename'] = task.id task.save() except Exception as e: sys.stderr.write(str(e) + "\nfailed to set up task for " + in_file) exit(1) project = 'd3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study' app_name = project + "/vep-1oo-annotate" manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/manifests/vcf_to_annotate-manifest.csv") head = next(manifest) ref_obj = get_vep_refs(api, project) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(draft_vep_task, line ): line for line in manifest} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' tasks\n') sys.stderr.flush() ###Output _____no_output_____ ###Markdown Copy metadata to outputs ###Code def add_metadata_to_outputs(task, phrase, in_key): if re.search(phrase, task.name): sys.stderr.write('Valid task found ' + task.name + '\n') metadata = task.inputs[in_key].metadata for out_key in task.outputs: # pdb.set_trace() try: if type(task.outputs[out_key]) is not list: file_obj = api.files.get(task.outputs[out_key].id) for key in metadata: file_obj.metadata[key] = metadata[key] file_obj.save() else: for output in task.outputs[out_key]: if type(output) is not list: file_obj = api.files.get(output.id) for key in metadata: file_obj.metadata[key] = metadata[key] file_obj.save() else: for item in output: if item is not None: file_obj = api.files.get(item.id) for key in metadata: file_obj.metadata[key] = metadata[key] file_obj.save() except Exception as e: print(e) print("Skipping " + out_key + " for " + task.name + " due to error") prefix = 'VEP R100 ANNOTATE' project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" key = 'input_vcf' print("You sure tag outputs with task prefix: " + prefix + "? Type \"YASS\" if so") check = input() if check == "YASS": tasks = api.tasks.query(project=project, status="COMPLETED").all() for task in tasks: add_metadata_to_outputs(task, prefix, key) else: sys.stderr.write("User did not type YASS, skipping\n") ###Output You sure tag outputs with task prefix: VEP R100 ANNOTATE? Type "YASS" if so YASS ###Markdown Get task outputs ###Code def write_to_manifest(out_fh, file_obj, out_key, task_name): out_fh.write(",".join([file_obj.id, file_obj.name, out_key, task_name]) + "\n") project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="COMPLETED").all() out = open('/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/manifests/test_vep_out.txt', 'w') out.write("id,name,output_category,task_name\n") phrase = "VEP R100 ANNOTATE: COVHA-20200311-P1-A01-CP" for task in tasks: if re.search(phrase, task.name): sys.stderr.write('Processing task: ' + task.name + "\n") for out_key in task.outputs: # try: if type(task.outputs[out_key]) is not list: file_obj = task.outputs[out_key] write_to_manifest(out, file_obj, out_key, task.name) if task.outputs[out_key].secondary_files is not None: write_to_manifest(out, task.outputs[out_key].secondary_files[0], out_key, task.name) else: for i in range(len(task.outputs[out_key])): if type(task.outputs[out_key][i]) is not list: write_to_manifest(out, task.outputs[out_key][i], out_key, task.name) if task.outputs[out_key][i].secondary_files is not None: write_to_manifest(out, task.outputs[out_key][i].secondary_files[0], out_key, task.name) else: for j in range(len(task.outputs[out_key][i])): if task.outputs[out_key][i][j] is not None: write_to_manifest(out, task.outputs[out_key][i][j], out_key, task.name) if task.outputs[out_key][i][j].secondary_files is not None: write_to_manifest(out, task.outputs[out_key][i][j].secondary_files[0], out_key, task.name) # except Exception as e: # print(e) # print("Skipping " + out_key + " for " + task.name + " due to error") out.close() ###Output Processing task: VEP R100 ANNOTATE: COVHA-20200311-P1-A01-CP ###Markdown Abort unresponsive and restart tasks ###Code import datetime import pytz project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="RUNNING") current = datetime.datetime.now() tz = pytz.timezone('America/New_York') prefix = "GATK RNAseq SNV" task_abort = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/TASK_RUN/aborted_and_restarted2.log", 'w') task_abort.write("Task ID\tTask name\tNew Task ID") for task in tasks: if re.search(prefix, task.name): for job in task.get_execution_details().jobs: if job.name == "preprocess_rnaseq_bam_sambamba_md_sorted": if job.status == "RUNNING": diff = (current-pytz.utc.localize(job.start_time, is_dst=None).astimezone(tz).replace(tzinfo=None)).seconds/3600 if diff > 2: task_abort.write(task.id + "\t" + task.name) in_dict = {} sys.stderr.write("Aborting " + task.id + "\t" + task.name + "\n" ) task.abort() new_task = task.clone(run=False) new_task.inputs['output_basename'] = new_task.id new_task.save() task_abort.write("\t" + new_task.id + "\n") task_abort.flush() else: break else: break task_abort.close() ###Output Aborting 2b233b53-4e04-4691-ba01-114e806a27b6 GATK RNAseq SNV: COVHA-20200403-P2-B06-N Aborting 26c0855b-3116-48fa-9f6f-680b3eadd3ef GATK RNAseq SNV: COVHA-20200403-P2-E04-N Aborting 44d400a2-4d1f-464e-93cf-32668e5da436 GATK RNAseq SNV: COVHA-20200314-P7-C08-P ###Markdown Restart failed tasks ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="FAILED") prefix = "GATK RNAseq SNV" task_restart = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/TASK_RUN/failed_and_restarted2.log", 'w') task_restart.write("Task ID\tTask name\tNew Task ID\n") run_list = ["GATK RNAseq SNV: COVHA-20200315-P9-F02-N", "GATK RNAseq SNV: COVHA-20200316-P12-F01-P","GATK RNAseq SNV: COVHA-20200403-P1-C06-P"] for task in tasks: if re.search(prefix, task.name) and task.name in run_list: task_restart.write(task.id + "\t" + task.name) new_task = task.clone(run=False) new_task.inputs['output_basename'] = new_task.id new_task.save() task_restart.write("\t" + new_task.id + "\n") task_restart.flush() task_restart.close() ###Output _____no_output_____ ###Markdown Get Failed list ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="FAILED") prefix = "GATK RNAseq SNV" task_failed = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/TASK_RUN/failed.log", 'w') task_failed.write("Task ID\tTask name\n") for task in tasks: if re.search(prefix, task.name): task_failed.write(task.id + "\t" + task.name + "\n") task_failed.close() ###Output _____no_output_____ ###Markdown Remove outputs from failed and aborted tasks ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="ABORTED") prefix = "GATK RNAseq SNV" print("You sure remove outputs from failed tasks with prefix: " + prefix + "? Type \"YASS\" if so") check = input() if check == "YASS": for task in tasks: if re.search(prefix, task.name): for key in task.outputs: if task.outputs[key] is not None: sys.stderr.write("Found files to remove from failed task: " + task.id + " " + task.name + "\n") try: if task.outputs[key].secondary_files is not None: sys.stderr.write("Removing secondary files\n") for i in range(0, len(task.outputs[key].secondary_files), 1): task.outputs[key].secondary_files[i].delete() except Exception as e: sys.stderr.write(str(e) + "\nFile with key " + key + " probably does not have secondaryFiles, skipping\n") try: task.outputs[key].delete() except Exception as e: sys.stderr.write(str(e) + "\nFile with key " + key + " was probably deleted before, skipping\n") sys.stderr.write("Finished processing " + task.id + "\n") ###Output You sure remove outputs from failed tasks with prefix: GATK RNAseq SNV? Type "YASS" if so YASS ###Markdown Rename _\d_ files ###Code manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/manifests/to_rename-manifest.csv") head = next(manifest) print("You sure you want to rename the files in that manifest? Type \"YASS\" if so") check = input() if check == "YASS": for line in manifest: info = line.split(',') cur = api.files.get(info[0]) new_name = cur.name[3:] sys.stderr.write("Renaming file with ID " + cur.id + " " + cur.name + " to " + new_name + "\n") cur.name = new_name cur.save() ###Output You sure you want to rename the files in that manifest? Type "YASS" if so YASS ###Markdown Load app into project ###Code # need to have converted app to json first using rabix! import json project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" f = open('/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/kfdrc_annoFuse_wf.json', 'r') app_raw = f.read() app = json.loads(app_raw) app_id = "kfdrc-annofuse-wf" # Create the Workflows a_id = (project + "/" + app_id) my_app_first = api.apps.install_app(id = a_id, raw = app) ###Output _____no_output_____ ###Markdown Create example bash calls from workflowWorks best with non-restarted WF ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" task_id = "00210a5f-77ec-4d07-9b1d-c08e5497e24c" out_file = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08-26_gatk4_rpt.tsv", "w") # task_id = "3c20cc8e-18d7-43f2-bc2c-4a76d38a88f8" task = api.tasks.get(task_id) jobs = {} temp = {} for job in task.get_execution_details().jobs: if job.status == "COMPLETED": check = job.name.split('_') cmd = job.command_line if job.command_line == None: # pdb.set_trace() cmd = "embedded script or task retry" sys.stderr.write("WARN: Job " + job.name + " had null cmd\n") if check[-1] == "s": key = "_".join(check[:-2]) if key not in temp: jobs[job.start_time] = {} jobs[job.start_time][key] = cmd temp[key] = 1 else: temp[key] += 1 else: jobs[job.start_time] = {} jobs[job.start_time][job.name] = cmd out_file.write("Step\tType\tNum scatter\tCommand\n") for rtime in sorted(jobs.keys()): for key in jobs[rtime]: rtype = "run step" sct = "NA" if key in temp and temp[key] > 1: rtype = "scatter" sct = str(temp[key]) cmds = jobs[rtime][key].split('\n') for cmd in cmds: out_file.write(key + "\t" + rtype + "\t" + sct + "\t" + cmd + "\n") out_file.close() ###Output _____no_output_____ ###Markdown Convert tsv to markdown table ###Code import sys # max desired col width max_w = 200 tsv_in = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08-26_gatk4_rpt.tsv") out_md = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08-26_gatk4_rpt.md", "w") data = [] max_len = [] for line in tsv_in: info = line.rstrip('\n').split('\t') data.append(info) if len(max_len) == 0: for item in info: max_len.append(len(item)) else: for i in range(len(max_len)): if len(info[i]) > max_w: max_len[i] = max_w elif len(info[i]) > max_len[i]: max_len[i] = len(info[i]) # print header first d_ct = [] for i in range(len(data[0])): d_ct.append(len(data[0][i])) out_md.write(" | " + data[0][i] + "".join([" "] * max_len[i])) d_ct[i] += max_len[i] out_md.write(" |\n") for i in range(len(data[0])): out_md.write(" | " + "".join(["-"] * d_ct[i])) out_md.write(" |\n") # pdb.set_trace() for i in range(1, len(data), 1): for j in range(len(data[i])): d_ct = len(data[i][j]) + 2 out_md.write(" | " + data[i][j] + "".join([" "] * max_len[j])) d_ct += max_len[j] out_md.write(" |\n") out_md.close() ###Output _____no_output_____ ###Markdown Get run times Get run times by step ###Code def get_job_run_time(task, phrase): data = [] if re.search(phrase, task.name): try: for job in task.get_execution_details().jobs: if job.status != "COMPLETED": sys.stderr.write("Skipping job likely killed due to spot instance kill for " + job.name + " from task " + task.id + "\n") else: data.append([job.name, str((job.end_time-job.start_time).seconds/3600)]) # pdb.set_trace() hold=1 return task.id, task.name, str(task.price.amount), str((task.end_time - task.start_time).seconds/3600), data except Exception as e: return [e, task.id] else: return [] project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" phrase = "GATK RNAseq SNV RPT" tasks = api.tasks.query(project=project, status="COMPLETED").all() actual_out = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/cost_est/gatk4_rpt_cov-irt-actual_cost.txt", "w") actual_out.write("Task name\tTask ID\tCost\tRun Time in hours\n") step_run = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/cost_est/gatk4_rpt_cov-irt_step_run_times.txt", "w") step_run.write("Run step\tRun time in hours\n") # for task in tasks: # result = get_job_run_time(task, phrase) # if len(result) > 0: # pdb.set_trace() # actual_out.write("\t".join(result[0:4]) + "\n") # for step in result[4]: # step_run.write("\t".join(step) + "\n") x = 1 m = 100 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(get_job_run_time, task, phrase): task for task in tasks} for result in concurrent.futures.as_completed(results): if len(result.result()) > 2: if x % m == 0: sys.stderr.write("Processed " + str(x) + " valid tasks\n") actual_out.write("\t".join(result.result()[0:4]) + "\n") for step in result.result()[4]: step_run.write("\t".join(step) + "\n") x += 1 elif len(result.result()) == 2: sys.stderr.write(str(result.result()[0]) + "\tFailed processing task ID " + result.result()[1] + "\n") exit(1) actual_out.close() step_run.close() ###Output _____no_output_____ ###Markdown Tag source files ###Code def tag_file(info, header): try: meta = info.rstrip('\n').split('\t') f_obj = api.files.get(meta[0]) metadata = {} for i in range(3, len(header), 1): metadata[header[i]] = meta[i] f_obj.metadata = metadata f_obj.save() except Exception as e: sys.stderr.write(str(e) + "\n") sys.stderr.write("Could not process " + info) exit(1) project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/rsem_amnifest_to_tag.tsv") head = next(manifest) header = head.rstrip("\n").split("\t") x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(tag_file, line, header): line for line in manifest} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' files\n') sys.stderr.flush() ###Output _____no_output_____ ###Markdown Set up GATK4 RNAseq WF Tasks ###Code def get_gatk_refs(api, project): try: ref_dict = {} ref_dict['reference_fasta'] = api.files.get('5f185f0de4b09d9af8ae456e') ref_dict['reference_dict'] = api.files.get('5f185f09e4b09d9af8ae4569') known_sites = [] known_sites.append(api.files.get('5f161613e4b0efd84a0fd4b8')) known_sites.append(api.files.get('5f1615e3e4b0efd84a0fd4a9')) ref_dict['knownsites'] = known_sites ref_dict['call_bed_file'] = api.files.get('5f186055e4b09d9af8ae4585') ref_dict['dbsnp_vcf'] = api.files.get('5f161572e4b0efd84a0fd49f') ref_dict['tool_name'] = 'STAR_GATK4' except Exception as e: sys.stderr.write(str(e) + "\nFailed to get REFS\n") exit(1) return ref_dict def draft_task(in_file): try: input_dict = {} for key in ref_obj: input_dict[key] = ref_obj[key] info = in_file.rstrip('\n').split('\t') input_dict['STAR_sorted_genomic_bam'] = api.files.get(info[0]) task_name = "GATK RNAseq SNV RPT: " + info[3] task = api.tasks.create(name=task_name, project=project, app=app_name, inputs=input_dict, run=False) task.inputs['output_basename'] = task.id task.save() except Exception as e: sys.stderr.write(str(e) + "\nfailed to set up task for " + in_file) exit(1) project = 'd3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study' app_name = project + "/d3b-gatk-rnaseq-snv-wf" manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08-10_bam_list.tsv") head = next(manifest) ref_obj = get_gatk_refs(api, project) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(draft_task, line ): line for line in manifest} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' tasks\n') sys.stderr.flush() ###Output _____no_output_____ ###Markdown Run VEP ###Code def get_vep_refs(api, project): try: ref_dict = {} ref_dict['reference'] = api.files.get('5f185f0de4b09d9af8ae456e') # un comment for using cache # ref_dict['cache'] = api.files.get('5eed0f54e4b0efd899f4afda') # ref_dict['merged_cache'] = True ref_dict['bgzipped_gtf'] = api.files.get('5f3550c2e4b0efd8002a853b') ref_dict['tool_name'] = 'STAR_GATK4' except Exception as e: sys.stderr.write(str(e) + "\nFailed to get REFS\n") exit(1) return ref_dict def draft_vep_task(in_file): try: input_dict = {} for key in ref_obj: input_dict[key] = ref_obj[key] info = in_file.rstrip('\n').split(',') input_dict['input_vcf'] = api.files.get(info[0]) task_name = "VEP R100 GTF ANNOTATE RPT: " + info[sidx] task = api.tasks.create(name=task_name, project=project, app=app_name, inputs=input_dict, run=False) task.inputs['output_basename'] = task.id task.save() except Exception as e: sys.stderr.write(str(e) + "\nfailed to set up task for " + in_file) exit(1) project = 'd3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study' app_name = project + "/vep-1oo-annotate" manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08_manifests/vcf-manifest.csv") head = next(manifest) header = head.rstrip('\n').split(',') sidx = header.index('sample_id') ref_obj = get_vep_refs(api, project) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(draft_vep_task, line ): line for line in manifest} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' tasks\n') sys.stderr.flush() x += 1 ###Output _____no_output_____ ###Markdown Run STAR Fusion ###Code def get_sf_refs(api, project): try: ref_dict = {} ref_dict['genome_tar'] = api.files.get('5f19e9cee4b0a6d31720b606') ref_dict['genome_untar_path'] = 'ctat_genome_lib_build_dir' except Exception as e: sys.stderr.write(str(e) + "\nFailed to get REFS\n") exit(1) return ref_dict def draft_sf_task(in_file): try: input_dict = {} for key in ref_obj: input_dict[key] = ref_obj[key] info = in_file.rstrip('\n').split(',') input_dict['Chimeric_junction'] = api.files.get(info[0]) task_name = "STAR FUSION: " + info[sidx] task = api.tasks.create(name=task_name, project=project, app=app_name, inputs=input_dict, run=False) task.inputs['SampleID'] = task.id task.save() except Exception as e: sys.stderr.write(str(e) + "\nfailed to set up task for " + in_file) exit(1) project = 'd3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study' app_name = project + "/star-fusion-covirt" manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08_manifests/chim_junction-manifest.csv") head = next(manifest) header = head.rstrip('\n').split(',') sidx = header.index('sample_id') ref_obj = get_sf_refs(api, project) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(draft_sf_task, line ): line for line in manifest} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' tasks\n') sys.stderr.flush() x += 1 ###Output _____no_output_____ ###Markdown Run arriba ###Code def get_arriba_refs(api, project): try: ref_dict = {} ref_dict['reference_fasta'] = api.files.get('5f185f0de4b09d9af8ae456e') ref_dict['gtf_anno'] = api.files.get('5f186055e4b09d9af8ae4585') except Exception as e: sys.stderr.write(str(e) + "\nFailed to get REFS\n") exit(1) return ref_dict def draft_arriba_task(samp_id): try: input_dict = {} for key in ref_obj: input_dict[key] = ref_obj[key] for key in inputs[samp_id]: input_dict[key] = api.files.get(inputs[samp_id][key]) task_name = "ARRIBA FUSION: " + samp_id task = api.tasks.create(name=task_name, project=project, app=app_name, inputs=input_dict, run=False) task.inputs['outFileNamePrefix'] = task.id task.save() except Exception as e: sys.stderr.write(str(e) + "\nfailed to set up task for " + in_file) exit(1) project = 'd3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study' app_name = project + "/arriba-fusion" inputs = {} # process two manifests, chimeric_sam, genome bam + bai, chim_sam = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08_manifests/chimeric_sam-manifest.csv") head = next(chim_sam) header = head.rstrip('\n').split(',') sidx = header.index('sample_id') for line in chim_sam: info = line.rstrip('\n').split(',') inputs[info[sidx]] = {} inputs[info[sidx]]['chimeric_sam_out'] = info[0] chim_sam.close() ba_manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08_manifests/bam_bai.csv") head = next(ba_manifest) header = head.rstrip('\n').split(',') sidx = header.index('sample_id') for line in ba_manifest: info = line.rstrip('\n').split(',') suffix = info[1][-3:] inputs[info[sidx]][('genome_aligned_' + suffix)] = info[0] ba_manifest.close() ref_obj = get_arriba_refs(api, project) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(draft_arriba_task, samp_id ): samp_id for samp_id in inputs} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' tasks\n') sys.stderr.flush() x += 1 # for samp_id in inputs: # draft_arriba_task(samp_id) ###Output _____no_output_____ ###Markdown Run annoFuse ###Code def get_af_refs(api, project): try: ref_dict = {} ref_dict['FusionGenome'] = api.files.get('5f19e9cee4b0a6d31720b606') ref_dict['genome_untar_path'] = 'ctat_genome_lib_build_dir' except Exception as e: sys.stderr.write(str(e) + "\nFailed to get REFS\n") exit(1) return ref_dict def draft_annofuse_task(samp_id): try: input_dict = {} for key in ref_obj: input_dict[key] = ref_obj[key] for key in inputs[samp_id]: input_dict[key] = api.files.get(inputs[samp_id][key]) input_dict['sample_name'] = samp_id task_name = "annoFuse: " + samp_id task = api.tasks.create(name=task_name, project=project, app=app_name, inputs=input_dict, run=False) task.inputs['output_basename'] = task.id task.save() except Exception as e: sys.stderr.write(str(e) + "\nfailed to set up task for " + in_file) exit(1) project = 'd3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study' app_name = project + "/kfdrc-annofuse-wf" inputs = {} # process two manifests, fusion files, rsem, rsem_files = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08-20_rsem_annfuse_manifest.tsv") head = next(rsem_files) header = head.rstrip('\n').split('\t') sidx = header.index('sample_id') for line in rsem_files: info = line.rstrip('\n').split('\t') inputs[info[sidx]] = {} inputs[info[sidx]]['rsem_expr_file'] = info[0] rsem_files.close() fusions = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/2020-08-20_fusion_results-manifest.csv") head = next(fusions) header = head.rstrip('\n').split(',') sidx = header.index('sample_id') for line in fusions: info = line.rstrip('\n').split(',') key = 'arriba_output_file' if re.search("STAR", info[1]): key = 'star_fusion_output_file' inputs[info[sidx]][key] = info[0] fusions.close() ref_obj = get_af_refs(api, project) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(draft_annofuse_task, samp_id ): samp_id for samp_id in inputs} for result in concurrent.futures.as_completed(results): if x % m == 0: sys.stderr.write('Processed ' + str(x) + ' tasks\n') sys.stderr.flush() x += 1 ###Output _____no_output_____ ###Markdown Copy metadata to outputs ###Code def add_metadata_to_outputs(task, phrase, in_key): if re.search(phrase, task.name): sys.stderr.write('Valid task found ' + task.name + '\n') metadata = {} for key in task.inputs[in_key].metadata: metadata[key] = task.inputs[in_key].metadata[key] for out_key in task.outputs: # pdb.set_trace() try: if type(task.outputs[out_key]) is not list: file_obj = api.files.get(task.outputs[out_key].id) file_obj.metadata = metadata file_obj.save() try: if task.outputs[out_key].secondary_files is not None: file_obj = api.files.get(task.outputs[out_key].secondary_files[0].id) file_obj.metadata = metadata file_obj.save() except Exception as e: sys.stderr.write(str(e) + "\nError processing secondary file for " + out_key + " in " + task.id + " skipping\n") else: for output in task.outputs[out_key]: if type(output) is not list: file_obj = api.files.get(output.id) file_obj.metadata = metadata file_obj.save() else: for item in output: if item is not None: file_obj = api.files.get(item.id) file_obj.metadata = metadata file_obj.save() except Exception as e: print(e) print("Skipping " + out_key + " for " + task.name + " due to error") prefix = 'VEP R100 GTF ANNOTATE RPT' project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" key = 'input_vcf' print("You sure you want to transfer input metadata to outputs with task prefix: " + prefix + "? Type \"YASS\" if so") check = input() if check == "YASS": tasks = api.tasks.query(project=project, status="COMPLETED").all() #for task in tasks: # add_metadata_to_outputs(task, prefix, key) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(add_metadata_to_outputs, task, prefix, key ): task for task in tasks} else: sys.stderr.write("User did not type YASS, skipping\n") ###Output _____no_output_____ ###Markdown Add tags to task outputs ###Code def add_tags_to_outputs(task, phrase, tags): if re.search(phrase, task.name): sys.stderr.write('Valid task found ' + task.name + '\n') for out_key in task.outputs: # pdb.set_trace() try: if type(task.outputs[out_key]) is not list: file_obj = api.files.get(task.outputs[out_key].id) file_obj.tags = tags file_obj.save() try: if task.outputs[out_key].secondary_files is not None: file_obj = api.files.get(task.outputs[out_key].secondary_files[0].id) file_obj.tags = tags file_obj.save() except Exception as e: sys.stderr.write(str(e) + "\nError processing secondary file for " + out_key + " in " + task.id + " skipping\n") else: for output in task.outputs[out_key]: if type(output) is not list: file_obj = api.files.get(output.id) file_obj.tags = tags file_obj.save() else: for item in output: if item is not None: file_obj = api.files.get(item.id) file_obj.tags = tags file_obj.save() except Exception as e: print(e) print("Skipping " + out_key + " for " + task.name + " due to error") prefix = 'VEP R100 GTF ANNOTATE' project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tags = ['GATK4', 'VEP', 'R100', 'GTF-ANNOTATED'] print("You sure tag outputs with task prefix: " + prefix + "? Type \"YASS\" if so") check = input() if check == "YASS": tasks = api.tasks.query(project=project, status="COMPLETED").all() #for task in tasks: # add_metadata_to_outputs(task, prefix, key) x = 1 m = 250 with concurrent.futures.ThreadPoolExecutor(16) as executor: results = {executor.submit(add_tags_to_outputs, task, prefix, tags ): task for task in tasks} else: sys.stderr.write("User did not type YASS, skipping\n") ###Output _____no_output_____ ###Markdown Get task outputs ###Code def write_to_manifest(out_fh, file_obj, out_key, task_name): out_fh.write(",".join([file_obj.id, file_obj.name, out_key, task_name]) + "\n") project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="COMPLETED").all() out = open('/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/manifests/test_vep_out.txt', 'w') out.write("id,name,output_category,task_name\n") phrase = "VEP R100 ANNOTATE: COVHA-20200311-P1-A01-CP" for task in tasks: if re.search(phrase, task.name): sys.stderr.write('Processing task: ' + task.name + "\n") for out_key in task.outputs: if type(task.outputs[out_key]) is not list: file_obj = task.outputs[out_key] write_to_manifest(out, file_obj, out_key, task.name) if task.outputs[out_key].secondary_files is not None: write_to_manifest(out, task.outputs[out_key].secondary_files[0], out_key, task.name) else: for i in range(len(task.outputs[out_key])): if type(task.outputs[out_key][i]) is not list: write_to_manifest(out, task.outputs[out_key][i], out_key, task.name) if task.outputs[out_key][i].secondary_files is not None: write_to_manifest(out, task.outputs[out_key][i].secondary_files[0], out_key, task.name) else: for j in range(len(task.outputs[out_key][i])): if task.outputs[out_key][i][j] is not None: write_to_manifest(out, task.outputs[out_key][i][j], out_key, task.name) if task.outputs[out_key][i][j].secondary_files is not None: write_to_manifest(out, task.outputs[out_key][i][j].secondary_files[0], out_key, task.name) out.close() ###Output _____no_output_____ ###Markdown Abort unresponsive and restart tasks ###Code import datetime import pytz project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="RUNNING") current = datetime.datetime.now() tz = pytz.timezone('America/New_York') prefix = "GATK RNAseq SNV" task_abort = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/TASK_RUN/aborted_and_restarted2.log", 'w') task_abort.write("Task ID\tTask name\tNew Task ID") for task in tasks: if re.search(prefix, task.name): for job in task.get_execution_details().jobs: if job.name == "preprocess_rnaseq_bam_sambamba_md_sorted": if job.status == "RUNNING": diff = (current-pytz.utc.localize(job.start_time, is_dst=None).astimezone(tz).replace(tzinfo=None)).seconds/3600 if diff > 2: task_abort.write(task.id + "\t" + task.name) in_dict = {} sys.stderr.write("Aborting " + task.id + "\t" + task.name + "\n" ) task.abort() new_task = task.clone(run=False) new_task.inputs['output_basename'] = new_task.id new_task.save() task_abort.write("\t" + new_task.id + "\n") task_abort.flush() else: break else: break task_abort.close() ###Output _____no_output_____ ###Markdown Restart failed tasks ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="FAILED") prefix = "GATK RNAseq SNV" task_restart = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/TASK_RUN/failed_and_restarted2.log", 'w') task_restart.write("Task ID\tTask name\tNew Task ID\n") run_list = ["GATK RNAseq SNV: COVHA-20200315-P9-F02-N", "GATK RNAseq SNV: COVHA-20200316-P12-F01-P","GATK RNAseq SNV: COVHA-20200403-P1-C06-P"] for task in tasks: if re.search(prefix, task.name) and task.name in run_list: task_restart.write(task.id + "\t" + task.name) new_task = task.clone(run=False) new_task.inputs['output_basename'] = new_task.id new_task.save() task_restart.write("\t" + new_task.id + "\n") task_restart.flush() task_restart.close() ###Output _____no_output_____ ###Markdown Get Failed list ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="FAILED") prefix = "GATK RNAseq SNV" task_failed = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/TASK_RUN/failed.log", 'w') task_failed.write("Task ID\tTask name\n") for task in tasks: if re.search(prefix, task.name): task_failed.write(task.id + "\t" + task.name + "\n") task_failed.close() ###Output _____no_output_____ ###Markdown Remove outputs from failed and aborted tasks ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="ABORTED") prefix = "GATK RNAseq SNV" print("You sure remove outputs from failed tasks with prefix: " + prefix + "? Type \"YASS\" if so") check = input() if check == "YASS": for task in tasks: if re.search(prefix, task.name): for key in task.outputs: if task.outputs[key] is not None: sys.stderr.write("Found files to remove from failed task: " + task.id + " " + task.name + "\n") try: if task.outputs[key].secondary_files is not None: sys.stderr.write("Removing secondary files\n") for i in range(0, len(task.outputs[key].secondary_files), 1): task.outputs[key].secondary_files[i].delete() except Exception as e: sys.stderr.write(str(e) + "\nFile with key " + key + " probably does not have secondaryFiles, skipping\n") try: task.outputs[key].delete() except Exception as e: sys.stderr.write(str(e) + "\nFile with key " + key + " was probably deleted before, skipping\n") sys.stderr.write("Finished processing " + task.id + "\n") ###Output _____no_output_____ ###Markdown Rename _\d_ files ###Code manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/to_rename.txt") head = next(manifest) print("You sure you want to rename the files in that manifest? Type \"YASS\" if so") check = input() sep = "\t" if check == "YASS": for line in manifest: info = line.split(sep) cur = api.files.get(info[0]) new_name = cur.name[3:] sys.stderr.write("Renaming file with ID " + cur.id + " " + cur.name + " to " + new_name + "\n") cur.name = new_name cur.save() ###Output _____no_output_____ ###Markdown Tag outputs by task seq id ###Code project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" tasks = api.tasks.query(project=project, status="COMPLETED").all() manifest = open('/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/manifests/2020-06-23_UPDATED_HUMAN_MANIFEST.txt') head = next(manifest) header = head.rstrip('\n').split("\t") phrase = "GATK RNAseq SNV RPT" meta_dict = {} for entry in manifest: info = entry.rstrip('\n').split('\t') meta_dict[info[0]] = {} for i in range(0, len(header), 1): meta_dict[info[0]][header[i]] = info[i] manifest.close() for task in tasks: if re.search(phrase, task.name): sys.stderr.write('Processing task: ' + task.name + "\n") parts = task.name.split() # Mason lab changed dashes to underscore seq_id = parts[-1].replace('-','_' ) if seq_id in meta_dict: for out_key in task.outputs: if type(task.outputs[out_key]) is not list: try: file_obj = api.files.get(task.outputs[out_key].id) file_obj.metadata = meta_dict[seq_id] file_obj.save() except Exception as e: sys.stderr.write(str(e) + "\n" + file_obj.name + " probably already tagged, skipping\n" ) try: if task.outputs[out_key].secondary_files is not None: file_obj = api.files.get(task.outputs[out_key].secondary_files[0].id) file_obj.metadata = meta_dict[seq_id] file_obj.save() except Exception as e: sys.stderr.write(str(e) + "\nError processing secondary file for " + out_key + " in " + task.id + " skipping\n") else: sys.stderr.write("Not in manifest: " + task.name + " " + task.id + "\n") ###Output _____no_output_____ ###Markdown Delete files by name ###Code manifest = open("/Users/brownm28/Documents/2020-Apr-8_RNAseq_snv_dev/delme_files.txt") project = "d3b-bixu/rs-vpf5jbc3-cov-irt-controlled-access-study" head = next(manifest) print("You sure you want to delete the files in that manifest? Type \"YASS\" if so") check = input() max_j = 25 ct = 0 found = 0 fnames = [] if check == "YASS": for line in manifest: fnames.append(line.rstrip('\n')) ct +=1 sys.stderr.write("Searching for " + str(ct) + " files to delete\n") total = len(fnames) for i in range(0, total, max_j): uset = i + max_j if uset > total: uset = total flist = api.files.query(project=project, names=fnames[i:uset]) for fobj in flist: sys.stderr.write("Deleting " + fobj.name + " with ID " + fobj.id) fobj.delete() found += 1 sys.stderr.write("Deleted " + str(found) + " files\n") ###Output _____no_output_____

examples/user_guide/Specifying_Meshes.ipynb

###Markdown This notebook demonstrates one way to use the Bokeh/HoloViews [Drawing Tools](Drawing_Tools.ipynb) and the EarthSim [Annotators](Annotators.ipynb) to define polygons and refine points to specify how to generate a ``FiligreeMesh`` irregular triangular grid covering an area of a map. This mesh can then be used as an input to a simulator that will use the indicated level of detail in each region of a map. ###Code import panel as pn import holoviews as hv import geoviews as gv import cartopy.crs as ccrs from earthsim.annotators import PolyAndPointAnnotator from earthsim.filigree import FiligreeMesh, FiligreeMeshDashboard hv.extension('bokeh') %opts Polygons (color='red' alpha=0.5 selection_alpha=0.8 nonselection_alpha=0.2) %opts Points (size=10 nonselection_alpha=0.5) [tools=['hover']] RGB [width=900 height=600] ###Output _____no_output_____ ###Markdown Simple workflow1. Edit the existing polygon or delete it and draw one or more polygons of your own2. Draw one or more refine points within this region, adding a numeric size for each one by editing the 'Size' column in the subsequent table. ###Code bounds = (-10130073.550868405, 3789592.5934560597, -10107809.875348726, 3815932.0009413) annot = PolyAndPointAnnotator(polys=[hv.Bounds(bounds)]) annot.panel() ###Output _____no_output_____ ###Markdown The ``FiligreeMesh`` class accepts a ``GeoAnnotator`` and adds the polygons and refine points drawn using it to an underlying filigree.FiligreeMesh. Once the polygons and points are added we can create a constant size function and declare the mesh size and then run and view the resultant mesh: ###Code mesh = FiligreeMesh(draw_helper=annot) mesh.mesh.create_constant_size_function(500, 5) mesh.mesh.set_outside_mesh_size(500) mesh.view() ###Output _____no_output_____ ###Markdown Here sizes should be in meters. Note that as of this writing, if you select size values that, when combined with the location of your point, extend beyond the boundaries of the polygon, Filigree will ignore that point, which can be confusing. DashboardInstead of splitting the above workflow across two notebook cells, we can instead organize it as a single plot, which computes the mesh whenever we press a button. ###Code annot = PolyAndPointAnnotator(extent=(-110, 42, -109, 43)) dashboard = FiligreeMeshDashboard(draw_helper=annot) dashboard.mesh.create_constant_size_function(500, 5) dashboard.mesh.set_outside_mesh_size(500) dashboard.panel() ###Output _____no_output_____ ###Markdown This notebook demonstrates one way to use the Bokeh/HoloViews [Drawing Tools](Drawing_Tools.ipynb) and the EarthSim [Annotators](Annotators.ipynb) to define polygons and refine points to specify how to generate a ``FiligreeMesh`` irregular triangular grid covering an area of a map. This mesh can then be used as an input to a simulator that will use the indicated level of detail in each region of a map. ###Code import holoviews as hv import geoviews as gv import cartopy.crs as ccrs import parambokeh from earthsim.annotators import PolyAndPointAnnotator from earthsim.filigree import FiligreeMesh, FiligreeMeshDashboard hv.extension('bokeh') ###Output _____no_output_____ ###Markdown Simple workflow1. Edit the existing polygon or delete it and draw one or more polygons of your own2. Draw one or more refine points within this region, adding a numeric size for each one by editing the 'Size' column in the subsequent table. ###Code %%opts Polygons (color='red' alpha=0.5 selection_alpha=0.8 nonselection_alpha=0.2) %%opts Points (size=10 nonselection_alpha=0.5) bounds = (-10130073.550868405, 3789592.5934560597, -10107809.875348726, 3815932.0009413) annot = PolyAndPointAnnotator(polys=[hv.Bounds(bounds)]) annot.view() ###Output _____no_output_____ ###Markdown The ``FiligreeMesh`` class accepts a ``GeoAnnotator`` and adds the polygons and refine points drawn using it to an underlying filigree.FiligreeMesh. Once the polygons and points are added we can create a constant size function and declare the mesh size and then run and view the resultant mesh: ###Code %%opts RGB [width=900 height=600] %%opts Points (size=10 color='blue') [tools=['hover']] mesh = FiligreeMesh(draw_helper=annot) mesh.mesh.create_constant_size_function(500, 5) mesh.mesh.set_outside_mesh_size(500) mesh.view() ###Output _____no_output_____ ###Markdown Here sizes should be in meters. Note that as of this writing, if you select size values that, when combined with the location of your point, extend beyond the boundaries of the polygon, Filigree will ignore that point, which can be confusing. DashboardInstead of splitting the above workflow across two notebook cells, we can instead organize it as a single plot, which computes the mesh whenever we press a button. ###Code %%opts Polygons (color='red' alpha=0.5 selection_alpha=0.8 nonselection_alpha=0.2) %%opts Points (size=10 nonselection_alpha=0.5) annot = PolyAndPointAnnotator() dashboard = FiligreeMeshDashboard(draw_helper=annot) dashboard.mesh.create_constant_size_function(500, 5) dashboard.mesh.set_outside_mesh_size(500) parambokeh.Widgets(dashboard) dashboard.view() ###Output _____no_output_____ ###Markdown This notebook demonstrates one way to use the Bokeh/HoloViews [Drawing Tools](Drawing_Tools.ipynb) and the EarthSim [Annotators](Annotators.ipynb) to define polygons and refine points to specify how to generate a ``FiligreeMesh`` irregular triangular grid covering an area of a map. This mesh can then be used as an input to a simulator that will use the indicated level of detail in each region of a map. ###Code import panel as pn import holoviews as hv import geoviews as gv import cartopy.crs as ccrs from earthsim.annotators import PolyAndPointAnnotator from earthsim.filigree import FiligreeMesh, FiligreeMeshDashboard hv.extension('bokeh') ###Output _____no_output_____ ###Markdown Simple workflow1. Edit the existing polygon or delete it and draw one or more polygons of your own2. Draw one or more refine points within this region, adding a numeric size for each one by editing the 'Size' column in the subsequent table. ###Code %%opts Polygons (color='red' alpha=0.5 selection_alpha=0.8 nonselection_alpha=0.2) %%opts Points (size=10 nonselection_alpha=0.5) bounds = (-10130073.550868405, 3789592.5934560597, -10107809.875348726, 3815932.0009413) annot = PolyAndPointAnnotator(polys=[hv.Bounds(bounds)]) annot.view() ###Output _____no_output_____ ###Markdown The ``FiligreeMesh`` class accepts a ``GeoAnnotator`` and adds the polygons and refine points drawn using it to an underlying filigree.FiligreeMesh. Once the polygons and points are added we can create a constant size function and declare the mesh size and then run and view the resultant mesh: ###Code %%opts RGB [width=900 height=600] %%opts Points (size=10 color='blue') [tools=['hover']] mesh = FiligreeMesh(draw_helper=annot) mesh.mesh.create_constant_size_function(500, 5) mesh.mesh.set_outside_mesh_size(500) mesh.view() ###Output _____no_output_____ ###Markdown Here sizes should be in meters. Note that as of this writing, if you select size values that, when combined with the location of your point, extend beyond the boundaries of the polygon, Filigree will ignore that point, which can be confusing. DashboardInstead of splitting the above workflow across two notebook cells, we can instead organize it as a single plot, which computes the mesh whenever we press a button. ###Code %%opts Polygons (color='red' alpha=0.5 selection_alpha=0.8 nonselection_alpha=0.2) %%opts Points (size=10 nonselection_alpha=0.5) annot = PolyAndPointAnnotator() dashboard = FiligreeMeshDashboard(draw_helper=annot) dashboard.mesh.create_constant_size_function(500, 5) dashboard.mesh.set_outside_mesh_size(500) pn.Row(dashboard.param, dashboard.view()) ###Output _____no_output_____

notebooks/Temperature Conversion.ipynb

###Markdown Fahrenheit to Celsius=========== ###Code Fahrenheit = 32.0 Celsius = (Fahrenheit - 32) * 5.0/9.0 print("Temperature: {F} Fahrenheit = {C} Celsius".format(F=Fahrenheit, C=Celsius)) ###Output Temperature: 32.0 Fahrenheit = 0.0 Celsius ###Markdown Celsius to Fahrenheit=========== ###Code Celsius = 100.0 Fahrenheit = 9.0/5.0 * Celsius + 32 print("Temperature: {C} Celsius = {F} Fahrenheit".format(F=Fahrenheit, C=Celsius)) ###Output Temperature: 100.0 Celsius = 212.0 Fahrenheit ###Markdown Plot Example======= ###Code %matplotlib inline import matplotlib.pyplot as plt def C2F(C): return 9.0/5.0 * C + 32 C2F(100) x = [C2F(c) for c in range(101)] x[0:10] plt.title("Temperature Conversion") plt.xlabel("Celsius") plt.ylabel("Fahrenheit") plt.plot(x) ###Output _____no_output_____

Challenge_September_2020.ipynb

###Markdown Ingham Medical Physics Coding Challenge - September 2020This Jupyter notebook describes the coding challenge for the Radiotherapy Computer Scientist position within the Ingham Institute Medical Physics Group hiring in September 2020. The goal of this challenge is to train a model to predict outcomes for cancer patients and present the results. DataThis task makes use of data obtained from The Cancer Imaging Archive: Head-Neck-Radiomics-HN1 (https://wiki.cancerimagingarchive.net/display/Public/Head-Neck-Radiomics-HN1) which is available under the Attribution-NonCommercial 3.0 Unported licence. This dataset includes clinical data and computed tomography (CT) from 137 head and neck squamous cell carcinoma (HNSCC) patients treated with radiotherapy. Structures within the CT images have also been manually delineated by an experienced radiation oncologist.Two CSV files provided alongside this notebook in the **data** directory: HN_ClinicalData.csvThis sheet contains the clinical data of the patients included within the Head-Neck-Radiomics-HN1 dataset. It provides information such as the patient's age, stage of disease and various outcomes. Additionally, these patients have also been randomly split into a **train** and **test** set (see the dataset column). HN_Radiomics.csvRadiomic features have been generated using the patient's image data available in the Head-Neck-Radiomics-HN1 dataset. The **pyradiomics** library was used to extract first-order and shape features from the patients CT scan. Features are computed per structure (region of interest).A structure of particular significance for radiotherapy is the Gross Tumour Volume (GTV). This describes the position and extent of the tissue identified as tumour (See https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1434601/ for more information). Note that patients may have more than one GTV, therefore these are named using GTV-1, GTV-2,... GTV-*n* where *n* is the number of tumour volumes for that patient. TaskUsing the data found in the two CSV files, train a model which can predict an outcome for a patient. A common outcome to predict would be the overall survival for the patient (can be found in the column *overall_survival_in_days* within the clinical data). Some different outcomes are also available within this clinical data such as the *recurrence_metastatic_free_survival_in_days*, *local_recurrence_in_days* and *distant_metastases_in_days*.Make use of the clinical data and radiomic features to attempt to predict these outcomes. Hint: The GTV will probably be the most useful structure to help you predict this since this describes the cancerous tissue. Since multiple GTV's are available for many patients, you will need think about a good way to combine these rows for those patients. There are also many radiomic features available, think about selecting a subset of these to train your model which you think might be useful to predict a particular outcome for a patient.Train the model using the patients in the **train** dataset (dataset column in the clinical data). Then test your model using the patients in the **test** dataset. Think about different algorithms you might want to try for your model. Doing a regression to predict the outcome might be difficult to get good results, so you could try assigning patients to a "good" or "bad" outcome class and turn this into a classification problem.Finally, generate one or more plots which show how well your model is performing to predict a certain outcome. NoteThe aim of this challenge is not to build a model with excellent results, so don't worry if your model isn't performing all that well. This is a cutting-edge topic of active research and is not easy to solve. What we want to see is how you approach a problem like this, how you present your results and your overall coding style. SubmissionIn this Jupyter notebook some Python code is provided to get you started with the challenge. The libraries you'll need are defined in the accompanying *requirements.txt* file. To complete the challenge, you can extend this notebook with your code. If you prefer, you can provide your solution in a separate file (or files) as well.If you would prefer to complete this task in a different programming language, no problem! Feel free to use R, MATLAB or anything else you feel is appropriate.The suggested way to submit your result to this challenge is to fork this GitHub repository and commit your results to your fork. Once complete just send us a link ([email protected]) to your forked repository. This will mean your submission is publicly visible. If you would prefer to keep your submission private, this is also no problem. You will just need to duplicate this repository (https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/duplicating-a-repository), then add **@pchlap** as a user to your private repository so that we can see your results.**Due Date:** September 30th @ 11.59pm AEST.If you have any questions, post them as an issue on this GitHub repository or directly email [email protected]. Resources - **pyradiomics** features: https://pyradiomics.readthedocs.io/en/latest/features.html - **pandas**: https://pandas.pydata.org/docs/ - **scikit-learn**: https://scikit-learn.org/stable/user_guide.html - **seaborn**: https://seaborn.pydata.org/index.html Good luck! ###Code from pathlib import Path # Define paths to our data data_path = Path("data") radiomics_path = data_path.joinpath("HN_Radiomics.csv") clinical_data_path = data_path.joinpath("HN_ClinicalData.csv") import pandas as pd # Load the data df_clinical_data = pd.read_csv(clinical_data_path) df_radiomics = pd.read_csv(radiomics_path) ###Output _____no_output_____ ###Markdown Extract and combine specific featuresThis cell demonstrates how you might extract radiomic features (VoxelVolume and SurfaceArea) for all GTVs. Since there can be multiple GTVs per patient, these are combined by summing the values for each patient here.You'll probably want to extend this to extract more features. Think about how you would combine other features, in other cases computing the mean value might be more appropriate or perhaps you don't want to combine them at all?Also, take a look at what else is available in the clinical data, perhaps you'd like to use some of these features as well (patient age or cancer stage). ###Code df_gtv_radiomics = df_radiomics[df_radiomics["Structure"].str.startswith("GTV")] df_gtv_radiomics = df_gtv_radiomics.groupby("id")[["VoxelVolume", "SurfaceArea"]].sum() # TODO: Extract more/different features ###Output _____no_output_____ ###Markdown Merge feature(s) with clinical dataThis cell combines the feature with the clinical data in a DataFrame. ###Code df = df_clinical_data.merge(df_gtv_radiomics, on="id") ###Output _____no_output_____ ###Markdown Plot our dataHere we plot the features we just extracted against the patient outcome (overall survival in days). ###Code import seaborn as sns pair_grid = sns.PairGrid(df, y_vars=["overall_survival_in_days"], x_vars=["VoxelVolume", "SurfaceArea"], height=6, hue="dataset") ax = pair_grid.map(sns.scatterplot) ax = pair_grid.add_legend() ###Output _____no_output_____ ###Markdown Fit your modelUsing the data you have prepared above, fit a model to see if you can predict the outcome of the patients. If you're not sure where to start, try using a linear regression...Regression not working well? Try turning this into a classification problem and see if you can instead predict a "good" or a "bad" outcome.Experiment with different algorithms for your model. There are many available in the sklearn library, but feel free to use something different if you prefer. ###Code from sklearn.linear_model import LinearRegression X_train = df[df["dataset"]=="train"][["VoxelVolume", "SurfaceArea"]] X_test = df[df["dataset"]=="test"][["VoxelVolume", "SurfaceArea"]] y_train = df[df["dataset"]=="train"]["overall_survival_in_days"] y_test = df[df["dataset"]=="test"]["overall_survival_in_days"] # TODO: Fit model... ###Output _____no_output_____ ###Markdown Plot ResultsVisualize the performance of your model with some plots. Try to be creative and think about some unique ways to allow others to explore your results. ###Code # TODO: Plot results... ###Output _____no_output_____

dev_setups_postgres.ipynb

###Markdown Dev Setups -- Connecting Python and SQLThe purpose of this Jupyter notebook is to demonstrate the usefulness of connecting python to a relational database by using a python toolkit called SQLAlchemy.***Note! The commands below were written for Python 2. Small adjustments will need to be made to some (i.e. Print statements) in Python 3.*** ***First off, what is a relational database?***Basically, it is a way to store data such that information can be retrieved from it.MySQL and PostgreSQL are examples of relational databases. For the purposes of an Insight project, you can use either one.Why would you use a relational database instead of a csv or two?**A few reasons:**- They scale easily- They are easy to query- It’s possible to do transactions in those cases where you need to write to a database, not just read from it- Everyone in industry uses them, so you should get familiar with them, too. ***What does a relational database look like? *****Let's setup PostgreSQL**We can take a look. First we need to set up a few things. The first thing we want to do is to get a PostgreSQL server up and running. Go to http://postgresapp.com/ and follow the three steps listed in the Quick Installation Guide. (If you aren't running a Mac, you can download PostgreSQL at http://www.postgresql.org/) -- you can also use homebrew, but your path will change below -- **If you're on a mac, you might need to add psql to PATH**:**Edit your .bash_profile in your home directory. Since you already installed Anaconda, it should look something like:**```export PATH="/Users/YOUR_USER_NAME/anaconda/bin:$PATH"```**Right below the line added by anaconda you can add this line:**```export PATH="/Applications/Postgres.app/Contents/Versions/latest/bin:$PATH"```**Save and reload the bash profile**```$ source .bash_profile```**The only user right now for PSQL is 'postgres', you can make your database and enter it with that username**```$ createdb birth_db -U postgres``````$ psql birth_db```**If you want to make a new user for this database you can make one now. Note: username in the below line must match your Mac/Linux username:**```CREATE USER username SUPERUSER PASSWORD 'yourpassword'```**Exit out of PSQL (\q) and test logging in through this user:**```$ psql birth_db -h localhost -U username``````$ \c ``` (once in PSQL to check how you're logged in)We'll come back to PostgreSQL in a moment. First, we'll set up SQLAlchemy. To get started we need to install two packages into the environment that might not be installed. Run the cell below or enter the commands (without !) into the command line. Note that if you did an Anaconda installation, sqlalchemy_utils is only available through pip, and if you didn't install pip into your environment (dev_setups_conda-part1.html) you will run into problems. Also, you need to install psycopg2 using conda, otherwise you will probably run into different problems. If you mainly installed packages using pip, change the next commands to reflect that. In jupyter you can run code in the command line with the "!" special character as you'll see in the next cell. We do this here for ease but it's generally considered poor practice. ###Code !pip install sqlalchemy_utils !conda install psycopg2 -y ## Python packages - you may have to pip install sqlalchemy, sqlalchemy_utils, and psycopg2. from sqlalchemy import create_engine from sqlalchemy_utils import database_exists, create_database import psycopg2 import pandas as pd ###Output _____no_output_____ ###Markdown (Optional) If Postgres isn't launched on startup **To have launchd start postgresql at login: **```ln -sfv /usr/local/opt/postgresql/*.plist ~/Library/LaunchAgents``` **Then to load postgresql now: **```launchctl load ~/Library/LaunchAgents/homebrew.mxcl.postgresql.plist``` **Or, if you don't want/need launchctl, you can just run: **```postgres -D /usr/local/var/postgres``` **into the command line and also look at [this page](http://postgresguide.com/) for more details.** Interfacing with PSQL through pythonUpdate your username and password in the cell below. Then run each cell. ###Code #In Python: Define your username and password used above. I've defined the database name (we're #using a dataset on births, so I call it birth_db). dbname = 'birth_db' username = 'brittany' pswd = '1test2' ## 'engine' is a connection to a database ## Here, we're using postgres, but sqlalchemy can connect to other things too. engine = create_engine('postgresql://%s:%s@localhost/%s'%(username,pswd,dbname)) print('postgresql://%s:%s@localhost/%s'%(username,pswd,dbname)) print(engine.url) # Replace localhost with IP address if accessing a remote server ## create a database (if it doesn't exist) if not database_exists(engine.url): create_database(engine.url) print(database_exists(engine.url)) print(engine.url) ###Output True postgresql://brittany:1test2@localhost/birth_db ###Markdown Getting some data Time to get some data, head over to https://drive.google.com/open?id=1YlN9vG2qY1DdtC9ni4ItPhoYm7GHTNfu and download the births2012_downsampled.csv. ###Code # load a database from the included CSV # edit the string below to account for where you saved the csv. csv_path = 'births2012_downsampled.csv' birth_data = pd.read_csv(csv_path) ## insert data into database from Python (proof of concept - this won't be useful for big data, of course) ## df is any pandas dataframe birth_data.to_sql('birth_data_table', engine, if_exists='replace') ###Output _____no_output_____ ###Markdown The above line (to_sql) is doing a lot of heavy lifting. It's reading a dataframe, it's creating a table, and adding the data to the table. So ** SQLAlchemy is quite useful! ** How this works outside of python:** open up the PostgreSQL app, click on the "Open psql" button in the bottom right corner, ** or alternatively type ```$ psql birth_db -h localhost -U username``` into the command line **Type the following into the terminal that opens up**`$ \c birth_db`**You should see something like the following**`$ You are now connected to database "birth_db" as user "username".`**Then try the following query:**`$ SELECT * FROM birth_data_table;` You can see the table we created! But it's kinda ugly and hard to read (type 'q' in terminal to end long output). **You can try a few other sample queries. Before you type in each one, ask yourself what you think the output will look like:**`SELECT * FROM birth_data_table WHERE infant_sex='M';``SELECT COUNT(infant_sex) FROM birth_data_table WHERE infant_sex='M';``SELECT COUNT(gestation_weeks), infant_sex FROM birth_data_table WHERE infant_sex = 'M' GROUP BY gestation_weeks, infant_sex;``SELECT gestation_weeks, COUNT(gestation_weeks) FROM birth_data_table WHERE infant_sex = 'M' GROUP BY gestation_weeks;` ###Code ## Now try the same queries, but in python! # connect: con = None con = psycopg2.connect(database = dbname, user = username, host='localhost', password=pswd) # query: sql_query = """ SELECT * FROM birth_data_table WHERE delivery_method='Cesarean'; """ birth_data_from_sql = pd.read_sql_query(sql_query,con) birth_data_from_sql.head() ###Output _____no_output_____ ###Markdown Is one method of querying the data faster than the other? Probably not for the amount of data you can fit on your machine. ###Code import time t0 = time.time() birth_data_from_sql = pd.read_sql_query(sql_query,con) t1 = time.time() total = t1-t0 print('total time take: ' + str(total) + ' seconds') birth_data = pd.read_csv(csv_path) t0 = time.time() birth_data=birth_data.loc[(birth_data['delivery_method'] == 'Cesarean')] t1 = time.time() total = t1-t0 print('total time take: ' + str(total) + ' seconds') ###Output total time take: 0.0013017654418945312 seconds

python/organization/twitter.ipynb

###Markdown Organization Activity on TwitterThe parameters in the cell below can be adjusted to explore other politicians and time frames. How to explore other organizations?The ***organization_id*** is an internal identifier that connects the different social media accounts. You can [use this other notebook](../organizations.ipynb?autorun=true) to get other the identifiers of other politicians.***Alternatively***, you can direcly use the [organizations API](http://mediamonitoring.gesis.org/api/organizations/swagger/), or access it with the [SMM Wrapper](https://pypi.org/project/smm-wrapper/). A. Set Up parameters ###Code # Parameters: organization_id = 440 from_date = '2017-09-01' to_date = '2018-12-31' aggregation = 'week' ###Output _____no_output_____ ###Markdown B. Using the SMM Organization API ###Code # create an instance of the smm wrapper from smm_wrapper import SMMOrganizations smm = SMMOrganizations() # using the api to get the tweets and replies tweets = smm.api.tweets_by(_id=organization_id, from_date=from_date, to_date=to_date, aggregate_by=aggregation) replies = smm.api.replies_to(_id=organization_id, from_date=from_date, to_date=to_date, aggregate_by=aggregation) ###Output _____no_output_____ ###Markdown C. Plotting ###Code import plotly from plotly import graph_objs as go plotly.offline.init_notebook_mode(connected=True) plotly.offline.iplot({ "data": [go.Scatter(x=tweets['labels'], y=tweets['values'], name='Tweets', line_shape='spline'), go.Scatter(x=replies['labels'], y=replies['values'], name='Replies', line_shape='spline')], "layout": go.Layout(title='Tweets and replies', yaxis=dict(title='N')) }) ###Output _____no_output_____

notebooks/exploratory/kernel-one-hot-encoding.ipynb

###Markdown One-Hot Kernel EncodingBased on [Structured Variationally Auto-encoded Optimization (Lu et al., 2018)](http://proceedings.mlr.press/v80/lu18c/lu18c.pdf)Suppose we have a set of base kernels $\mathcal{B} = \{A, B, C\}$ and a set of operations $\mathcal{O} = \{+, \times, Stop\}$$\hat{B} = \{A_1, A_2, ..., A_D, B_1, B_2, ..., B_D, C_1, C_2, ..., C_D\}$\begin{bmatrix} A_1 & B_1 & C_1 \\A_2 & B_2 & C_2 \\\vdots & \vdots & \vdots \\A_D & B_D & C_D\end{bmatrix}We will 1-hot encode vectors for both, kernels and operations. We need $|\mathcal{B}|D$ bits to reprensent a kernel applied to a single dimension.Any expression $S$ is transformed into a binary vector by recurrently attaching the 1-hot vectors of each kernel and operation. When the operation is Stop the vector is completed with zeros. For example, let $D=8$ and let $N_{max}$ be the number of operations. $A_1 + B_2 * C_8$ Stop ...100000000000000000000000 100 000000000100000000000000 010 000000000000000000000001 001 000 Kernel Encoding: $ABC$$A_1: 1000 0000 0000 0000 0000 0000$$A_2: 0100 0000 0000 0000 0000 0000$$B_1: 0000 0000 1000 0000 0000 0000$$B_2: 0000 0000 0100 0000 0000 0000$$C_1: 0000 0000 0000 0000 1000 0000$$C_1: 0000 0000 0000 0000 0100 0000$$C_8: 0000 0000 0000 0000 0000 0001$ ###Code # one-hot encode operations add = bin(0b100) # 0b100 mult = bin(0b010) # 0b010 stop = bin(0b001) # 0b001 kernel_families = ['A', 'B', 'C'] D = 4 def encode_kernel(family, dim): i = kernel_families.index(family) + 1 shift = i * D - dim return 0b1 << shift n_bits = int(len(kernel_families) * D) for family in kernel_families: for d in range(1, D + 1): kern_encoding = encode_kernel(family, d) print(family + str(d) + ':', format(kern_encoding, '0' + str(n_bits) +'b')) print('') A1 = encode_kernel('A', 1) B2 = encode_kernel('B', 2) C8 = encode_kernel('C', 8) print('A1 + B2 * C8 = ', bin(A1) + add + bin(B2) + mult + bin(C8) + stop + bin(0b000)) add ###Output _____no_output_____

templates/Notebook_Template_With_TableContents.ipynb

###Markdown  ###Code %%html <h1 align='center'>Title</h1> <h4 align='center'>Grade $\mid$ Topic $\mid$ Notebook Author</h4> import matplotlib.pyplot as plt import ipywidgets from ipywidgets import widgets, interact, interact_manual, Button, Layout from IPython.display import Javascript, display def table_of_cont(boolean_val): if boolean_val == True: fig = plt.figure(figsize=(20,18)) table_of_contents = ["Table of Contents","Introduction","Subtitle I", \ "Subtitle II","Conclusion","References"] number_of_items = len(table_of_contents) ax = fig.add_subplot(331) ax.axis("Off") ax.invert_yaxis() for i in range(number_of_items): if i==0: ax.text(0,i/5,table_of_contents[i],fontsize=25) else: ax.text(0,i/5,table_of_contents[i],fontsize=18) ax1 = fig.add_subplot(332) ax1.axis("Off") ax2 = fig.add_subplot(333) ax2.axis("Off") plt.show() long_name = {'description_width': 'initial'} show_table_button = widgets.Button( value=True, description='Show Table of Contents', disabled=False, button_style='info', # 'success', 'info', 'warning', 'danger' or '' tooltip='Description', style=long_name, icon='check' ) def run_current(ev): display(Javascript('IPython.notebook.execute_cell_range(IPython.notebook.get_selected_index()+0,IPython.notebook.get_selected_index()+1)')) ai_button_show = widgets.Button(button_style='info',description="Show Table of Contents", layout=Layout(width='25%', height='30px') ) ai_button_hide = widgets.Button(button_style='info',description="Hide Table of Contents", layout=Layout(width='25%', height='30px') ) button_ctr = 0 button_ctr += 1 if(button_ctr % 2 == 0): display(ai_button_hide) ai_button_hide.on_click( run_current ) val = True table_of_cont(val) else: display(ai_button_show) ai_button_show.on_click( run_current ) val = False table_of_cont(val) %%html <h2 align='center'>Introduction</h2> <h5 align='center'> Motivate and introduce the content and context of your notebook. Why are you creating this notebook? What will you teach? Why should the reader care?</h5> %%html <h2 align='center'>Background</h2> <h5 align='center'>Include the background information about your content. Include examples and explanation to help guide your notebooks. </h5> %%html <h2 align='center'>Examples</h2> <h5 align='center'>Use Python or your own explanations to provide examples and interactivity to help teach and showcase the concepts to the student.</h5> %matplotlib notebook from matplotlib import pyplot as plt from ipywidgets import widgets,Layout from IPython.display import Javascript import numpy as np def run_cells(ev): display(Javascript('IPython.notebook.execute_cell_range(IPython.notebook.get_selected_index(),IPython.notebook.get_selected_index()+1)')) mean_exercise_button = widgets.Button( button_style='info',description="Create Canvas", layout=Layout(width='20%', height='30px') ) # On button click, execute the next cell class LineBuilder: def __init__(self, line): self.line = line self.xs = list(line.get_xdata()) self.ys = list(line.get_ydata()) self.cid = line.figure.canvas.mpl_connect('button_press_event', self) def __call__(self, event): print('click', event) if event.inaxes!=self.line.axes: return self.xs.append(event.xdata) self.ys.append(event.ydata) self.line.set_data(self.xs, self.ys) self.line.figure.canvas.draw() fig = plt.figure() ax = fig.add_subplot(111) ax.set_title('Interactive Plot: Click to build line segments') line, = ax.plot([0], [0]) # empty line linebuilder = LineBuilder(line) plt.show() display(mean_exercise_button) mean_exercise_button.on_click( run_cells ) %%html <h3 align='center'>Additional content I</h3> Other supporting material, videos, or links. %%html <h3 align='center'>Exercises I</h3> <h5>Question 1</h5> Print question here from ipywidgets import interact_manual,widgets s = {'description_width': 'initial'} @interact(answer =widgets.Select( options=["Select option","Option 1",\ "Option 3","Option 2",\ "Option 4"], value='Select option', description="Sample Question", disabled=False, style=s )) def reflective_angle_question(answer): if answer=="Select option": print("Click on the correct answer.\n") elif answer=="Option 1": print("Correct!\nReiterate main point.") elif answer != "Option 1" or answer != "Select Option": print("Provide feedback that points to correct question") %%html <h5>Question 2</h5> Print question here from ipywidgets import interact_manual,widgets s = {'description_width': 'initial'} @interact(answer =widgets.Select( options=["Select option","Option 1",\ "Option 3","Option 2",\ "Option 4"], value='Select option', description="Sample Question", disabled=False, style=s )) def reflective_angle_question(answer): if answer=="Select option": print("Click on the correct answer.\n") elif answer=="Option 1": print("Correct!\nReiterate main point.") elif answer != "Option 1" or answer != "Select Option": print("Provide feedback that points to correct question") %%html <h2 align='center'>Conclusion</h2> <h5 align='center'>Summarize your notebook. Reiterate the lesson and important takeaways. </h5> %%html <h2 align='center'>References</h2> ###Output _____no_output_____

data_cleaning/05-exercise-inconsistent-data-entry.ipynb

###Markdown **This notebook is an exercise in the [Data Cleaning](https://www.kaggle.com/learn/data-cleaning) course. You can reference the tutorial at [this link](https://www.kaggle.com/alexisbcook/inconsistent-data-entry).**--- In this exercise, you'll apply what you learned in the **Inconsistent data entry** tutorial. SetupThe questions below will give you feedback on your work. Run the following cell to set up the feedback system. ###Code from learntools.core import binder binder.bind(globals()) from learntools.data_cleaning.ex5 import * print("Setup Complete") ###Output _____no_output_____ ###Markdown Get our environment set upThe first thing we'll need to do is load in the libraries and dataset we'll be using. We use the same dataset from the tutorial. ###Code # modules we'll use import pandas as pd import numpy as np # helpful modules import fuzzywuzzy from fuzzywuzzy import process import chardet # read in all our data professors = pd.read_csv("../input/pakistan-intellectual-capital/pakistan_intellectual_capital.csv") # set seed for reproducibility np.random.seed(0) ###Output _____no_output_____ ###Markdown Next, we'll redo all of the work that we did in the tutorial. ###Code # convert to lower case professors['Country'] = professors['Country'].str.lower() # remove trailing white spaces professors['Country'] = professors['Country'].str.strip() # get the top 10 closest matches to "south korea" countries = professors['Country'].unique() matches = fuzzywuzzy.process.extract("south korea", countries, limit=10, scorer=fuzzywuzzy.fuzz.token_sort_ratio) def replace_matches_in_column(df, column, string_to_match, min_ratio = 47): # get a list of unique strings strings = df[column].unique() # get the top 10 closest matches to our input string matches = fuzzywuzzy.process.extract(string_to_match, strings, limit=10, scorer=fuzzywuzzy.fuzz.token_sort_ratio) # only get matches with a ratio > 90 close_matches = [matches[0] for matches in matches if matches[1] >= min_ratio] # get the rows of all the close matches in our dataframe rows_with_matches = df[column].isin(close_matches) # replace all rows with close matches with the input matches df.loc[rows_with_matches, column] = string_to_match # let us know the function's done print("All done!") replace_matches_in_column(df=professors, column='Country', string_to_match="south korea") countries = professors['Country'].unique() ###Output _____no_output_____ ###Markdown 1) Examine another columnWrite code below to take a look at all the unique values in the "Graduated from" column. ###Code # TODO: Your code here professors['Graduated from'].unique() ###Output _____no_output_____ ###Markdown Do you notice any inconsistencies in the data? Can any of the inconsistencies in the data be fixed by removing white spaces at the beginning and end of cells?Once you have answered these questions, run the code cell below to get credit for your work. ###Code # Check your answer (Run this code cell to receive credit!) q1.check() # Line below will give you a hint #q1.hint() ###Output _____no_output_____ ###Markdown 2) Do some text pre-processingConvert every entry in the "Graduated from" column in the `professors` DataFrame to remove white spaces at the beginning and end of cells. ###Code # TODO: Your code here professors['Graduated from'] = professors['Graduated from'].str.strip() # Check your answer q2.check() # Lines below will give you a hint or solution code #q2.hint() #q2.solution() ###Output _____no_output_____ ###Markdown 3) Continue working with countriesIn the tutorial, we focused on cleaning up inconsistencies in the "Country" column. Run the code cell below to view the list of unique values that we ended with. ###Code # get all the unique values in the 'City' column countries = professors['Country'].unique() # sort them alphabetically and then take a closer look countries.sort() countries ###Output _____no_output_____ ###Markdown Take another look at the "Country" column and see if there's any more data cleaning we need to do.It looks like 'usa' and 'usofa' should be the same country. Correct the "Country" column in the dataframe to replace 'usofa' with 'usa'.**Use the most recent version of the DataFrame (with the whitespaces at the beginning and end of cells removed) from question 2.** ###Code # TODO: Your code here! matches = fuzzywuzzy.process.extract('usa', countries, limit=10, scorer=fuzzywuzzy.fuzz.token_sort_ratio) print(matches) replace_matches_in_column(df=professors, column='Country', string_to_match="usa", min_ratio=64) # Check your answer q3.check() # Lines below will give you a hint or solution code #q3.hint() #q3.solution() ###Output _____no_output_____

Pandas/panda_marging_joining_conca.ipynb

###Markdown concatenation ###Code pd.concat([df1,df2,df3],axis=1) left = pd.DataFrame({'key': ['K0', 'K1', 'K2', 'K3'], 'A': ['A0', 'A1', 'A2', 'A3'], 'B': ['B0', 'B1', 'B2', 'B3']}) right = pd.DataFrame({'key': ['K0', 'K1', 'K2', 'K3'], 'C': ['C0', 'C1', 'C2', 'C3'], 'D': ['D0', 'D1', 'D2', 'D3']}) left right ###Output _____no_output_____ ###Markdown marging ###Code pd.merge(left,right,how='inner',on='key') left1 = pd.DataFrame({'key': ['K0', 'K1', 'K2', 'K3'], 'key1': ['K0', 'K1', 'K2', 'K3'], 'A': ['A0', 'A1', 'A2', 'A3'], 'B': ['B0', 'B1', 'B2', 'B3']}) right1 = pd.DataFrame({'key': ['K0', 'K1', 'K2', 'K3'], 'key1': ['K0', 'K1', 'K2', 'K3'], 'C': ['C0', 'C1', 'C2', 'C3'], 'D': ['D0', 'D1', 'D2', 'D3']}) right1 left1 pd.merge(right1,left1,on=['key','key1']) ###Output _____no_output_____ ###Markdown joinning ###Code left = pd.DataFrame({'A': ['A0', 'A1', 'A2'], 'B': ['B0', 'B1', 'B2']}, index=['k0', 'k1', 'k2']) right = pd.DataFrame({'C': ['C0', 'C1', 'C2'], 'D': ['D0', 'D1', 'D2']}, index=['k0', 'k2', 'k3']) left right left.join(right) ###Output _____no_output_____

Data_Analytics.ipynb

###Markdown General Log File ###Code # Load "general log" file... general_log = pd.read_json('data/general_log.json') # ...and show a sample from this data general_log.sample(10, random_state=RND_SEED) # Deepening 'user_host' field print(general_log['user_host'].describe()) # Show all the host (; prevent from printing the cell final value) [print(x) for x in general_log['user_host'].unique()]; ###Output guest[guest] @ [185.9.209.177] rdsadmin[rdsadmin] @ localhost [127.0.0.1] rdsadmin[rdsadmin] @ localhost [] [rdsadmin] @ localhost [] [guest] @ [185.9.209.177] guest[guest] @ [172.31.36.183] [guest] @ [172.31.36.183] ###Markdown Seven unique user in total had interacted with the DB (Non-Query included) and the `rdsadmin` a lot of time. By the way there are only two categories, "guest" and "rdsadmin". ###Code # Deepening 'server_id' field general_log['server_id'].astype(str).describe() ###Output _____no_output_____ ###Markdown The server is just one. Comments on "general_log" file- `event_time` show when the event is happened;- `user_host` the user (name and addr) that caused the event, may be choosen as predictor...- `thread_id` the thread assigned to the associated process on server, not useful for prediction i guess...- `server_id` the server identification name, looks like is always the same, not useful;- `command_type` we are interested in `Query` command types wich is the majority, not a useful field for predicion...- `argument` when is a Query contains a SQL expression and we should extract more features from this.Let's see the "slow log" file... Slow Log File ###Code # Load "slow log" file... slow_log = pd.read_json('data/slow_log.json') # ...and show a sample from this data slow_log.sample(10, random_state=RND_SEED) # Deepening 'user_host' field (now in the dataset) slow_log['user_host'].describe() slow_log['user_host'].unique() ###Output _____no_output_____ ###Markdown We should aggregate this in just two categories: `guest` and `admin`. ###Code # Deepening 'sql_text' field slow_log['sql_text'].describe() ###Output _____no_output_____ ###Markdown `SELECT 1` query is executed more often than the others, let's see if has a fixed execution time or depends on when it is executed... ###Code # Query time conversion def query_time_converer(df): time = df['query_time'].dt.hour * 3600 time += df['query_time'].dt.minute * 60 time += df['query_time'].dt.second time += df['query_time'].dt.microsecond * 1e-6 time += df['query_time'].dt.nanosecond * 1e-9 time /= 1e-6 # To microseconds df['query_time'] = time # Extract all SELECT 1 timings select_timings = slow_log[['sql_text', 'query_time']].loc[slow_log['sql_text'] == 'SELECT 1'].copy() query_time_converer(select_timings) # Mean executution time of SELECT 1 print('Mean execution time of SELECT 1:', round(select_timings['query_time'].mean(), 2), 'microseconds') # Standard deviation for execution time of SELECT 1 print('Standard deviation :', round(select_timings['query_time'].std(), 2), 'microseconds') ###Output Mean execution time of SELECT 1: 1009.65 microseconds Standard deviation : 3838.58 microseconds ###Markdown Execution time of such a simple query has a relative low mean but high standard deviation, this means can be very variable around mean value depending on when is executed. Comments on "slow_log" file- `start_time` is the time when the timer start, may be used as order key if considering a time series of events;- `user_host` same as general log seen before;- `query_time` the total time the query takes, this should be the target variable for the model (needs some conversion);- `lock_time` the time the query spend locking resources in DB i guess, is a sub-time of query time (?);- `rows_sent` the number of rows returned from the query, using this as predictor may cause data leak in prediction;- `rows_examined` similar to `rows_sent` show the rows the query iterate before returning (maybe looking up for some condition), using this for prediction may lead to data leak (model perform well on test then degenerate in production);- `db` the db name, since all queries are generated I think this field is not important;- `last_insert_id` the id of last inserted or updated row in a table by this query (?);- `insert_id` the id of first inserted or update row in a table by this query (?);- `server_id` same as general log seen before;- `sql_text` same as `argument` field in general log when the event is a Query type, contains the SQL query code;- `thread_id` same as general log seen before.First impression is that for the task of predicting query execution time I need just the "slow_log" file since it contains all the useful information to extract features and train a model. Not only slow queries are recorded but also that one with 0 execution time. Number of samples is a bit low so may be necessary a cross-validation for better evaluation. To exploit rows_sent and rows_examinated is tempting but we know this values only after the query execute so in a real context we receive a query without no knowledge about the number of rows will be used till the end of execution. Dataset feature selection/engineering ###Code # Define the raw dataset... dataset = slow_log[['start_time', 'user_host', 'sql_text', 'query_time']].copy() # ...and show a sample dataset.sample(10, random_state=RND_SEED) # Sort values by time dataset.sort_values(by='start_time', inplace=True, ignore_index=True) dataset.head(5) # Aggregating user hosts in two categories: guest and admin dataset['user_host'] = dataset['user_host'].apply(lambda h: 'admin' if 'admin' in h else 'guest') dataset.head(5) # Query execution time conversion query_time_converer(dataset) dataset.head(5) ###Output _____no_output_____ ###Markdown Feature extraction ###Code # All queries to lowercase dataset['sql_text'] = dataset['sql_text'].apply(lambda q: str.lower(q)) dataset.sample(3, random_state=RND_SEED) # Categorical features: Tables accessed by query # Table names has been grabbed from DDL File cat_patterns = {'use customer': r'customer', 'use lineitem': r'lineitem', 'use nation': r'nation', 'use orders': r'orders', 'use part': r'part', 'use partsupp': r'partsupp', 'use region': r'region', 'use supplier': r'supplier'} for cname, pt in cat_patterns.items(): dataset[cname.replace(' ', '_')] = dataset['sql_text'].apply(lambda q: 'yes' if re.search(pt, q) else 'no') # Numeric feature: Query number of chars dataset['charlen'] = dataset['sql_text'].apply(lambda q: len(q)) # Numeric feature: Query number of tokens (this take some seconds) dataset['num_tokens'] = dataset['sql_text'].apply(lambda q: len(sqlparse.parse(q)[0].tokens)) # Numeric features: Count nested queries or repetition patterns = {'num functions': r'[a-z]+\(.*\)', 'num select': r'\s?select\s', 'num from': r'\s?from\s', 'num where': r'\s?where\s', 'num join': r'join', 'num order by': r'\sorder by\s'} for cname, pt in patterns.items(): dataset[cname.replace(' ', '_')] = dataset['sql_text'].apply(lambda q: len(re.findall(pt, q)) ) # Show a dataset sample dataset.sample(100, random_state=RND_SEED) ###Output _____no_output_____ ###Markdown Plotting ###Code # Plot settings sns.set_color_codes('bright') # Color palette sns.set(font_scale=1.2) # Font size sns.set_style("white") # Whithe background with lines # Plot relations between numerical features in data, univariate distribution on diagonal. pplot = sns.pairplot(data=dataset[['query_time', 'charlen', 'num_tokens', 'num_functions', 'num_where']], diag_kind='kde') # Plot user_host by query times distribution ax = sns.catplot(x='user_host', y='query_time', data=dataset, height=5, aspect=2) ###Output _____no_output_____ ###Markdown It's clear that some guest users are slowing down the DB with particular queries, some queries perform way badly respect to others. ###Code ax = sns.catplot(x='num_select', y='query_time', hue='num_where', data=dataset, height=5, aspect=2) ax = sns.catplot(x='num_select', y='query_time', hue='num_from', data=dataset, height=5, aspect=2) ax = sns.catplot(x='num_where', y='query_time', hue='num_functions', data=dataset, height=5, aspect=2) ax = sns.catplot(x='num_functions', y='query_time', data=dataset, height=5, aspect=2) sx = sns.catplot(x='num_join', y='query_time', data=dataset, height=5, aspect=2) ###Output _____no_output_____ ###Markdown Save dataset for model training ###Code dataset.to_csv('queries_dataset.csv', index=False) ###Output _____no_output_____ ###Markdown 길이가 긴 니크롬선의 전압과 전류 사이의 관계를 학습합니다. 데이터 준비 ###Code import pandas as pd import numpy as np filepath = './dataset/short_line.csv' short_df = pd.read_csv(filepath) short_Voltage = np.array(short_df['Voltage']) short_Ampare = np.array([0.04, 0.08, 0.11, 0.15]) short_train_input = short_Voltage.reshape(-1, 1) short_train_target = short_Ampare ###Output _____no_output_____ ###Markdown 실험한 데이터 시각화하기 ###Code import matplotlib.pyplot as plt plt.scatter(short_Voltage, short_Ampare) plt.xlabel('Voltage') plt.ylabel('Ampere') plt.show() ###Output _____no_output_____ ###Markdown 실험해본 데이터를 시각화해 보았을때 데이터가 매우 선형적인 것을 확인해 보실수가 있습니다.이제 우리는 이 데이터들을 학습시킨후 시각화를 해 보아서 전압과 전류 사이에 관계를분석해 보도록 하겠습니다. 긴 니크롬선의 전압과 전류 사이의 관계를 나타내는 직선을 학습하기 데이터 분석위 산점도는 매우 선형적인 모양이므로 우리는 위 데이터를이 일차함수를 활용하여 데이터를 학습시키도록 하겠습니다. ###Code from sklearn.linear_model import LinearRegression short_lr = LinearRegression() short_lr.fit(short_train_input, short_train_target) ###Output _____no_output_____ ###Markdown 학습한 직선 그래프로 나타내기 ###Code print(short_lr.coef_, short_lr.intercept_) plt.scatter(short_Voltage, short_Ampare, color='red') plt.plot([0, 6], [0*short_lr.coef_ + short_lr.intercept_, 6*short_lr.coef_+short_lr.intercept_], 'r') plt.xlabel('Voltage') plt.ylabel('Ampere') plt.show() ###Output _____no_output_____ ###Markdown 성공적으로 길이가 긴 니크롬선의 전류를 흘려 보냈을때 전압과 전류 사이의 관계를 학습했습니다.위에 직선을 보았을때 위 직선은 일차함수의 그래프 이므로 전압과 전류의 세기는 비례한다라는걸증명할수 있습니다. 길이가 짧은 니크롬선의 전압과 전류 사이의 관계를 학습합니다. 데이터 준비 ###Code filepath = './dataset/long_line.csv' long_df = pd.read_csv(filepath) long_Voltage = np.array(short_df['Voltage']) long_Ampare = np.array([0.08, 0.15, 0.22, 0.30]) long_train_input = long_Voltage.reshape(-1, 1) long_train_target = long_Ampare ###Output _____no_output_____ ###Markdown 실험한 데이터 시각화하기 ###Code plt.scatter(long_train_input, long_train_target) plt.xlabel('Voltage') plt.ylabel('Ampere') plt.show() ###Output _____no_output_____ ###Markdown 마찬가지로 이 산점도도 매우 선형적인 그래프를 가지고 있으므로 일차함수를 사용하여모델을 학습하도록 하겠습니다. 모델 학습하기 ###Code long_lr = LinearRegression() long_lr.fit(long_train_input, long_train_target) ###Output _____no_output_____ ###Markdown 학습한 직선 시각화하기 ###Code print(long_lr.coef_, long_lr.intercept_) plt.title('Voltage and Ampare Amalysis') plt.scatter(short_Voltage, short_Ampare, color='red') plt.scatter(long_Voltage, long_Ampare) plt.plot([0, 6], [0*short_lr.coef_ + short_lr.intercept_, 6*short_lr.coef_+short_lr.intercept_], 'r') plt.plot([0, 6], [0*long_lr.coef_ + long_lr.intercept_, 6*long_lr.coef_+long_lr.intercept_]) plt.xlabel('Voltage') plt.ylabel('Ampere') plt.show() ###Output _____no_output_____ ###Markdown 위 그래프로 우리가 알수있는것은 전기 회로에서 전압과 전류는 비례한다. 이때 전압이 일정하면니크롬선의 길이와 전류의 세기는 반비례한다. 라는것을 알수 있습니다. 데이터 예측하기전압이 20V일때 전류의 세기를 예측합니다. ###Code long_lr.predict([[20]]) short_lr.predict([[20]]) ###Output _____no_output_____ ###Markdown 학습한 그래프 시각화하기 ###Code plt.title('Voltage and Ampare Amalysis') plt.scatter(short_Voltage, short_Ampare, color='red') plt.scatter(long_Voltage, long_Ampare) plt.scatter(20, 0.97833333, marker="^") plt.scatter(20, 0.485, marker="^") plt.plot([0, 20], [0*short_lr.coef_ + short_lr.intercept_, 20*short_lr.coef_+short_lr.intercept_], 'r') plt.plot([0, 20], [0*long_lr.coef_ + long_lr.intercept_, 20*long_lr.coef_+long_lr.intercept_]) plt.xlabel('Voltage') plt.ylabel('Ampere') plt.show() ###Output _____no_output_____

prepare_data/explore_and_convert_FDDB.ipynb

###Markdown The purpose of this script is to explore images/annotations of the FDDB dataset. Also it converts face ellipses into face bounding boxes. Also it converts annotations into json format. ###Code IMAGES_DIR = os.path.expanduser('~/datasets/fddb/originalPics/') BOXES_DIR = os.path.expanduser('~/datasets/fddb/FDDB-folds/') RESULT_DIR = os.path.expanduser('data/fddb/val/') ###Output _____no_output_____ ###Markdown Read data ###Code # collect paths to all images all_paths = [] for path, subdirs, files in tqdm(os.walk(IMAGES_DIR)): for name in files: all_paths.append(os.path.join(path, name)) metadata = pd.DataFrame(all_paths, columns=['full_path']) # strip root folder metadata['path'] = metadata.full_path.apply(lambda x: os.path.relpath(x, IMAGES_DIR)) # all unique endings metadata.path.apply(lambda x: x.split('.')[-1]).unique() # number of images len(metadata) annotation_files = os.listdir(BOXES_DIR) annotation_files = [f for f in annotation_files if f.endswith('ellipseList.txt')] annotation_files = [os.path.join(BOXES_DIR, f) for f in annotation_files] def ellipse_to_box(major_axis_radius, minor_axis_radius, angle, center_x, center_y): half_h = major_axis_radius * np.sin(-angle) half_w = minor_axis_radius * np.sin(-angle) xmin, xmax = center_x - half_w, center_x + half_w ymin, ymax = center_y - half_h, center_y + half_h return xmin, ymin, xmax, ymax def get_boxes(path): with open(path, 'r') as f: content = f.readlines() content = [s.strip() for s in content] boxes = {} num_lines = len(content) i = 0 name = None while i < num_lines: s = content[i] if 'big/img' in s: if name is not None: assert len(boxes[name]) == num_boxes name = s + '.jpg' boxes[name] = [] i += 1 num_boxes = int(content[i]) i += 1 else: numbers = [float(f) for f in s.split(' ')[:5]] major_axis_radius, minor_axis_radius, angle, center_x, center_y = numbers xmin, ymin, xmax, ymax = ellipse_to_box( major_axis_radius, minor_axis_radius, angle, center_x, center_y ) if xmin == xmax or ymin == ymax: num_boxes -= 1 else: boxes[name].append(( min(xmin, xmax), min(ymin, ymax), max(xmin, xmax), max(ymin, ymax) )) i += 1 return boxes boxes = {} for p in annotation_files: boxes.update(get_boxes(p)) # check number of images with annotations # and number of boxes # (these values are taken from the official website) assert len(boxes) == 2845 assert sum(len(b) for b in boxes.values()) == 5171 - 1 # one box is empty metadata = metadata.loc[metadata.path.apply(lambda x: x in boxes)] metadata = metadata.reset_index(drop=True) ###Output _____no_output_____ ###Markdown Show bounding boxes ###Code def draw_boxes_on_image(path, boxes): image = Image.open(path) draw = ImageDraw.Draw(image, 'RGBA') width, height = image.size for b in boxes: xmin, ymin, xmax, ymax = b fill = (255, 255, 255, 45) outline = 'red' draw.rectangle( [(xmin, ymin), (xmax, ymax)], fill=fill, outline=outline ) return image i = random.randint(0, len(metadata) - 1) # choose a random image some_boxes = boxes[metadata.path[i]] draw_boxes_on_image(metadata.full_path[i], some_boxes) ###Output _____no_output_____ ###Markdown Convert ###Code def get_annotation(path, name, width, height): annotation = { "filename": name, "size": {"depth": 3, "width": width, "height": height} } objects = [] for b in boxes[path]: xmin, ymin, xmax, ymax = b objects.append({"bndbox": {"ymin": ymin, "ymax": ymax, "xmax": xmax, "xmin": xmin}, "name": "face"}) annotation["object"] = objects return annotation if not os.path.exists(RESULT_DIR): os.makedirs(RESULT_DIR) shutil.rmtree(RESULT_DIR, ignore_errors=True) os.mkdir(RESULT_DIR) os.mkdir(os.path.join(RESULT_DIR, 'images')) os.mkdir(os.path.join(RESULT_DIR, 'annotations')) for T in tqdm(metadata.itertuples()): # get width and height of an image image = cv2.imread(T.full_path) h, w, c = image.shape assert c == 3 # name of the image name = '-'.join(T.path.split('/')[:3]) + '_' + T.path.split('/')[-1] assert name.endswith('.jpg') # copy the image shutil.copy(T.full_path, os.path.join(RESULT_DIR, 'images', name)) # save annotation for it d = get_annotation(T.path, name, w, h) json_name = name[:-4] + '.json' json.dump(d, open(os.path.join(RESULT_DIR, 'annotations', json_name), 'w')) ###Output 0it [00:00, ?it/s] ###Markdown The purpose of this script is to explore images/annotations of the FDDB dataset. Also it converts face ellipses into face bounding boxes. Also it converts annotations into json format. ###Code IMAGES_DIR = '/home/gpu2/hdd/dan/FDDB/originalPics/' BOXES_DIR = '/home/gpu2/hdd/dan/FDDB/FDDB-folds/' RESULT_DIR = '/home/gpu2/hdd/dan/FDDB/val/' ###Output _____no_output_____ ###Markdown Read data ###Code # collect paths to all images all_paths = [] for path, subdirs, files in tqdm(os.walk(IMAGES_DIR)): for name in files: all_paths.append(os.path.join(path, name)) metadata = pd.DataFrame(all_paths, columns=['full_path']) # strip root folder metadata['path'] = metadata.full_path.apply(lambda x: os.path.relpath(x, IMAGES_DIR)) # all unique endings metadata.path.apply(lambda x: x.split('.')[-1]).unique() # number of images len(metadata) annotation_files = os.listdir(BOXES_DIR) annotation_files = [f for f in annotation_files if f.endswith('ellipseList.txt')] annotation_files = [os.path.join(BOXES_DIR, f) for f in annotation_files] def ellipse_to_box(major_axis_radius, minor_axis_radius, angle, center_x, center_y): half_h = major_axis_radius * np.sin(-angle) half_w = minor_axis_radius * np.sin(-angle) xmin, xmax = center_x - half_w, center_x + half_w ymin, ymax = center_y - half_h, center_y + half_h return xmin, ymin, xmax, ymax def get_boxes(path): with open(path, 'r') as f: content = f.readlines() content = [s.strip() for s in content] boxes = {} num_lines = len(content) i = 0 name = None while i < num_lines: s = content[i] if 'big/img' in s: if name is not None: assert len(boxes[name]) == num_boxes name = s + '.jpg' boxes[name] = [] i += 1 num_boxes = int(content[i]) i += 1 else: numbers = [float(f) for f in s.split(' ')[:5]] major_axis_radius, minor_axis_radius, angle, center_x, center_y = numbers xmin, ymin, xmax, ymax = ellipse_to_box( major_axis_radius, minor_axis_radius, angle, center_x, center_y ) if xmin == xmax or ymin == ymax: num_boxes -= 1 else: boxes[name].append(( min(xmin, xmax), min(ymin, ymax), max(xmin, xmax), max(ymin, ymax) )) i += 1 return boxes boxes = {} for p in annotation_files: boxes.update(get_boxes(p)) # check number of images with annotations # and number of boxes # (these values are taken from the official website) assert len(boxes) == 2845 assert sum(len(b) for b in boxes.values()) == 5171 - 1 # one box is empty metadata = metadata.loc[metadata.path.apply(lambda x: x in boxes)] metadata = metadata.reset_index(drop=True) ###Output _____no_output_____ ###Markdown Show bounding boxes ###Code def draw_boxes_on_image(path, boxes): image = Image.open(path) draw = ImageDraw.Draw(image, 'RGBA') width, height = image.size for b in boxes: xmin, ymin, xmax, ymax = b fill = (255, 255, 255, 45) outline = 'red' draw.rectangle( [(xmin, ymin), (xmax, ymax)], fill=fill, outline=outline ) return image i = random.randint(0, len(metadata) - 1) # choose a random image some_boxes = boxes[metadata.path[i]] draw_boxes_on_image(metadata.full_path[i], some_boxes) ###Output _____no_output_____ ###Markdown Convert ###Code def get_annotation(path, name, width, height): annotation = { "filename": name, "size": {"depth": 3, "width": width, "height": height} } objects = [] for b in boxes[path]: xmin, ymin, xmax, ymax = b objects.append({"bndbox": {"ymin": ymin, "ymax": ymax, "xmax": xmax, "xmin": xmin}, "name": "face"}) annotation["object"] = objects return annotation shutil.rmtree(RESULT_DIR, ignore_errors=True) os.mkdir(RESULT_DIR) os.mkdir(os.path.join(RESULT_DIR, 'images')) os.mkdir(os.path.join(RESULT_DIR, 'annotations')) for T in tqdm(metadata.itertuples()): # get width and height of an image image = cv2.imread(T.full_path) h, w, c = image.shape assert c == 3 # name of the image name = '-'.join(T.path.split('/')[:3]) + '_' + T.path.split('/')[-1] assert name.endswith('.jpg') # copy the image shutil.copy(T.full_path, os.path.join(RESULT_DIR, 'images', name)) # save annotation for it d = get_annotation(T.path, name, w, h) json_name = name[:-4] + '.json' json.dump(d, open(os.path.join(RESULT_DIR, 'annotations', json_name), 'w')) ###Output _____no_output_____

2.Datasets_for_NLP/1_strings_in_python.ipynb

###Markdown **Strings declaration** ###Code # Strings can be specified using single quotes monty = 'Monty Python' print(monty) # ... or double quotes circus = "Monty Python's Flying Circus" print(circus) # If a string contains a single quote, we must backslash-escape the quote circus = 'Monty Python\'s Flying Circus' print(circus) # Sometimes strings go over several lines. # Python provides us with various ways of entering them: # a) Using backslash couplet = "Shall I compare thee to a Summer's day?"\ "Thou are more lovely and more temperate:" print(couplet) # b) Using parentheses: couplet = ("Rough winds do shake the darling buds of May," "And Summer's lease hath all too short a date:") print(couplet) # c) Using a triple-quoted string (to keep the newlines): couplet = """Shall I compare thee to a Summer's day? Thou are more lovely and more temperate:""" print(couplet) couplet = '''Rough winds do shake the darling buds of May, And Summer's lease hath all too short a date:''' print(couplet) ###Output Shall I compare thee to a Summer's day?Thou are more lovely and more temperate: Rough winds do shake the darling buds of May,And Summer's lease hath all too short a date: Shall I compare thee to a Summer's day? Thou are more lovely and more temperate: Rough winds do shake the darling buds of May, And Summer's lease hath all too short a date: ###Markdown **Basic operations** ###Code # Concatenation display('very' + 'very' + 'very') display('very' * 4) # Accessing individual characters display(monty) display(monty[0]) display(monty[3]) display(monty[5]) # -1 is the index of the last character display(monty[-1]) # -N is the index of the last N character display(monty[-2]) # Iterate characters in strings sent = 'colorless green ideas sleep furiously' for char in sent: print(char, end=' ') ###Output c o l o r l e s s g r e e n i d e a s s l e e p f u r i o u s l y ###Markdown **Substrings** ###Code # We use [ ] for slides (e.g. for substrings or sublists) # It starts at the first index but finishes one before the end index display(monty) display(monty[6:10]) display(monty[-4:-1]) # If we omit the first value, the substring begins at the start of the string or list display(monty[:5]) # If we omit the second value, the substring continues to the end of the string or list display(monty[6:]) ###Output _____no_output_____ ###Markdown **Basic search** ###Code # We can check if a string is contained in other using the in operator: phrase = 'And now for something completely different' if 'thing' in phrase: print('found "thing"') # We can also find the position of a string within other using find(): monty.find('Python') ###Output found "thing" ###Markdown **Other useful methods**|Method | Functionality||------|------||`s.find(t)` | index of first instance of string t inside `s` (`-1` if not found)||`s.rfind(t)` | index of last instance of string t inside `s` (`-1` if not found)||`s.index(t)` | like `s.find(t)` except it raises `ValueError` if not found||`s.rindex(t)` | like `s.rfind(t)` except it raises `ValueError` if not found||`s.join(text)` | combine the words of the text into a string using `s` as the glue||`s.split(t)` | split `s` into a list wherever a `t` is found (whitespace by default)||`s.splitlines()` | split `s` into a list of strings, one per line||`s.lower()` | a lowercased version of the string `s`||`s.upper()` | an uppercased version of the string `s`||`s.title()` | a titlecased version of the string `s`||`s.strip()` | a copy of `s` without leading or trailing whitespace||`s.replace(t, u)` | replace instances of `t` with `u` inside `s`| **Unicode** ###Code print(ord('ñ')) # 241 in decimal is the same than 0x00F1 in hexadecimal n_tilde = '\u00F1' print(n_tilde) python_emoji = '\U0001F40D' print('Learning', python_emoji) ###Output 241 ñ Learning 🐍 ###Markdown **Regular expressions** ###Code import re txt = "The rain in Spain" x = re.findall("ai", txt) print(x) # r prefix to a string indicates that the string is a raw string # (i.e. backslashes \ should be treated literally and not as escape characters) x = re.search(r"\bS\w+", txt) # Match object # The Match object has properties and methods used to retrieve information about the search, and the result: # .span() returns a tuple containing the start-, and end positions of the match # .string returns the string passed into the function # .group() returns the part of the string where there was a match print(x.span()) print(x.string) print(x.group()) ###Output ['ai', 'ai'] (12, 17) The rain in Spain Spain

LS_DS_141_Statistics_Probability_and_Inference_Ale_Ruperti.ipynb

###Markdown Lambda School Data Science Module 141 Statistics, Probability, and Inference Prepare - examine what's available in SciPyAs we delve into statistics, we'll be using more libraries - in particular the [stats package from SciPy](https://docs.scipy.org/doc/scipy/reference/tutorial/stats.html). ###Code from scipy import stats dir(stats) # As usual, lots of stuff here! There's our friend, the normal distribution norm = stats.norm() print(norm.mean()) print(norm.std()) print(norm.var()) # And a new friend - t t1 = stats.t(5) # 5 is df "shape" parameter print(t1.mean()) print(t1.std()) print(t1.var()) t1.std()**2 ###Output _____no_output_____ ###Markdown *(Picture from [Wikipedia](https://en.wikipedia.org/wiki/Student's_t-distribution/media/File:Student_t_pdf.svg))*The t-distribution is "normal-ish" - the larger the parameter (which reflects its degrees of freedom - more input data/features will increase it), the closer to true normal. ###Code t2 = stats.t(30) # Will be closer to normal print(t2.mean()) print(t2.std()) print(t2.var()) ###Output 0.0 1.0350983390135313 1.0714285714285714 ###Markdown Why is it different from normal? To better reflect the tendencies of small data and situations with unknown population standard deviation. In other words, the normal distribution is still the nice pure ideal in the limit (thanks to the central limit theorem), but the t-distribution is much more useful in many real-world situations.History sidenote - this is "Student":*(Picture from [Wikipedia](https://en.wikipedia.org/wiki/File:William_Sealy_Gosset.jpg))*His real name is William Sealy Gosset, and he published under the pen name "Student" because he was not an academic. He was a brewer, working at Guinness and using trial and error to determine the best ways to yield barley. He's also proof that, even 100 years ago, you don't need official credentials to do real data science! Live Lecture - let's perform and interpret a t-testWe'll generate our own data, so we can know and alter the "ground truth" that the t-test should find. We will learn about p-values and how to interpret "statistical significance" based on the output of a hypothesis test. ###Code # TODO - during class, but please help! survey_data = [0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0] import numpy as np import pandas as pd df = pd.DataFrame(survey_data) df.describe() df.plot.hist() # Now with confidence! import scipy scipy.stats.ttest_1samp(survey_data, 0.5) # the t-statistic is the ratio of the departure of the estimated value of a # parameter from its hypothesized value to its standard error # We want to calculate: tstat = 2.364321853156195 sample_stderr = 0.478518 / np.sqrt(len(survey_data)) sample_mean = 0.660000 null_hypothesis_mean = 0.5 t_stat = (sample_mean - null_hypothesis_mean) / sample_stderr print(t_stat) len(survey_data) # Science! Reproducibility... import random def make_soda_data(n=50): return pd.DataFrame([random.randint(0, 1) for _ in range(n)]) make_soda_data().describe() t_statistics = [] n_experiments = 10000 for _ in range(n_experiments): df = make_soda_data() ttest = scipy.stats.ttest_1samp(df, 0.5) t_statistics.append(ttest.statistic) pd.DataFrame(t_) ###Output _____no_output_____ ###Markdown Assignment - apply the t-test to real dataYour assignment is to determine which issues have "statistically significant" differences between political parties in this [1980s congressional voting data](https://archive.ics.uci.edu/ml/datasets/Congressional+Voting+Records). The data consists of 435 instances (one for each congressperson), a class (democrat or republican), and 16 binary attributes (yes or no for voting for or against certain issues). Be aware - there are missing values!Your goals:1. Load and clean the data (or determine the best method to drop observations when running tests)2. Using hypothesis testing, find an issue that democrats support more than republicans with p < 0.013. Using hypothesis testing, find an issue that republicans support more than democrats with p < 0.014. Using hypothesis testing, find an issue where the difference between republicans and democrats has p > 0.1 (i.e. there may not be much of a difference)Note that this data will involve *2 sample* t-tests, because you're comparing averages across two groups (republicans and democrats) rather than a single group against a null hypothesis.Stretch goals:1. Refactor your code into functions so it's easy to rerun with arbitrary variables2. Apply hypothesis testing to your personal project data (for the purposes of this notebook you can type a summary of the hypothesis you formed and tested) ###Code ### 1) LOAD AND CLEAN THE DATA ### data = pd.read_csv('https://archive.ics.uci.edu/ml/machine-learning-databases/voting-records/house-votes-84.data', names = ['Party', 'Vote 1', 'Vote 2', 'Vote 3','Vote 4','Vote 5','Vote 6','Vote 7','Vote 8','Vote 9','Vote 10','Vote 11','Vote 12','Vote 13','Vote 14','Vote 15', 'Vote 16']) data.head() # Loaded data and renamed columns along attribute info provided with data set. # We have the voting record of all 435 congressmen on 16 issues, delineated by the party affiliation of each congressman. # Missing values are most likely abstentions: The congressman/woman abstained from voting on the issue. # In order to count them, we need to count the '?' since pandas doesn't treat them as NaNs: attributes = data.apply(pd.value_counts) attributes.head(1) # Well there's a TON of abstentions. No surprise there. # In order to calculate t tests later on I'm going to convert votes from strings into integers # -1 for N, 0, for ?, and 1 for Y. data.replace(to_replace = 'n', value = -1, inplace=True) data.replace(to_replace = 'y', value = 1, inplace=True) data.replace(to_replace = '?', value = 0, inplace=True) data.head() ### 2) Using hypothesis testing, find an issue that democrats support more than republicans with p < 0.01 ### # Let's start by splitting up data into 2 dataframes. One for democrats and another for republicans. democrats = data.loc[data['Party']=='democrat'] republicans = data.loc[data['Party']=='republican'] republicans.head() democrats.describe() republicans.describe() mean_votes = pd.DataFrame( {'Democrats': democrats.mean(), 'Republicans': republicans.mean() }) mean_votes ###Output _____no_output_____ ###Markdown **Just eye-balling it with the mean, we can see that Vote 3 is really favored by Dems over Reps. ** ###Code ###Output _____no_output_____

03 - GridSearchCV - LGBM.ipynb

###Markdown 03 - GridSearchCV - LGBM Imports ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns sns.set(style="white") ###Output _____no_output_____ ###Markdown Constants ###Code n_components = 1000 models_folder = "models/" train_data_fn = models_folder+'train_data.pkl' target_fn = models_folder+'target.pkl' test_data_fn = models_folder+'test_data.pkl' weight_multiplier_fn = models_folder+"weight_multiplier.pkl" ###Output _____no_output_____ ###Markdown Functions ###Code import os.path from sklearn.externals import joblib def Load(filename): if os.path.isfile(filename): return joblib.load(filename) def Save(obj, filename): joblib.dump(obj, filename) ###Output _____no_output_____ ###Markdown Loading data ###Code import scipy data = scipy.sparse.load_npz("train_sparse_matrix_after_scale.npz") target = Load(target_fn) weight_multiplier = Load(weight_multiplier_fn) ###Output _____no_output_____ ###Markdown Splitting dataset ###Code from sklearn.model_selection import train_test_split X_train, X_validation, Y_train, Y_validation = train_test_split(data, target.ravel(), train_size=0.8, random_state=42) ###Output /home/aavdeev/anaconda3/lib/python3.6/site-packages/sklearn/model_selection/_split.py:2026: FutureWarning: From version 0.21, test_size will always complement train_size unless both are specified. FutureWarning) ###Markdown CatBoost Classifier ###Code import lightgbm as lgbm import re tuned_parameters = { 'num_leaves': [50,1000,10000,10000], 'max_depth':[10,20,30,40], 'min_child_samples':[30,50,100], 'max_bin':[50,100,200], 'subsample':[0.1,0.4,0.7], 'subsample_freq':[2,30,100], 'colsample_bytree':[0.2,0.3,0.7], 'min_child_weight':[2,3,6], 'subsample_for_bin':[10,100,200], 'min_split_gain':[1.1,2.0,10.0], 'reg_alpha':[2,3,5,7,8], 'reg_lambda':[0,0.2,0.8], 'metric':['auc'], 'learning_rate':[0.05,0.1,0.005], 'objective':['binary'], 'scale_pos_weight':[1,weight_multiplier,1/weight_multiplier], } %%time from sklearn.model_selection import GridSearchCV,RandomizedSearchCV clf = RandomizedSearchCV(lgbm.LGBMClassifier(nthread=8, verbose_eval=32), tuned_parameters, cv=4, n_iter=100, scoring='roc_auc', random_state=42, verbose=2) %%time clf.fit(X_train, Y_train) def report(results, n_top=3): for i in range(1, n_top + 1): candidates = np.flatnonzero(results['rank_test_score'] == i) for candidate in candidates: print("Model with rank: {0}".format(i)) print("Mean validation score: {0:.3f} (std: {1:.3f})".format( results['mean_test_score'][candidate], results['std_test_score'][candidate])) print("Parameters: {0}".format(results['params'][candidate])) print("") print("RandomizedSearchCV") report(clf.cv_results_) params = clf.best_params_ # params = {'subsample_freq': 2, 'subsample_for_bin': 100, 'subsample': 0.7, 'scale_pos_weight': 1, 'reg_lambda': 0.2, 'reg_alpha': 7, 'objective': 'binary', 'num_leaves': 50, 'min_split_gain': 2.0, 'min_child_weight': 3, 'min_child_samples': 100, 'metric': 'auc', 'max_depth': 20, 'max_bin': 100, 'learning_rate': 0.1, 'colsample_bytree': 0.7} evals_results = {} num_boost_round=3000 early_stopping_rounds=200 feval=None model = lgbm.train(params, d_train, valid_sets=[d_train, d_valid], valid_names=['train','valid'], evals_result=evals_results, num_boost_round=num_boost_round, early_stopping_rounds=early_stopping_rounds, verbose_eval=10, feval=feval) n_estimators = model.best_iteration print("\nModel Report") print("n_estimators : ", n_estimators) print("AUC"+":", evals_results['valid']['auc'][n_estimators-1]) from sklearn.metrics import roc_auc_score predicted = model.predict(X_validation) print("ROC AUC score:",roc_auc_score(Y_validation, predicted)) Save(model,"lgbm_model.pkl") ###Output _____no_output_____ ###Markdown Test Data ###Code test_data = scipy.sparse.load_npz("test_sparse_matrix_after_scale.npz") Y_test = model.predict(test_data, num_iteration=model.best_iteration) print(Y_test.max()) print(Y_test.mean()) ###Output _____no_output_____ ###Markdown Saving test predictions ###Code predictions = pd.DataFrame(Y_test) predictions.to_csv("solution_lgbm.csv",header=None, index=None) ###Output _____no_output_____

nbs/02-ppo.ipynb

###Markdown PPO for transformer models> A Pytorch implementation of Proximal Policy Optimization for transfomer models. This follows the language model approach proposed in paper ["Fine-Tuning Language Models from Human Preferences"](https://arxiv.org/pdf/1909.08593.pdf) and is similar to the [original implementation](https://github.com/openai/lm-human-preferences). The two main differences are 1) the method is implemented in Pytorch and 2) works with the `transformer` library by Hugging Face. ###Code # default_exp ppo # export import numpy as np import torch.nn.functional as F from torch.optim import Adam import torch import collections import time import random from trl_custom.core import (logprobs_from_logits, whiten, clip_by_value, entropy_from_logits, flatten_dict, average_torch_dicts, stats_to_np, stack_dicts, add_suffix) ###Output _____no_output_____ ###Markdown KL-controllersTo ensure that the learned policy does not deviate too much from the original language model the KL divergence between the policy and a reference policy (the language model before PPO training) is used as an additional reward signal. Large KL-divergences are punished and staying close to the reference is rewarded.Two controllers are presented in the paper: an adaptive log-space proportional controller and a fixed controller. ###Code # exports class AdaptiveKLController: """ Adaptive KL controller described in the paper: https://arxiv.org/pdf/1909.08593.pdf """ def __init__(self, init_kl_coef, target, horizon): self.value = init_kl_coef self.target = target self.horizon = horizon def update(self, current, n_steps): target = self.target proportional_error = np.clip(current / target - 1, -0.2, 0.2) mult = 1 + proportional_error * n_steps / self.horizon self.value *= mult # exports class FixedKLController: """Fixed KL controller.""" def __init__(self, kl_coef): self.value = kl_coef def update(self, current, n_steps): pass # exports class PPOTrainer: """ The PPO_trainer uses Proximal Policy Optimization to optimise language models. """ default_params = { "lr": 1.41e-5, "adap_kl_ctrl": True, "init_kl_coef":0.2, "target": 6, "horizon":10000, "gamma":1, "lam":0.95, "cliprange": .2, "cliprange_value":.2, "vf_coef":.1, "batch_size": 256, "forward_batch_size": 16, "ppo_epochs": 4, } def __init__(self, policy_model, ref_model, value_model, **ppo_params): """ Initialize PPOTrainer. Args: model (torch.model): Hugging Face transformer model with value head ref_model (torch.model): Hugging Face transformer reference model used for KL penalty ppo_params (dict or None): PPO parameters for training. Can include following keys: 'lr' (float): Adam learning rate, default: 1.41e-5 'batch_size' (int): Number of samples per optimisation step, default: 256 'forward_batch_size' (int): Number of samples forward passed through model at a time, default: 16 'ppo_epochs' (int): Number of optimisation epochs per batch of samples, default: 4 'gamma' (float)): Gamma parameter for advantage calculation, default: 1. 'lam' (float): Lambda parameter for advantage calcualation, default: 0.95 'cliprange_value' (float): Range for clipping values in loss calculation, default: 0.2 'cliprange' (float): Range for clipping in PPO policy gradient loss, default: 0.2 'vf_coef' (float): Scaling factor for value loss, default: 0.1 'adap_kl_ctrl' (bool): Use adaptive KL control, otherwise linear, default: True 'init_kl_coef' (float): Initial KL penalty coefficient (used for adaptive and linear control), default: 0.2 'target' (float): Target KL value for adaptive KL control, default: 6.0 'horizon' (float): Horizon for adaptive KL control, default: 10000 """ self.ppo_params = self.default_params self.ppo_params.update(ppo_params) self.ref_model = ref_model self.policy_model = policy_model self.value_model = value_model self.policy_optimizer = Adam(policy_model.parameters(), lr=self.ppo_params['lr']) self.value_optimizer = Adam(value_model.parameters(), lr=self.ppo_params['lr']) if self.ppo_params['adap_kl_ctrl']: self.kl_ctl = AdaptiveKLController(self.ppo_params['init_kl_coef'], self.ppo_params['target'], self.ppo_params['horizon']) else: self.kl_ctl = FixedKLController(self.ppo_params['init_kl_coef']) def step(self, query, response, scores): """ Run a PPO optimisation step. args: query (torch.tensor): tensor containing the encoded queries, shape [batch_size, query_length] response (torch.tensor): tensor containing the encoded responses, shape [batch_size, response_length] scores (torch.tensor): tensor containing the scores, shape [batch_size] returns: train_stats (dict): a summary of the training statistics """ bs = self.ppo_params['batch_size'] timing = dict() t0 = time.time() gen_len = response.shape[1] model_input = torch.cat((query, response), axis=1) t = time.time() logprobs, ref_logprobs, values = self.batched_forward_pass(model_input, gen_len) timing['time/ppo/forward_pass'] = time.time()-t t = time.time() rewards, non_score_reward, kl_coef = self.compute_rewards(scores, logprobs, ref_logprobs) timing['time/ppo/compute_rewards'] = time.time()-t t = time.time() all_stats = [] idxs = list(range(bs)) for _ in range(self.ppo_params['ppo_epochs']): random.shuffle(idxs) for i in range(bs): idx = idxs[i] train_stats = self.train_minibatch(logprobs[idx:idx+1], values[idx:idx+1], rewards[idx:idx+1], response[idx:idx+1], model_input[idx:idx+1]) all_stats.append(train_stats) timing['time/ppo/optimize_step'] = time.time()-t t = time.time() train_stats = stack_dicts(all_stats) # reshape advantages/ratios such that they are not averaged. train_stats['policy/advantages'] = torch.flatten(train_stats['policy/advantages']).unsqueeze(0) train_stats['policy/ratio'] = torch.flatten(train_stats['policy/ratio']).unsqueeze(0) stats = self.record_step_stats(scores=scores, logprobs=logprobs, ref_logprobs=ref_logprobs, non_score_reward=non_score_reward, train_stats=train_stats, kl_coef=kl_coef) stats = stats_to_np(stats) timing['time/ppo/calc_stats'] = time.time()-t self.kl_ctl.update(stats['objective/kl'], self.ppo_params['batch_size']) timing['time/ppo/total'] = time.time()-t0 stats.update(timing) return stats def batched_forward_pass(self, model_input, gen_len): """Calculate model outputs in multiple batches.""" bs = self.ppo_params['batch_size'] fbs = self.ppo_params['forward_batch_size'] logprobs = [] ref_logprobs = [] values = [] for i in range(int(self.ppo_params['batch_size']/fbs)): m_input = model_input[i*fbs:(i+1)*fbs] logits, _, _ = self.policy_model(m_input) _, _, v = self.value_model(m_input) ref_logits, _, _ = self.ref_model(m_input) values.append(v[:, -gen_len-1:-1].detach()) logprobs.append(logprobs_from_logits(logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) ref_logprobs.append(logprobs_from_logits(ref_logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) return torch.cat(logprobs), torch.cat(ref_logprobs), torch.cat(values) def train_minibatch(self, logprobs, values, rewards, response, model_input): """Train one PPO minibatch""" loss_p, train_stats = self.loss_policy(logprobs, values, rewards, response, model_input) loss_v = self.loss_value(values, rewards, response, model_input) self.policy_optimizer.zero_grad() self.value_optimizer.zero_grad() loss_p.backward() loss_v.backward() self.policy_optimizer.step() self.value_optimizer.step() return train_stats def compute_rewards(self, scores, logprobs, ref_logprobs): """Compute per token rewards from scores and KL-penalty.""" kl = logprobs - ref_logprobs non_score_reward = -self.kl_ctl.value * kl rewards = non_score_reward.clone().detach() rewards[:, -1] += scores return rewards, non_score_reward, self.kl_ctl.value def loss_value(self, values, rewards, response, model_input): """Calculate value loss""" lastgaelam = 0 advantages_reversed = [] gen_len = response.shape[1] for t in reversed(range(gen_len)): nextvalues = values[:, t + 1] if t < gen_len - 1 else 0.0 delta = rewards[:, t] + self.ppo_params['gamma'] * nextvalues - values[:, t] lastgaelam = delta + self.ppo_params['gamma'] * self.ppo_params['lam'] * lastgaelam advantages_reversed.append(lastgaelam) advantages = torch.stack(advantages_reversed[::-1]).transpose(0, 1) returns = advantages + values advantages = whiten(advantages) advantages = advantages.detach() logits, _, _ = self.policy_model(model_input) _, _, vpred = self.value_model(model_input) logprob = logprobs_from_logits(logits[:,:-1,:], model_input[:, 1:]) #only the generation part of the values/logprobs is needed logprob, vpred = logprob[:, -gen_len:], vpred[:,-gen_len-1:-1] vpredclipped = clip_by_value(vpred, values - self.ppo_params["cliprange_value"], values + self.ppo_params["cliprange_value"]) vf_losses1 = (vpred - returns)**2 vf_losses2 = (vpredclipped - returns)**2 vf_loss = .5 * torch.mean(torch.max(vf_losses1, vf_losses2)) return self.ppo_params['vf_coef'] * vf_loss def loss_policy(self, old_logprobs, values, rewards, response, model_input): """Calculate policy loss.""" lastgaelam = 0 advantages_reversed = [] gen_len = response.shape[1] for t in reversed(range(gen_len)): nextvalues = values[:, t + 1] if t < gen_len - 1 else 0.0 delta = rewards[:, t] + self.ppo_params['gamma'] * nextvalues - values[:, t] lastgaelam = delta + self.ppo_params['gamma'] * self.ppo_params['lam'] * lastgaelam advantages_reversed.append(lastgaelam) advantages = torch.stack(advantages_reversed[::-1]).transpose(0, 1) returns = advantages + values advantages = whiten(advantages) advantages = advantages.detach() logits, _, _ = self.policy_model(model_input) _, _, vpred = self.value_model(model_input) logprob = logprobs_from_logits(logits[:,:-1,:], model_input[:, 1:]) #only the generation part of the values/logprobs is needed logprob, vpred = logprob[:, -gen_len:], vpred[:,-gen_len-1:-1] vpredclipped = clip_by_value(vpred, values - self.ppo_params["cliprange_value"], values + self.ppo_params["cliprange_value"]) vf_losses1 = (vpred - returns)**2 vf_losses2 = (vpredclipped - returns)**2 vf_loss = .5 * torch.mean(torch.max(vf_losses1, vf_losses2)) vf_clipfrac = torch.mean(torch.gt(vf_losses2, vf_losses1).double()) ratio = torch.exp(logprob - old_logprobs) pg_losses = -advantages * ratio pg_losses2 = -advantages * torch.clamp(ratio, 1.0 - self.ppo_params['cliprange'], 1.0 + self.ppo_params['cliprange']) pg_loss = torch.mean(torch.max(pg_losses, pg_losses2)) pg_clipfrac = torch.mean(torch.gt(pg_losses2, pg_losses).double()) entropy = torch.mean(entropy_from_logits(logits)) approxkl = .5 * torch.mean((logprob - old_logprobs)**2) policykl = torch.mean(logprob - old_logprobs) return_mean, return_var = torch.mean(returns), torch.var(returns) value_mean, value_var = torch.mean(values), torch.var(values) stats = dict( loss=dict(policy=pg_loss, value=vf_loss), policy=dict(entropy=entropy, approxkl=approxkl,policykl=policykl, clipfrac=pg_clipfrac, advantages=advantages, advantages_mean=torch.mean(advantages), ratio=ratio), returns=dict(mean=return_mean, var=return_var), val=dict(vpred=torch.mean(vpred), error=torch.mean((vpred - returns) ** 2), clipfrac=vf_clipfrac, mean=value_mean, var=value_var), ) return pg_loss, flatten_dict(stats) def record_step_stats(self, kl_coef, **data): """Record training step statistics.""" kl = data['logprobs'] - data['ref_logprobs'] mean_kl = torch.mean(torch.sum(kl, axis=-1)) mean_entropy = torch.mean(torch.sum(-data['logprobs'], axis=1)) mean_non_score_reward =torch.mean(torch.sum(data['non_score_reward'], axis=1)) stats = { 'objective/kl': mean_kl, 'objective/kl_dist': kl, 'objective/logprobs': data['logprobs'], 'objective/ref_logprobs': data['ref_logprobs'], 'objective/kl_coef': kl_coef, 'objective/entropy': mean_entropy, 'ppo/mean_non_score_reward': mean_non_score_reward, } for k, v in data['train_stats'].items(): stats[f'ppo/{k}'] = torch.mean(v, axis=0) stats['ppo/val/var_explained'] = 1 - stats['ppo/val/error'] / stats['ppo/returns/var'] return stats ###Output _____no_output_____ ###Markdown PPO for transformer models> A Pytorch implementation of Proximal Policy Optimization for transfomer models. This follows the language model approach proposed in paper ["Fine-Tuning Language Models from Human Preferences"](https://arxiv.org/pdf/1909.08593.pdf) and is similar to the [original implementation](https://github.com/openai/lm-human-preferences). The two main differences are 1) the method is implemented in Pytorch and 2) works with the `transformer` library by Hugging Face. ###Code # default_exp ppo # export import numpy as np import torch.nn.functional as F from torch.optim import Adam import torch import collections import time import random from trl.core import (logprobs_from_logits, whiten, clip_by_value, entropy_from_logits, flatten_dict, average_torch_dicts, stats_to_np, stack_dicts, add_suffix) ###Output _____no_output_____ ###Markdown KL-controllersTo ensure that the learned policy does not deviate to much from the original language model the KL divergence between the policy and a reference policy (the language model before PPO training) is used as an additional reward signal. Large KL-divergences are punished and staying close to the reference is rewarded.Two controllers are presented in the paper: an adaptive log-space proportional controller and a fixed controller. ###Code # exports class AdaptiveKLController: """ Adaptive KL controller described in the paper: https://arxiv.org/pdf/1909.08593.pdf """ def __init__(self, init_kl_coef, target, horizon): self.value = init_kl_coef self.target = target self.horizon = horizon def update(self, current, n_steps): target = self.target proportional_error = np.clip(current / target - 1, -0.2, 0.2) mult = 1 + proportional_error * n_steps / self.horizon self.value *= mult # exports class FixedKLController: """Fixed KL controller.""" def __init__(self, kl_coef): self.value = kl_coef def update(self, current, n_steps): pass # exports class PPOTrainer: """ The PPO_trainer uses Proximal Policy Optimization to optimise language models. """ default_params = { "lr": 1.41e-5, "adap_kl_ctrl": True, "init_kl_coef":0.2, "target": 6, "horizon":10000, "gamma":1, "lam":0.95, "cliprange": .2, "cliprange_value":.2, "vf_coef":.1, "batch_size": 256, "forward_batch_size": 16, "ppo_epochs": 4, } def __init__(self, model, ref_model, **ppo_params): """ Initialize PPOTrainer. Args: model (torch.model): Hugging Face transformer GPT2 model with value head ref_model (torch.model): Hugging Face transformer GPT2 refrence model used for KL penalty ppo_params (dict or None): PPO parameters for training. Can include following keys: 'lr' (float): Adam learning rate, default: 1.41e-5 'batch_size' (int): Number of samples per optimisation step, default: 256 'forward_batch_size' (int): Number of samples forward passed through model at a time, default: 16 'ppo_epochs' (int): Number of optimisation epochs per batch of samples, default: 4 'gamma' (float)): Gamma parameter for advantage calculation, default: 1. 'lam' (float): Lambda parameter for advantage calcualation, default: 0.95 'cliprange_value' (float): Range for clipping values in loss calculation, default: 0.2 'cliprange' (float): Range for clipping in PPO policy gradient loss, default: 0.2 'vf_coef' (float): Scaling factor for value loss, default: 0.1 'adap_kl_ctrl' (bool): Use adaptive KL control, otherwise linear, default: True 'init_kl_coef' (float): Initial KL penalty coefficient (used for adaptive and linear control), default: 0.2 'target' (float): Target KL value for adaptive KL control, default: 6.0 'horizon' (float): Horizon for adaptive KL control, default: 10000 """ self.ppo_params = self.default_params self.ppo_params.update(ppo_params) self.ref_model = ref_model self.model = model self.optimizer = Adam(model.parameters(), lr=self.ppo_params['lr']) if self.ppo_params['adap_kl_ctrl']: self.kl_ctl = AdaptiveKLController(self.ppo_params['init_kl_coef'], self.ppo_params['target'], self.ppo_params['horizon']) else: self.kl_ctl = FixedKLController(self.ppo_params['init_kl_coef']) def step(self, query, response, scores): """ Run a PPO optimisation step. args: query (torch.tensor): tensor containing the encoded queries, shape [batch_size, query_length] response (torch.tensor): tensor containing the encoded responses, shape [batch_size, response_length] scores (torch.tensor): tensor containing the scores, shape [batch_size] returns: train_stats (dict): a summary of the training statistics """ bs = self.ppo_params['batch_size'] timing = dict() t0 = time.time() gen_len = response.shape[1] model_input = torch.cat((query, response), axis=1) t = time.time() logprobs, ref_logprobs, values = self.batched_forward_pass(model_input, gen_len) timing['time/ppo/forward_pass'] = time.time()-t t = time.time() rewards, non_score_reward, kl_coef = self.compute_rewards(scores, logprobs, ref_logprobs) timing['time/ppo/compute_rewards'] = time.time()-t t = time.time() all_stats = [] idxs = list(range(bs)) for _ in range(self.ppo_params['ppo_epochs']): random.shuffle(idxs) for i in range(bs): idx = idxs[i] train_stats = self.train_minibatch(logprobs[idx:idx+1], values[idx:idx+1], rewards[idx:idx+1], query[idx:idx+1], response[idx:idx+1], model_input[idx:idx+1]) all_stats.append(train_stats) timing['time/ppo/optimize_step'] = time.time()-t t = time.time() train_stats = stack_dicts(all_stats) # reshape advantages/ratios such that they are not averaged. train_stats['policy/advantages'] = torch.flatten(train_stats['policy/advantages']).unsqueeze(0) train_stats['policy/ratio'] = torch.flatten(train_stats['policy/ratio']).unsqueeze(0) stats = self.record_step_stats(scores=scores, logprobs=logprobs, ref_logprobs=ref_logprobs, non_score_reward=non_score_reward, train_stats=train_stats, kl_coef=kl_coef) stats = stats_to_np(stats) timing['time/ppo/calc_stats'] = time.time()-t self.kl_ctl.update(stats['objective/kl'], self.ppo_params['batch_size']) timing['time/ppo/total'] = time.time()-t0 stats.update(timing) return stats def batched_forward_pass(self, model_input, gen_len): """Calculate model outputs in multiple batches.""" bs = self.ppo_params['batch_size'] fbs = self.ppo_params['forward_batch_size'] logprobs = [] ref_logprobs = [] values = [] for i in range(int(self.ppo_params['batch_size']/fbs)): m_input = model_input[i*fbs:(i+1)*fbs] logits, _, v = self.model(m_input) ref_logits, _, _ = self.ref_model(m_input) values.append(v[:, -gen_len-1:-1].detach()) logprobs.append(logprobs_from_logits(logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) ref_logprobs.append(logprobs_from_logits(ref_logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) return torch.cat(logprobs), torch.cat(ref_logprobs), torch.cat(values) def train_minibatch(self, logprobs, values, rewards, query, response, model_input): """Train one PPO minibatch""" loss_p, loss_v, train_stats = self.loss(logprobs, values, rewards, query, response, model_input) loss = loss_p + loss_v self.optimizer.zero_grad() loss.backward() self.optimizer.step() return train_stats def compute_rewards(self, scores, logprobs, ref_logprobs): """Compute per token rewards from scores and KL-penalty.""" kl = logprobs - ref_logprobs non_score_reward = -self.kl_ctl.value * kl rewards = non_score_reward.clone().detach() rewards[:, -1] += scores return rewards, non_score_reward, self.kl_ctl.value def loss(self, old_logprobs, values, rewards, query, response, model_input): """Calculate policy and value losses.""" lastgaelam = 0 advantages_reversed = [] gen_len = response.shape[1] for t in reversed(range(gen_len)): nextvalues = values[:, t + 1] if t < gen_len - 1 else 0.0 delta = rewards[:, t] + self.ppo_params['gamma'] * nextvalues - values[:, t] lastgaelam = delta + self.ppo_params['gamma'] * self.ppo_params['lam'] * lastgaelam advantages_reversed.append(lastgaelam) advantages = torch.stack(advantages_reversed[::-1]).transpose(0, 1) returns = advantages + values advantages = whiten(advantages) advantages = advantages.detach() logits, _, vpred = self.model(model_input) logprob = logprobs_from_logits(logits[:,:-1,:], model_input[:, 1:]) #only the generation part of the values/logprobs is needed logprob, vpred = logprob[:, -gen_len:], vpred[:,-gen_len-1:-1] vpredclipped = clip_by_value(vpred, values - self.ppo_params["cliprange_value"], values + self.ppo_params["cliprange_value"]) vf_losses1 = (vpred - returns)**2 vf_losses2 = (vpredclipped - returns)**2 vf_loss = .5 * torch.mean(torch.max(vf_losses1, vf_losses2)) vf_clipfrac = torch.mean(torch.gt(vf_losses2, vf_losses1).double()) ratio = torch.exp(logprob - old_logprobs) pg_losses = -advantages * ratio pg_losses2 = -advantages * torch.clamp(ratio, 1.0 - self.ppo_params['cliprange'], 1.0 + self.ppo_params['cliprange']) pg_loss = torch.mean(torch.max(pg_losses, pg_losses2)) pg_clipfrac = torch.mean(torch.gt(pg_losses2, pg_losses).double()) loss = pg_loss + self.ppo_params['vf_coef'] * vf_loss entropy = torch.mean(entropy_from_logits(logits)) approxkl = .5 * torch.mean((logprob - old_logprobs)**2) policykl = torch.mean(logprob - old_logprobs) return_mean, return_var = torch.mean(returns), torch.var(returns) value_mean, value_var = torch.mean(values), torch.var(values) stats = dict( loss=dict(policy=pg_loss, value=vf_loss, total=loss), policy=dict(entropy=entropy, approxkl=approxkl,policykl=policykl, clipfrac=pg_clipfrac, advantages=advantages, advantages_mean=torch.mean(advantages), ratio=ratio), returns=dict(mean=return_mean, var=return_var), val=dict(vpred=torch.mean(vpred), error=torch.mean((vpred - returns) ** 2), clipfrac=vf_clipfrac, mean=value_mean, var=value_var), ) return pg_loss, self.ppo_params['vf_coef'] * vf_loss, flatten_dict(stats) def record_step_stats(self, kl_coef, **data): """Record training step statistics.""" kl = data['logprobs'] - data['ref_logprobs'] mean_kl = torch.mean(torch.sum(kl, axis=-1)) mean_entropy = torch.mean(torch.sum(-data['logprobs'], axis=1)) mean_non_score_reward =torch.mean(torch.sum(data['non_score_reward'], axis=1)) stats = { 'objective/kl': mean_kl, 'objective/kl_dist': kl, 'objective/logprobs': data['logprobs'], 'objective/ref_logprobs': data['ref_logprobs'], 'objective/kl_coef': kl_coef, 'objective/entropy': mean_entropy, 'ppo/mean_non_score_reward': mean_non_score_reward, } for k, v in data['train_stats'].items(): stats[f'ppo/{k}'] = torch.mean(v, axis=0) stats['ppo/val/var_explained'] = 1 - stats['ppo/val/error'] / stats['ppo/returns/var'] return stats ###Output _____no_output_____ ###Markdown PPO for transformer models> A Pytorch implementation of Proximal Policy Optimization for transfomer models. This follows the language model approach proposed in paper ["Fine-Tuning Language Models from Human Preferences"](https://arxiv.org/pdf/1909.08593.pdf) and is similar to the [original implementation](https://github.com/openai/lm-human-preferences). The two main differences are 1) the method is implemented in Pytorch and 2) works with the `transformer` library by Hugging Face. ###Code # default_exp ppo # export import numpy as np import torch.nn.functional as F from torch.optim import Adam import torch import collections import time import random from trl.core import (logprobs_from_logits, whiten, clip_by_value, entropy_from_logits, flatten_dict, average_torch_dicts, stats_to_np, stack_dicts, add_suffix) ###Output _____no_output_____ ###Markdown KL-controllersTo ensure that the learned policy does not deviate to much from the original language model the KL divergence between the policy and a reference policy (the language model before PPO training) is used as an additional reward signal. Large KL-divergences are punished and staying close to the reference is rewarded.Two controllers are presented in the paper: an adaptive log-space proportional controller and a fixed controller. ###Code # exports class AdaptiveKLController: """ Adaptive KL controller described in the paper: https://arxiv.org/pdf/1909.08593.pdf """ def __init__(self, init_kl_coef, target, horizon): self.value = init_kl_coef self.target = target self.horizon = horizon def update(self, current, n_steps): target = self.target proportional_error = np.clip(current / target - 1, -0.2, 0.2) mult = 1 + proportional_error * n_steps / self.horizon self.value *= mult # exports class FixedKLController: """Fixed KL controller.""" def __init__(self, kl_coef): self.value = kl_coef def update(self, current, n_steps): pass # exports class PPOTrainer: """ The PPO_trainer uses Proximal Policy Optimization to optimise language models. """ default_params = { "lr": 1.41e-5, "adap_kl_ctrl": True, "init_kl_coef":0.2, "target": 6, "horizon":10000, "gamma":1, "lam":0.95, "cliprange": .2, "cliprange_value":.2, "vf_coef":.1, "batch_size": 256, "forward_batch_size": 16, "ppo_epochs": 4, } def __init__(self, model, ref_model, **ppo_params): """ Initialize PPOTrainer. Args: model (torch.model): Hugging Face transformer GPT2 model with value head ref_model (torch.model): Hugging Face transformer GPT2 refrence model used for KL penalty ppo_params (dict or None): PPO parameters for training. Can include following keys: 'lr' (float): Adam learning rate, default: 1.41e-5 'batch_size' (int): Number of samples per optimisation step, default: 256 'forward_batch_size' (int): Number of samples forward passed through model at a time, default: 16 'ppo_epochs' (int): Number of optimisation epochs per batch of samples, default: 4 'gamma' (float)): Gamma parameter for advantage calculation, default: 1. 'lam' (float): Lambda parameter for advantage calcualation, default: 0.95 'cliprange_value' (float): Range for clipping values in loss calculation, default: 0.2 'cliprange' (float): Range for clipping in PPO policy gradient loss, default: 0.2 'vf_coef' (float): Scaling factor for value loss, default: 0.1 'adap_kl_ctrl' (bool): Use adaptive KL control, otherwise linear, default: True 'init_kl_coef' (float): Initial KL penalty coefficient (used for adaptive and linear control), default: 0.2 'target' (float): Target KL value for adaptive KL control, default: 6.0 'horizon' (float): Horizon for adaptive KL control, default: 10000 """ self.ppo_params = self.default_params self.ppo_params.update(ppo_params) self.ref_model = ref_model self.model = model self.optimizer = Adam(model.parameters(), lr=self.ppo_params['lr']) self.kl_ctl = AdaptiveKLController(self.ppo_params['init_kl_coef'], self.ppo_params['target'], self.ppo_params['horizon']) def step(self, query, response, scores): """ Run a PPO optimisation step. args: query (torch.tensor): tensor containing the encoded queries, shape [batch_size, query_length] response (torch.tensor): tensor containing the encoded responses, shape [batch_size, response_length] scores (torch.tensor): tensor containing the scores, shape [batch_size] returns: train_stats (dict): a summary of the training statistics """ bs = self.ppo_params['batch_size'] timing = dict() t0 = time.time() gen_len = response.shape[1] model_input = torch.cat((query, response), axis=1) t = time.time() logprobs, ref_logprobs, values = self.batched_forward_pass(model_input, gen_len) timing['time/ppo/forward_pass'] = time.time()-t t = time.time() rewards, non_score_reward, kl_coef = self.compute_rewards(scores, logprobs, ref_logprobs) timing['time/ppo/compute_rewards'] = time.time()-t t = time.time() all_stats = [] idxs = list(range(bs)) for _ in range(self.ppo_params['ppo_epochs']): random.shuffle(idxs) for i in range(bs): idx = idxs[i] train_stats = self.train_minibatch(logprobs[idx:idx+1], values[idx:idx+1], rewards[idx:idx+1], query[idx:idx+1], response[idx:idx+1], model_input[idx:idx+1]) all_stats.append(train_stats) timing['time/ppo/optimize_step'] = time.time()-t t = time.time() train_stats = stack_dicts(all_stats) # reshape advantages/ratios such that they are not averaged. train_stats['policy/advantages'] = torch.flatten(train_stats['policy/advantages']).unsqueeze(0) train_stats['policy/ratio'] = torch.flatten(train_stats['policy/ratio']).unsqueeze(0) stats = self.record_step_stats(scores=scores, logprobs=logprobs, ref_logprobs=ref_logprobs, non_score_reward=non_score_reward, train_stats=train_stats, kl_coef=kl_coef) stats = stats_to_np(stats) timing['time/ppo/calc_stats'] = time.time()-t self.kl_ctl.update(stats['objective/kl'], self.ppo_params['batch_size']) timing['time/ppo/total'] = time.time()-t0 stats.update(timing) return stats def batched_forward_pass(self, model_input, gen_len): """Calculate model outputs in multiple batches.""" bs = self.ppo_params['batch_size'] fbs = self.ppo_params['forward_batch_size'] logprobs = [] ref_logprobs = [] values = [] for i in range(int(self.ppo_params['batch_size']/fbs)): m_input = model_input[i*fbs:(i+1)*fbs] logits, _, v = self.model(m_input) ref_logits, _, _ = self.ref_model(m_input) values.append(v[:, -gen_len-1:-1].detach()) logprobs.append(logprobs_from_logits(logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) ref_logprobs.append(logprobs_from_logits(ref_logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) return torch.cat(logprobs), torch.cat(ref_logprobs), torch.cat(values) def train_minibatch(self, logprobs, values, rewards, query, response, model_input): """Train one PPO minibatch""" loss_p, loss_v, train_stats = self.loss(logprobs, values, rewards, query, response, model_input) loss = loss_p + loss_v self.optimizer.zero_grad() loss.backward() self.optimizer.step() return train_stats def compute_rewards(self, scores, logprobs, ref_logprobs): """Compute per token rewards from scores and KL-penalty.""" kl = logprobs - ref_logprobs non_score_reward = -self.kl_ctl.value * kl rewards = non_score_reward.clone().detach() rewards[:, -1] += scores return rewards, non_score_reward, self.kl_ctl.value def loss(self, old_logprobs, values, rewards, query, response, model_input): """Calculate policy and value losses.""" lastgaelam = 0 advantages_reversed = [] gen_len = response.shape[1] for t in reversed(range(gen_len)): nextvalues = values[:, t + 1] if t < gen_len - 1 else 0.0 delta = rewards[:, t] + self.ppo_params['gamma'] * nextvalues - values[:, t] lastgaelam = delta + self.ppo_params['gamma'] * self.ppo_params['lam'] * lastgaelam advantages_reversed.append(lastgaelam) advantages = torch.stack(advantages_reversed[::-1]).transpose(0, 1) returns = advantages + values advantages = whiten(advantages) advantages = advantages.detach() logits, _, vpred = self.model(model_input) logprob = logprobs_from_logits(logits[:,:-1,:], model_input[:, 1:]) #only the generation part of the values/logprobs is needed logprob, vpred = logprob[:, -gen_len:], vpred[:,-gen_len-1:-1] vpredclipped = clip_by_value(vpred, values - self.ppo_params["cliprange_value"], values + self.ppo_params["cliprange_value"]) vf_losses1 = (vpred - returns)**2 vf_losses2 = (vpredclipped - returns)**2 vf_loss = .5 * torch.mean(torch.max(vf_losses1, vf_losses2)) vf_clipfrac = torch.mean(torch.gt(vf_losses2, vf_losses1).double()) ratio = torch.exp(logprob - old_logprobs) pg_losses = -advantages * ratio pg_losses2 = -advantages * torch.clamp(ratio, 1.0 - self.ppo_params['cliprange'], 1.0 + self.ppo_params['cliprange']) pg_loss = torch.mean(torch.max(pg_losses, pg_losses2)) pg_clipfrac = torch.mean(torch.gt(pg_losses2, pg_losses).double()) loss = pg_loss + self.ppo_params['vf_coef'] * vf_loss entropy = torch.mean(entropy_from_logits(logits)) approxkl = .5 * torch.mean((logprob - old_logprobs)**2) policykl = torch.mean(logprob - old_logprobs) return_mean, return_var = torch.mean(returns), torch.var(returns) value_mean, value_var = torch.mean(values), torch.var(values) stats = dict( loss=dict(policy=pg_loss, value=vf_loss, total=loss), policy=dict(entropy=entropy, approxkl=approxkl,policykl=policykl, clipfrac=pg_clipfrac, advantages=advantages, advantages_mean=torch.mean(advantages), ratio=ratio), returns=dict(mean=return_mean, var=return_var), val=dict(vpred=torch.mean(vpred), error=torch.mean((vpred - returns) ** 2), clipfrac=vf_clipfrac, mean=value_mean, var=value_var), ) return pg_loss, self.ppo_params['vf_coef'] * vf_loss, flatten_dict(stats) def record_step_stats(self, kl_coef, **data): """Record training step statistics.""" kl = data['logprobs'] - data['ref_logprobs'] mean_kl = torch.mean(torch.sum(kl, axis=-1)) mean_entropy = torch.mean(torch.sum(-data['logprobs'], axis=1)) mean_non_score_reward =torch.mean(torch.sum(data['non_score_reward'], axis=1)) stats = { 'objective/kl': mean_kl, 'objective/kl_dist': kl, 'objective/logprobs': data['logprobs'], 'objective/ref_logprobs': data['ref_logprobs'], 'objective/kl_coef': kl_coef, 'objective/entropy': mean_entropy, 'ppo/mean_non_score_reward': mean_non_score_reward, } for k, v in data['train_stats'].items(): stats[f'ppo/{k}'] = torch.mean(v, axis=0) stats['ppo/val/var_explained'] = 1 - stats['ppo/val/error'] / stats['ppo/returns/var'] return stats ###Output _____no_output_____ ###Markdown PPO for transformer models> A Pytorch implementation of Proximal Policy Optimization for transfomer models. This follows the language model approach proposed in paper ["Fine-Tuning Language Models from Human Preferences"](https://arxiv.org/pdf/1909.08593.pdf) and is similar to the [original implementation](https://github.com/openai/lm-human-preferences). The two main differences are 1) the method is implemented in Pytorch and 2) works with the `transformer` library by Hugging Face. ###Code # default_exp ppo # export import numpy as np import torch.nn.functional as F from torch.optim import Adam import torch import collections import time import random from trl.core import (logprobs_from_logits, whiten, clip_by_value, entropy_from_logits, flatten_dict, average_torch_dicts, stats_to_np, stack_dicts, add_suffix) ###Output _____no_output_____ ###Markdown KL-controllersTo ensure that the learned policy does not deviate to much from the original language model the KL divergence between the policy and a reference policy (the language model before PPO training) is used as an additional reward signal. Large KL-divergences are punished and staying close to the reference is rewarded.Two controllers are presented in the paper: an adaptive log-space proportional controller and a fixed controller. ###Code # exports class AdaptiveKLController: """ Adaptive KL controller described in the paper: https://arxiv.org/pdf/1909.08593.pdf """ def __init__(self, init_kl_coef, target, horizon): self.value = init_kl_coef self.target = target self.horizon = horizon def update(self, current, n_steps): target = self.target proportional_error = np.clip(current / target - 1, -0.2, 0.2) mult = 1 + proportional_error * n_steps / self.horizon self.value *= mult # exports class FixedKLController: """Fixed KL controller.""" def __init__(self, kl_coef): self.value = kl_coef def update(self, current, n_steps): pass # exports class PPOTrainer: """ The PPO_trainer uses Proximal Policy Optimization to optimise language models. """ default_params = { "lr": 1.41e-5, "adap_kl_ctrl": True, "init_kl_coef":0.2, "target": 6, "horizon":10000, "gamma":1, "lam":0.95, "cliprange": .2, "cliprange_value":.2, "vf_coef":.1, "batch_size": 256, "forward_batch_size": 16, "ppo_epochs": 4, } def __init__(self, model, ref_model, **ppo_params): """ Initialize PPOTrainer. Args: model (torch.model): Hugging Face transformer GPT2 model with value head ref_model (torch.model): Hugging Face transformer GPT2 refrence model used for KL penalty ppo_params (dict or None): PPO parameters for training. Can include following keys: 'lr' (float): Adam learning rate, default: 1.41e-5 'batch_size' (int): Number of samples per optimisation step, default: 256 'forward_batch_size' (int): Number of samples forward passed through model at a time, default: 16 'ppo_epochs' (int): Number of optimisation epochs per batch of samples, default: 4 'gamma' (float)): Gamma parameter for advantage calculation, default: 1. 'lam' (float): Lambda parameter for advantage calcualation, default: 0.95 'cliprange_value' (float): Range for clipping values in loss calculation, default: 0.2 'cliprange' (float): Range for clipping in PPO policy gradient loss, default: 0.2 'vf_coef' (float): Scaling factor for value loss, default: 0.1 'adap_kl_ctrl' (bool): Use adaptive KL control, otherwise linear, default: True 'init_kl_coef' (float): Initial KL penalty coefficient (used for adaptive and linear control), default: 0.2 'target' (float): Target KL value for adaptive KL control, default: 6.0 'horizon' (float): Horizon for adaptive KL control, default: 10000 """ self.ppo_params = self.default_params self.ppo_params.update(ppo_params) self.ref_model = ref_model self.model = model self.optimizer = Adam(model.parameters(), lr=self.ppo_params['lr']) self.kl_ctl = AdaptiveKLController(self.ppo_params['init_kl_coef'], self.ppo_params['target'], self.ppo_params['horizon']) def step(self, query, response, scores): """ Run a PPO optimisation step. args: query (torch.tensor): tensor containing the encoded queries, shape [batch_size, query_length] response (torch.tensor): tensor containing the encoded responses, shape [batch_size, response_length] scores (torch.tensor): tensor containing the scores, shape [batch_size] returns: train_stats (dict): a summary of the training statistics """ bs = self.ppo_params['batch_size'] timing = dict() t0 = time.time() gen_len = response.shape[1] model_input = torch.cat((query, response), axis=1) t = time.time() logprobs, ref_logprobs, values = self.batched_forward_pass(model_input, gen_len) timing['time/ppo/forward_pass'] = time.time()-t t = time.time() rewards, non_score_reward, kl_coef = self.compute_rewards(scores, logprobs, ref_logprobs) timing['time/ppo/compute_rewards'] = time.time()-t t = time.time() all_stats = [] idxs = list(range(bs)) for _ in range(self.ppo_params['ppo_epochs']): random.shuffle(idxs) for i in range(bs): idx = idxs[i] train_stats = self.train_minibatch(logprobs[idx:idx+1], values[idx:idx+1], rewards[idx:idx+1], query[idx:idx+1], response[idx:idx+1], model_input[idx:idx+1]) all_stats.append(train_stats) timing['time/ppo/optimize_step'] = time.time()-t t = time.time() train_stats = stack_dicts(all_stats) # reshape advantages/ratios such that they are not averaged. train_stats['policy/advantages'] = torch.flatten(train_stats['policy/advantages']).unsqueeze(0) train_stats['policy/ratio'] = torch.flatten(train_stats['policy/ratio']).unsqueeze(0) stats = self.record_step_stats(scores=scores, logprobs=logprobs, ref_logprobs=ref_logprobs, non_score_reward=non_score_reward, train_stats=train_stats, kl_coef=kl_coef) stats = stats_to_np(stats) timing['time/ppo/calc_stats'] = time.time()-t self.kl_ctl.update(stats['objective/kl'], self.ppo_params['batch_size']) timing['time/ppo/total'] = time.time()-t0 stats.update(timing) return stats def batched_forward_pass(self, model_input, gen_len): """Calculate model outputs in multiple batches.""" bs = self.ppo_params['batch_size'] fbs = self.ppo_params['forward_batch_size'] logprobs = [] ref_logprobs = [] values = [] for i in range(int(self.ppo_params['batch_size']/fbs)): m_input = model_input[i*fbs:(i+1)*fbs] logits, _, v = self.model(m_input) ref_logits, _, _ = self.ref_model(m_input) values.append(v[:, -gen_len-1:-1].detach()) logprobs.append(logprobs_from_logits(logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) ref_logprobs.append(logprobs_from_logits(ref_logits[:,:-1,:], m_input[:,1:])[:, -gen_len:].detach()) return torch.cat(logprobs), torch.cat(ref_logprobs), torch.cat(values) def train_minibatch(self, logprobs, values, rewards, query, response, model_input): """Train one PPO minibatch""" loss_p, loss_v, train_stats = self.loss(logprobs, values, rewards, query, response, model_input) loss = loss_p + loss_v self.optimizer.zero_grad() loss.backward() self.optimizer.step() return train_stats def compute_rewards(self, scores, logprobs, ref_logprobs): """Compute per token rewards from scores and KL-penalty.""" kl = logprobs - ref_logprobs non_score_reward = -self.kl_ctl.value * kl rewards = non_score_reward.clone().detach() rewards[:, -1] += scores return rewards, non_score_reward, self.kl_ctl.value def loss(self, old_logprobs, values, rewards, query, response, model_input): """Calculate policy and value losses.""" lastgaelam = 0 advantages_reversed = [] gen_len = response.shape[1] for t in reversed(range(gen_len)): nextvalues = values[:, t + 1] if t < gen_len - 1 else 0.0 delta = rewards[:, t] + self.ppo_params['gamma'] * nextvalues - values[:, t] lastgaelam = delta + self.ppo_params['gamma'] * self.ppo_params['lam'] * lastgaelam advantages_reversed.append(lastgaelam) advantages = torch.stack(advantages_reversed[::-1]).transpose(0, 1) returns = advantages + values advantages = whiten(advantages) advantages = advantages.detach() logits, _, vpred = self.model(model_input) logprob = logprobs_from_logits(logits[:,:-1,:], model_input[:, 1:]) #only the generation part of the values/logprobs is needed logprob, vpred = logprob[:, -gen_len:], vpred[:,-gen_len-1:-1] vpredclipped = clip_by_value(vpred, values - self.ppo_params["cliprange_value"], values + self.ppo_params["cliprange_value"]) vf_losses1 = (vpred - returns)**2 vf_losses2 = (vpredclipped - returns)**2 vf_loss = .5 * torch.mean(torch.max(vf_losses1, vf_losses2)) vf_clipfrac = torch.mean(torch.gt(vf_losses2, vf_losses1).double()) ratio = torch.exp(logprob - old_logprobs) pg_losses = -advantages * ratio pg_losses2 = -advantages * torch.clamp(ratio, 1.0 - self.ppo_params['cliprange'], 1.0 + self.ppo_params['cliprange']) pg_loss = torch.mean(torch.max(pg_losses, pg_losses2)) pg_clipfrac = torch.mean(torch.gt(pg_losses2, pg_losses).double()) loss = pg_loss + self.ppo_params['vf_coef'] * vf_loss entropy = torch.mean(entropy_from_logits(logits)) approxkl = .5 * torch.mean((logprob - old_logprobs)**2) policykl = torch.mean(logprob - old_logprobs) return_mean, return_var = torch.mean(returns), torch.var(returns) value_mean, value_var = torch.mean(values), torch.var(values) stats = dict( loss=dict(policy=pg_loss, value=vf_loss, total=loss), policy=dict(entropy=entropy, approxkl=approxkl,policykl=policykl, clipfrac=pg_clipfrac, advantages=advantages, advantages_mean=torch.mean(advantages), ratio=ratio), returns=dict(mean=return_mean, var=return_var), val=dict(vpred=torch.mean(vpred), error=torch.mean((vpred - returns) ** 2), clipfrac=vf_clipfrac, mean=value_mean, var=value_var), ) return pg_loss, self.ppo_params['vf_coef'] * vf_loss, flatten_dict(stats) def record_step_stats(self, kl_coef, **data): """Record training step statistics.""" kl = data['logprobs'] - data['ref_logprobs'] mean_kl = torch.mean(torch.sum(kl, axis=-1)) mean_entropy = torch.mean(torch.sum(-data['logprobs'], axis=1)) mean_non_score_reward =torch.mean(torch.sum(data['non_score_reward'], axis=1)) stats = { 'objective/kl': mean_kl, 'objective/kl_dist': kl, 'objective/logprobs': data['logprobs'], 'objective/ref_logprobs': data['ref_logprobs'], 'objective/kl_coef': kl_coef, 'objective/entropy': mean_entropy, 'ppo/mean_non_score_reward': mean_non_score_reward, } for k, v in data['train_stats'].items(): stats[f'ppo/{k}'] = torch.mean(v, axis=0) stats['ppo/val/var_explained'] = 1 - stats['ppo/val/error'] / stats['ppo/returns/var'] return stats ###Output _____no_output_____

notebooks/Learning Units/Models/Supervised/Linear Regression.ipynb

###Markdown Linear RegressionIn this learning unit, we will dive into linear regression, one of the most commonly used techniques for regression tasks.It is assumed that you have read the previous learning units on regression and that you have a working understanding of Python and the Numpy library, which are covered in previous learning units as well. Practical exampleLet's say that we are a real estate agent and we would like to know for how much we could try to sell a house, based on some specifications about it. We have access to a large database containing information about houses such as the number of bedrooms, whether they have a garage, the square footage, and so on. We also have access to how much these houses were sold for. Surely we can make use of this information to make better guesses than by solely relying on our gut feeling.If you had to write down a rule of thumb to estimate the price of a house if you were given some information about it, what would that rule be?You could of course guess the same price regardless of the house, but surely, a shack in the middle of the woods will cost less than a mansion in Beverly Hills. So there must be a better way!From experience, you might have realized that bigger houses generally sell for more. The more bedrooms, special features like a garden, a garage, etc. usually tend to influence the prize of the house. So how could you use this logic and transpose that as a rule that you can follow mechanically?You could define how much each bedroom costs, or how much having a garage will hike up the price of the house. That way, you simply have to look at your features, calculate how much each of these will cost, and add them all together. Of course, there might be a minimum price for which every house will go for.In code, it could look like this ###Code # Define costs minimum_cost = 80000 bedroom_cost = 25000 garage_cost = 10000 square_foot_price = 100 def price(n_bedrooms, n_garages, square_footage): """ returns the price of a house in dollars """ return minimum_cost + bedroom_cost * n_bedrooms + garage_cost * n_garages + square_foot_price * square_footage ###Output _____no_output_____ ###Markdown Now, we can estimate the price of houses! ###Code price(n_bedrooms=3, n_garages = 1, square_footage = 1000) ###Output _____no_output_____ ###Markdown Of course, in this example, we just gave you the cost of each feature, but what if you did not know them beforehand? How could you find costs that will give you good estimates for house prices?This is what linear regression tries to accomplish. It automatically finds the proper _costs_ such that if you add them all together, you will make the best guess about the price of the house. What does the model look like?One of the most important part of machine learning is to understand what the model is, what's under the hood.A linear regression model will be defined by a collection of weights or coefficients related to features, such that, if given features, we can compute an estimate the following way:```pythondef predict(features): return coefficients.dot(features)```The model can be represented by its coefficients, meaning that the size of the model is proportional to the number of features, not the size of the training data. The offsetTo be complete, it is important to add an offset to the features. This allows the model to account for some value like the minimum price of the house as we described in the previous section. The offset will simply be a "dummy" feature that will always equal 1. How does the model learn?Of course, what we will want to do is train our model such that it automatically finds the best coefficients.As explained in the learning unit about regression, a better model is traditionally the one that minizes the mean-squared error. Therefore, we could sample random coefficients and then pick the ones that optimize this criterion. In theory, if we sample enough coefficients, we should be able to eventually find the best ones. Obviously, in practice, this does not work. As there is an infinite number of possible coefficients, we cannot sample them all, and therefore we might miss out on the best coefficients and be stuck with suboptimal ones.So how can we be smarter?Let's take an example with one feature `x` and a target variable `y`. Obviously, the same principles apply to cases with more features.> It is also important to note that linear regression only works with numerical features, meaning that categorical features would have to be transformed into numerical features.> Linear regression cannot handle missing values, and therefore, either data points with missing values should be omitted, or inputation should be performed.> See the learning unit about preprocessing for more information ###Code import numpy as np # Create the data n_samples = 20 x = np.arange(n_samples) y = np.arange(n_samples) # Plotting the data import matplotlib.pyplot as plt plt.figure(1,figsize=(10,5)) plt.title("Simple linear regression problem: The data") plt.xlabel("feature") plt.ylabel("target") plt.plot(x,y,'bx') plt.show() ###Output _____no_output_____ ###Markdown Obviously, you can clearly see that all of these points sit on the line `y = x` with offset = 0. But how can the computer see it?Let's say that the model first starts with a random guess about the coefficients. ###Code # Initialize the coefficients with random values coefficients = np.random.rand(2) print("coefficients =",coefficients) def predict(coefficients): """ Function computing the output of the model based on coefficients """ return coefficients[0] + coefficients[1] * x # Plot the target variable as well as the output of the model plt.figure(1,figsize=(10,5)) plt.title("Simple linear regression problem: Random guess for the coefficients") plt.xlabel("feature") plt.ylabel("target") target, = plt.plot(x, y,'bx') model, = plt.plot(x, predict(coefficients),'r') plt.legend([target, model], ["Target values", "Current model"]) plt.show() ###Output coefficients = [ 0.73699517 0.05088406] ###Markdown As a human, if you had to tell the computer how to improve, you would probably say something in the line of "your line should be steeper". This is something that the computer can do by adjusting the current coefficients of the model.This raises two questions:- How can the computer know whether to increase or decrease each coefficient?- How much should the computer increase or decrease each coefficient?The first problem is being solved by the computer as humans would. It will try increasing and decreasing each coefficient and see which direction helps by looking at which decreases the mean-squared error. Hopefully, if you brush off your calculus knowledge, you'll realize that we just described computing the derivative of the mean-squared error with respect to each coefficient!In code, computing the mean-squared error with respect to the coefficients will look like this: ###Code def MSE(coefficients): return np.mean((predict(coefficients)-y)**2) print("Current MSE =", MSE(coefficients)) ###Output Current MSE = 98.5041803484 ###Markdown Thankfully, the mean-squared error is a function that has a derivative that can be derived analytically. Its derivative is defined as: ###Code def derivative_MSE(coefficients): # Compute error error = predict(coefficients) - y # Adding the offset to the features features = np.array([[1, feature] for feature in x]) return 0.5 * error.dot(features)/features.shape[0] print("Current derivatives =", derivative_MSE(coefficients)) ###Output Current derivatives = [ -4.13980313 -55.10718225] ###Markdown The sign of the derivative will tell us whether we need to increase or decrease each coefficient. Since we are trying to minimize the function, a negative derivative means that we have to increase the coefficient and vice versa.This can be easily shown by actually increasing and decreasing each coefficient by a small value and then computing the mean-squared error. If the mean-squared error is smaller, it means that this direction is good. ###Code epsilon = 0.1 coef = np.array([0.5,0.5]) # Current MSE current = MSE(coef) print("Current MSE =", current) # Current derivative (negative values mean that the coefficients must be increased) print("Current deratives = ", derivative_MSE(coef),"\n") print("decrease of MSE by increasing coef[0] = ", current - MSE(np.array([coef[0] + epsilon, coef[1]]))) print("decrease of MSE by decreasing coef[0] = ", current - MSE(np.array([coef[0] - epsilon, coef[1]]))) print("decrease of MSE by increasing coef[1] = ", current - MSE(np.array([coef[0], coef[1] + epsilon]))) print("decrease of MSE by decreasing coef[1] = ", current - MSE(np.array([coef[0], coef[1] - epsilon]))) ###Output Current MSE = 26.375 Current deratives = [ -2.125 -28.5 ] decrease of MSE by increasing coef[0] = 0.84 decrease of MSE by decreasing coef[0] = -0.86 decrease of MSE by increasing coef[1] = 10.165 decrease of MSE by decreasing coef[1] = -12.635 ###Markdown Now we need to answer the second question: "how much should we modify the current coefficients". Indeed, modifying them too much might backfire and modifying them too little might make the training very slow.Thankfully, the derivatives do not only provide us with the direction in which we should modify our coefficients, but they also give us an indication of how _useful_ it is to modify them. Indeed, a derivative with a high absolute value will indicate that a large change in the function can be achieved by modifying the coefficient in that direction. Vice versa, a derivative close to zero indicates that little to no improvement will be achieved.We can therefore use our derivatives as an indicator of how much we should modify each coefficient. In order to be even more in control, we will introduce a learning rate $\alpha$ which will scale these modifications. A higher learning-rate means that the modifications will be _harsher_, and vice versa.Updating the coefficients will look like this: ###Code def update_coefficients(coefficients, learning_rate): """ function updating coefficients based on their derivatives """ derivatives = derivative_MSE(coefficients) return coefficients - learning_rate*derivatives def run_update(learning_rate): """ updates coefficients, prints information about the update and plot it """ print("Current coefficients =", coefficients) print("Current MSE = ", MSE(coefficients)) print("Current derivatives =", derivative_MSE(coefficients),"\n") new_coefficients = update_coefficients(coefficients,learning_rate) print("New coefficients =", new_coefficients) print("New MSE = ", MSE(new_coefficients)) print("New derivatives =", derivative_MSE(new_coefficients),"\n") plt.figure(1,figsize=(10,5)) plt.title("Simple linear regression problem: Updated") plt.xlabel("feature") plt.ylabel("target") target, = plt.plot(x, y,'bx') old, = plt.plot(x, predict(coefficients),'r') new, = plt.plot(x, predict(new_coefficients),'g') plt.legend([target, old, new], ['Target variable', 'Old coefficients', 'New coefficients']) plt.show() ###Output _____no_output_____ ###Markdown First, let's see what happens when we pick a good learning rate. ###Code run_update(learning_rate=0.02) ###Output Current coefficients = [ 0.73699517 0.05088406] Current MSE = 98.5041803484 Current derivatives = [ -4.13980313 -55.10718225] New coefficients = [ 0.81979123 1.1530277 ] New MSE = 5.94768089539 New derivatives = [ 1.13677721 13.34346913] ###Markdown As we can see, the model with the updated coefficients is closer to the target variable, and therefore has a smaller mean-squared error. We can also see that the derivatives themselves have decreased, indicating that we are getting _closer_ to finding the optimal coefficients.Now let's see what happens when the learning rate is too high. ###Code run_update(learning_rate=0.1) ###Output Current coefficients = [ 0.73699517 0.05088406] Current MSE = 98.5041803484 Current derivatives = [ -4.13980313 -55.10718225] New coefficients = [ 1.15097548 5.56160228] New MSE = 2670.89490215 New derivatives = [ 22.24309859 287.14607461] ###Markdown As you can see, the line did move in the direction of the target variable, but went too far, which ended up being worse than before we did anything at all. You can also see that the derivatives are now even larger than before, meaning that if we performed another update, we would be even worse off than before.Now, we'll see what happens when the learning rate happens to be too small. ###Code run_update(learning_rate=0.00005) ###Output Current coefficients = [ 0.73699517 0.05088406] Current MSE = 98.5041803484 Current derivatives = [ -4.13980313 -55.10718225] New coefficients = [ 0.73720216 0.05363942] New MSE = 97.894340939 New derivatives = [ -4.12661168 -54.93605562] ###Markdown You can see that, whilst not being as bad as setting it too high, setting the learning rate too low will result in very slow updates, which in the worst case could lead to the training stopping early.Now that we've shown how to update the coefficients once, we can keep on going! Indeed, we can update the coefficients until we reach a stopping criterion. This can be a certain number of update steps, a certain amount of time, or most commonly, whenever the MSE decreases by less than a factor _epsilon_. This method is most commonly known as gradient descent.Doing the latter will look like this: ###Code def find_best_coefficients(original_coefficients, learning_rate, epsilon): """ runs gradient descent to find the best coefficients """ coef = original_coefficients.copy() old_MSE = float('inf') new_MSE = MSE(coef) # Loops until convergence while(old_MSE - new_MSE > epsilon): old_MSE = MSE(coef) # Update the coefficients coef -= learning_rate * derivative_MSE(coef) new_MSE = MSE(coef) # Plot the results plt.figure(1,figsize=(10,5)) plt.title("Simple linear regression problem: solved") plt.xlabel("feature") plt.ylabel("target") target, = plt.plot(x, y,'bx') old, = plt.plot(x, predict(coefficients),'r') new, = plt.plot(x, predict(coef),'g') plt.legend([target, old, new], ['Target variable', 'Original coefficients', 'Final coefficients']) plt.show() return {"MSE":MSE(coef), "coefficients":coef} find_best_coefficients(original_coefficients = coefficients, learning_rate = 0.002, epsilon = 0.000001) ###Output _____no_output_____ ###Markdown As you can see, we managed to find weights that _almost_ fit our data perfectly. This may not always happen. Indeed, if the data contains noise, a linear model might not be able to represent the data perfectly. However, the technique that we described will still find the best line explaining the data.Here is an example below. ###Code noise_level = 0.5 # Add gaussian noise to the data y = y + (2*np.random.normal(0,noise_level,len(y)) - 1) original_coef = np.random.rand(2) find_best_coefficients(original_coefficients = original_coef, learning_rate = 0.001, epsilon = 0.0001) ###Output _____no_output_____

examples/gallery/demos/bokeh/mandelbrot_section.ipynb

###Markdown Most examples work across multiple plotting backends, this example is also available for:* [Matplotlib - mandelbrot section](../matplotlib/mandelbrot_section.ipynb)HoloViews demo that used to be showcased on the [holoviews.org ###Code import numpy as np import holoviews as hv from holoviews import opts hv.extension('bokeh') ###Output _____no_output_____ ###Markdown Load the data ###Code import io try: from urllib2 import urlopen except: from urllib.request import urlopen raw = urlopen('http://assets.holoviews.org/data/mandelbrot.npy').read() array = np.load(io.BytesIO(raw)).astype(np.float32)[::4,::4] ###Output _____no_output_____ ###Markdown Plot ###Code dots = np.linspace(-0.45, 0.45, 19) fractal = hv.Image(array) # First example on the old holoviews.org homepage was: # ((fractal * hv.HLine(y=0)).hist() + fractal.sample(y=0)) layouts = {y: (fractal * hv.Points(fractal.sample([(i,y) for i in dots])) + fractal.sample(y=y) + hv.operation.threshold(fractal, level=np.percentile(fractal.sample(y=y)['z'], 90)) + hv.operation.contours(fractal, levels=[np.percentile(fractal.sample(y=y)['z'], 60)])) for y in np.linspace(-0.3, 0.3, 11)} # Half the frames of the bokeh version composition = hv.HoloMap(layouts, kdims='Y').collate().cols(2) composition.options(opts.Contours(show_legend=False), opts.Points(scaling_factor=50)) ###Output _____no_output_____ ###Markdown Most examples work across multiple plotting backends, this example is also available for:* [Matplotlib - mandelbrot section](../matplotlib/mandelbrot_section.ipynb)HoloViews demo that used to be showcased on the [holoviews.org ###Code import numpy as np import holoviews as hv from holoviews import dim, opts hv.extension('bokeh') ###Output _____no_output_____ ###Markdown Load the data ###Code import io try: from urllib2 import urlopen except: from urllib.request import urlopen raw = urlopen('http://assets.holoviews.org/data/mandelbrot.npy').read() array = np.load(io.BytesIO(raw)).astype(np.float16)[::2,::2] ###Output _____no_output_____ ###Markdown Plot ###Code dots = np.linspace(-0.45, 0.45, 19) fractal = hv.Image(array) # First example on the old holoviews.org homepage was: # ((fractal * hv.HLine(y=0)).hist() + fractal.sample(y=0)) layouts = {y: (fractal * hv.Points(fractal.sample([(i,y) for i in dots])) + fractal.sample(y=y) + hv.operation.threshold(fractal, level=np.percentile(fractal.sample(y=y)['z'], 90)) + hv.operation.contours(fractal, levels=[np.percentile(fractal.sample(y=y)['z'], 60)])) for y in np.linspace(-0.3, 0.3, 21)} layout = hv.HoloMap(layouts, kdims='Y').collate() layout.opts( opts.Contours(color='w', show_legend=False), opts.Points(size=dim('z')*10)).cols(2) ###Output _____no_output_____ ###Markdown Most examples work across multiple plotting backends, this example is also available for:* [Matplotlib - mandelbrot section](../matplotlib/mandelbrot_section.ipynb)HoloViews demo that used to be showcased on the [holoviews.org ###Code import numpy as np import holoviews as hv hv.extension('bokeh') ###Output _____no_output_____ ###Markdown Load the data ###Code import io try: from urllib2 import urlopen except: from urllib.request import urlopen raw = urlopen('http://assets.holoviews.org/data/mandelbrot.npy').read() array = np.load(io.BytesIO(raw)).astype(np.float32)[::4,::4] ###Output _____no_output_____ ###Markdown Plot ###Code %%opts Points [scaling_factor=50] Contours [show_legend=False] (color='w') dots = np.linspace(-0.45, 0.45, 19) fractal = hv.Image(array) # First example on the old holoviews.org homepage was: # ((fractal * hv.HLine(y=0)).hist() + fractal.sample(y=0)) layouts = {y: (fractal * hv.Points(fractal.sample([(i,y) for i in dots])) + fractal.sample(y=y) + hv.operation.threshold(fractal, level=np.percentile(fractal.sample(y=y)['z'], 90)) + hv.operation.contours(fractal, levels=[np.percentile(fractal.sample(y=y)['z'], 60)])) for y in np.linspace(-0.3, 0.3, 11)} # Half the frames of the bokeh version hv.HoloMap(layouts, kdims=['Y']).collate().cols(2) ###Output _____no_output_____ ###Markdown Most examples work across multiple plotting backends, this example is also available for:* [Matplotlib - mandelbrot section](../matplotlib/mandelbrot_section.ipynb)HoloViews demo that used to be showcased on the [holoviews.org ###Code import numpy as np import holoviews as hv hv.extension('bokeh') ###Output _____no_output_____ ###Markdown Load the data ###Code import io try: from urllib2 import urlopen except: from urllib.request import urlopen raw = urlopen('http://assets.holoviews.org/data/mandelbrot.npy').read() array = np.load(io.BytesIO(raw)).astype(np.float32)[::4,::4] ###Output _____no_output_____ ###Markdown Plot ###Code %%opts Points [scaling_factor=50] Contours [show_legend=False] (color='w') dots = np.linspace(-0.45, 0.45, 19) fractal = hv.Image(array) # First example on the old holoviews.org homepage was: # ((fractal * hv.HLine(y=0)).hist() + fractal.sample(y=0)) layouts = {y: (fractal * hv.Points(fractal.sample([(i,y) for i in dots])) + fractal.sample(y=y) + hv.operation.threshold(fractal, level=np.percentile(fractal.sample(y=y)['z'], 90)) + hv.operation.contours(fractal, levels=[np.percentile(fractal.sample(y=y)['z'], 60)])) for y in np.linspace(-0.3, 0.3, 11)} # Half the frames of the bokeh version hv.HoloMap(layouts, kdims='Y').collate().cols(2) ###Output _____no_output_____

code/chap05mine.ipynb

###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census - un abs(census - un) abs(census - un) / un abs(census - un) / un * 100 ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code shift = .4 t_0 = get_first_label(census) t_r = 1970 t_end = get_last_label(census) p_0 = census[t_0] p_r = census[t_r] p_end = get_last_value(census) elapsed_time_range = t_end - t_r total_growth_range = p_end - p_r annual_growth_range = total_growth_range / elapsed_time_range results = TimeSeries() results[t_0] = census[t_0]-shift results for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig03.pdf') ###Output Saving figure to file figs/chap03-fig03.pdf ###Markdown Modeling and Simulation in PythonChapter 5: DesignCopyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # If you want the figures to appear in the notebook, # and you want to interact with them, use # %matplotlib notebook # If you want the figures to appear in the notebook, # and you don't want to interact with them, use # %matplotlib inline # If you want the figures to appear in separate windows, use # %matplotlib qt5 # To switch from one to another, you have to select Kernel->Restart %matplotlib inline from modsim import * ###Output _____no_output_____ ###Markdown SIR implementationWe'll use a `State` object to represent the number or fraction of people in each compartment. ###Code init = State(S=89, I=1, R=0) init ###Output _____no_output_____ ###Markdown To convert from number of people to fractions, we divide through by the total. ###Code init /= sum(init) init ###Output _____no_output_____ ###Markdown `make_system` creates a `System` object with the given parameters. ###Code def make_system(beta, gamma): """Make a system object for the SIR model. beta: contact rate in days gamma: recovery rate in days returns: System object """ init = State(S=89, I=1, R=0) init /= sum(init) t0 = 0 t_end = 7 * 14 return System(init=init, t0=t0, t_end=t_end, beta=beta, gamma=gamma) ###Output _____no_output_____ ###Markdown Here's an example with hypothetical values for `beta` and `gamma`. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) ###Output _____no_output_____ ###Markdown The update function takes the state during the current time step and returns the state during the next time step. ###Code def update1(state, system): """Update the SIR model. state: State with variables S, I, R system: System with beta and gamma returns: State object """ s, i, r = state infected = system.beta * i * s recovered = system.gamma * i s -= infected i += infected - recovered r += recovered return State(S=s, I=i, R=r) ###Output _____no_output_____ ###Markdown To run a single time step, we call it like this: ###Code state = update1(init, system) state ###Output _____no_output_____ ###Markdown Now we can run a simulation by calling the update function for each time step. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. system: System object update_func: function that updates state returns: State object for final state """ state = system.init for t in linrange(system.t0, system.t_end): state = update_func(state, system) return state ###Output _____no_output_____ ###Markdown The result is the state of the system at `t_end` ###Code run_simulation(system, update1) ###Output _____no_output_____ ###Markdown **Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. After 14 weeks, how many students, total, have been infected?Hint: what is the change in `S` between the beginning and the end of the simulation? ###Code tc = 4 # time between contacts in days tr = 5 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) s_start = system.init.S s_start end = run_simulation(system, update1) s_end = end.S s_end change_in_s = s_start - s_end change_in_s ###Output _____no_output_____ ###Markdown Using Series objects If we want to store the state of the system at each time step, we can use one `TimeSeries` object for each state variable. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. Add three Series objects to the System: S, I, R system: System object update_func: function that updates state """ S = TimeSeries() I = TimeSeries() R = TimeSeries() state = system.init t0 = system.t0 S[t0], I[t0], R[t0] = state for t in linrange(system.t0, system.t_end): state = update_func(state, system) S[t+1], I[t+1], R[t+1] = state system.S = S system.I = I system.R = R ###Output _____no_output_____ ###Markdown Here's how we call it. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) run_simulation(system, update1) ###Output _____no_output_____ ###Markdown And then we can plot the results. ###Code def plot_results(S, I, R): """Plot the results of a SIR model. S: TimeSeries I: TimeSeries R: TimeSeries """ plot(S, '--', color='blue', label='Susceptible') plot(I, '-', color='red', label='Infected') plot(R, ':', color='green', label='Recovered') decorate(xlabel='Time (days)', ylabel='Fraction of population') ###Output _____no_output_____ ###Markdown Here's what they look like. ###Code plot_results(system.S, system.I, system.R) savefig('chap05-fig01.pdf') ###Output Saving figure to file chap05-fig01.pdf ###Markdown Using a DataFrame Instead of making three `TimeSeries` objects, we can use one `DataFrame`.We have to use `loc` to indicate which row we want to assign the results to. But then Pandas does the right thing, matching up the state variables with the columns of the `DataFrame`. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. Add a DataFrame to the System: results system: System object update_func: function that updates state """ frame = DataFrame(columns=system.init.index) frame.loc[system.t0] = system.init for t in linrange(system.t0, system.t_end): frame.loc[t+1] = update_func(frame.loc[t], system) system.results = frame ###Output _____no_output_____ ###Markdown Here's how we run it, and what the result looks like. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day sir = make_system(beta, gamma) run_simulation(system, update1) system.results.head() ###Output _____no_output_____ ###Markdown We can extract the results and plot them. ###Code frame = system.results plot_results(frame.S, frame.I, frame.R) ###Output _____no_output_____ ###Markdown **Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. Simulate this scenario for 14 days and plot the results. ###Code tc = 4 tr = 5 beta = 1/tc gamma = 1/tr sir = make_system(beta, gamma) end = run_simulation(system, update1) frame = system.results plot_results(frame.S, frame.I, frame.R) ###Output _____no_output_____ ###Markdown Metrics Given the results, we can compute metrics that quantify whatever we are interested in, like the total number of sick students, for example. ###Code def calc_total_infected(system): """Fraction of population infected during the simulation. system: System object with results. returns: fraction of population """ frame = system.results return frame.S[system.t0] - frame.S[system.t_end] ###Output _____no_output_____ ###Markdown Here's an example.| ###Code system.beta = 0.333 system.gamma = 0.25 run_simulation(system, update1) print(system.beta, system.gamma, calc_total_infected(system)) ###Output 0.333 0.25 0.467162931836 ###Markdown **Exercise:** Write functions that take a `System` object as a parameter, extract the `results` object from it, and compute the other metrics mentioned in the book:1. The fraction of students who are sick at the peak of the outbreak.2. The day the outbreak peaks.3. The fraction of students who are sick at the end of the semester.Hint: If you have a `TimeSeries` called `I`, you can compute the largest value of the series like this: I.max()And the index of the largest value like this: I.idxmax()You can read about these functions in the `Series` [documentation](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.html). ###Code def peak_infected(sytsem): frame = system.results return frame.I.max() def outbreak_day(system): frame = system.results return frame.I.idxmax() def sick_at_end(system): frame = system.results return frame.I[system.t_end] print(peak_infected(system), outbreak_day(system), sick_at_end(system)) ###Output 0.0435362026876 30 0.000674194315603 ###Markdown What if? We can use this model to evaluate "what if" scenarios. For example, this function models the effect of immunization by moving some fraction of the population from S to R before the simulation starts. ###Code def add_immunization(system, fraction): """Immunize a fraction of the population. Moves the given fraction from S to R. system: System object fraction: number from 0 to 1 """ system.init.S -= fraction system.init.R += fraction ###Output _____no_output_____ ###Markdown Let's start again with the system we used in the previous sections. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) system.beta, system.gamma ###Output _____no_output_____ ###Markdown And run the model without immunization. ###Code run_simulation(system, update1) calc_total_infected(system) ###Output _____no_output_____ ###Markdown Now with 10% immunization. ###Code system2 = make_system(beta, gamma) add_immunization(system2, 0.1) run_simulation(system2, update1) calc_total_infected(system2) ###Output _____no_output_____ ###Markdown 10% immunization leads to a drop in infections of 16 percentage points.Here's what the time series looks like for S, with and without immunization. ###Code plot(system.results.S, '-', label='No immunization') plot(system2.results.S, 'g--', label='10% immunization') decorate(xlabel='Time (days)', ylabel='Fraction susceptible') savefig('chap05-fig02.pdf') ###Output Saving figure to file chap05-fig02.pdf ###Markdown Now we can sweep through a range of values for the fraction of the population who are immunized. ###Code immunize_array = linspace(0, 1, 11) for fraction in immunize_array: system = make_system(beta, gamma) add_immunization(system, fraction) run_simulation(system, update1) print(fraction, calc_total_infected(system)) ###Output 0.0 0.468320811029 0.1 0.30650802854 0.2 0.161365457006 0.3 0.0728155898425 0.4 0.035520216753 0.5 0.0196887157825 0.6 0.0116220579983 0.7 0.00683873780062 0.8 0.00369649625371 0.9 0.00148153267227 1.0 -0.000161212109412 ###Markdown This function does the same thing and stores the results in a `Sweep` object. ###Code def sweep_immunity(immunize_array): """Sweeps a range of values for immunity. immunize_array: array of fraction immunized returns: Sweep object """ sweep = SweepSeries() for fraction in immunize_array: system = make_system(beta, gamma) add_immunization(system, fraction) run_simulation(system, update1) sweep[fraction] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Here's how we run it. ###Code immunize_array = linspace(0, 1, 21) infected_sweep = sweep_immunity(immunize_array) ###Output _____no_output_____ ###Markdown And here's what the results look like. ###Code plot(infected_sweep) decorate(xlabel='Fraction immunized', ylabel='Total fraction infected', title='Fraction infected vs. immunization rate', legend=False) savefig('chap05-fig03.pdf') ###Output Saving figure to file chap05-fig03.pdf ###Markdown If 40% of the population is immunized, less than 4% of the population gets sick. Logistic function To model the effect of a hand-washing campaign, I'll use a [generalized logistic function](https://en.wikipedia.org/wiki/Generalised_logistic_function), which is a convenient function for modeling curves that have a generally sigmoid shape. The parameters of the GLF correspond to various features of the curve in a way that makes it easy to find a function that has the shape you want, based on data or background information about the scenario. ###Code def logistic(x, A=0, B=1, C=1, M=0, K=1, Q=1, nu=1): """Computes the generalize logistic function. A: controls the lower bound B: controls the steepness of the transition C: not all that useful, AFAIK M: controls the location of the transition K: controls the upper bound Q: shift the transition left or right nu: affects the symmetry of the transition returns: float or array """ exponent = -B * (x - M) denom = C + Q * exp(exponent) return A + (K-A) / denom ** (1/nu) ###Output _____no_output_____ ###Markdown The following array represents the range of possible spending. ###Code spending = linspace(0, 1200, 21) spending ###Output _____no_output_____ ###Markdown `compute_factor` computes the reduction in `beta` for a given level of campaign spending.`M` is chosen so the transition happens around \$500.`K` is the maximum reduction in `beta`, 20%.`B` is chosen by trial and error to yield a curve that seems feasible. ###Code def compute_factor(spending): """Reduction factor as a function of spending. spending: dollars from 0 to 1200 returns: fractional reduction in beta """ return logistic(spending, M=500, K=0.2, B=0.01) ###Output _____no_output_____ ###Markdown Here's what it looks like. ###Code percent_reduction = compute_factor(spending) * 100 plot(spending, percent_reduction) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Percent reduction in infection rate', title='Effect of hand washing on infection rate', legend=False) savefig('chap05-fig04.pdf') ###Output Saving figure to file chap05-fig04.pdf ###Markdown **Exercise:** Modify the parameters `M`, `K`, and `B`, and see what effect they have on the shape of the curve. Read about the [generalized logistic function on Wikipedia](https://en.wikipedia.org/wiki/Generalised_logistic_function). Modify the other parameters and see what effect they have. ###Code def compute_factor1(spending): return logistic(spending, M=800, K=0.6, B=0.07) percent_reduction1 = compute_factor1(spending)*100 plot(spending, percent_reduction1) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Percent reduction in infection rate', title='Effect of hand washing on infection rate', legend=False) def compute_factor2(spending): return logistic(spending, A=0, K=45) percent_reduction2 = compute_factor2(spending) plot(spending, percent_reduction2) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Percent reduction in infection rate', title='Effect of hand washing on infection rate', legend=False) ###Output _____no_output_____ ###Markdown Hand washing Now we can model the effect of a hand-washing campaign by modifying `beta` ###Code def add_hand_washing(system, spending): """Modifies system to model the effect of hand washing. system: System object spending: campaign spending in USD """ factor = compute_factor(spending) system.beta *= (1 - factor) ###Output _____no_output_____ ###Markdown Let's start with the same values of `beta` and `gamma` we've been using. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day beta, gamma ###Output _____no_output_____ ###Markdown Now we can sweep different levels of campaign spending. ###Code spending_array = linspace(0, 1200, 13) for spending in spending_array: system = make_system(beta, gamma) add_hand_washing(system, spending) run_simulation(system, update1) print(spending, system.beta, calc_total_infected(system)) ###Output 0.0 0.332887143272 0.466770231236 100.0 0.332134252669 0.464141650401 200.0 0.330171608455 0.457217006313 300.0 0.325386471865 0.439887202912 400.0 0.315403905242 0.401630646271 500.0 0.3 0.33703425949 600.0 0.284596094758 0.267317030568 700.0 0.274613528135 0.22184699046 800.0 0.269828391545 0.200791598416 900.0 0.267865747331 0.192392183393 1000.0 0.267112856728 0.189213207818 1100.0 0.26683150821 0.18803175228 1200.0 0.266727403413 0.187595503995 ###Markdown Here's a function that sweeps a range of spending and stores the results in a `Sweep` object. ###Code def sweep_hand_washing(spending_array): """Run simulations with a range of spending. spending_array: array of dollars from 0 to 1200 returns: Sweep object """ sweep = SweepSeries() for spending in spending_array: system = make_system(beta, gamma) add_hand_washing(system, spending) run_simulation(system, update1) sweep[spending] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Here's how we run it. ###Code spending_array = linspace(0, 1200, 20) infected_sweep = sweep_hand_washing(spending_array) ###Output _____no_output_____ ###Markdown And here's what it looks like. ###Code plot(infected_sweep) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Total fraction infected', title='Effect of hand washing on total infections', legend=False) savefig('chap05-fig05.pdf') ###Output Saving figure to file chap05-fig05.pdf ###Markdown Now let's put it all together to make some public health spending decisions. Optimization Suppose we have \$1200 to spend on any combination of vaccines and a hand-washing campaign. ###Code num_students = 90 budget = 1200 price_per_dose = 100 max_doses = int(budget / price_per_dose) dose_array = linrange(max_doses) max_doses ###Output _____no_output_____ ###Markdown We can sweep through a range of doses from, 0 to `max_doses`, model the effects of immunization and the hand-washing campaign, and run simulations.For each scenario, we compute the fraction of students who get sick. ###Code for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) run_simulation(system, update1) print(doses, system.init.S, system.beta, calc_total_infected(system)) ###Output 0.0 0.988888888889 0.266727403413 0.187595503995 1.0 0.977777777778 0.26683150821 0.174580718826 2.0 0.966666666667 0.267112856728 0.162909838349 3.0 0.955555555556 0.267865747331 0.153508349478 4.0 0.944444444444 0.269828391545 0.148565092315 5.0 0.933333333333 0.274613528135 0.152945950611 6.0 0.922222222222 0.284596094758 0.174964415024 7.0 0.911111111111 0.3 0.217343161684 8.0 0.9 0.315403905242 0.259071044488 9.0 0.888888888889 0.325386471865 0.278402884103 10.0 0.877777777778 0.330171608455 0.277914534623 11.0 0.866666666667 0.332134252669 0.267357496693 12.0 0.855555555556 0.332887143272 0.252796945636 ###Markdown The following function wraps that loop and stores the results in a `Sweep` object. ###Code def sweep_doses(dose_array): """Runs simulations with different doses and campaign spending. dose_array: range of values for number of vaccinations return: Sweep object with total number of infections """ sweep = SweepSeries() for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) run_simulation(system, update1) sweep[doses] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Now we can compute the number of infected students for each possible allocation of the budget. ###Code infected_sweep = sweep_doses(dose_array) ###Output _____no_output_____ ###Markdown And plot the results. ###Code plot(infected_sweep) decorate(xlabel='Doses of vaccine', ylabel='Total fraction infected', title='Total infections vs. doses', legend=False) savefig('chap05-fig06.pdf') ###Output Saving figure to file chap05-fig06.pdf ###Markdown **Exercise:** Suppose the price of the vaccine drops to $50 per dose. How does that affect the optimal allocation of the spending? ###Code num_students = 90 budget = 1200 price_per_dose = 50 max_doses = int(budget / price_per_dose) dose_array = linrange(max_doses) max_doses def sweep_doses1(dose_array): sweep = SweepSeries() for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) run_simulation(system, update1) sweep[doses] = calc_total_infected(system) return sweep infected_sweep1 = sweep_doses1(dose_array) plot(infected_sweep1) decorate(xlabel='Doses of vaccine', ylabel='Total fraction infected', title='Total infections vs. doses', legend=False) ###Output _____no_output_____ ###Markdown **Exercise:** Suppose we have the option to quarantine infected students. For example, a student who feels ill might be moved to an infirmary, or a private dorm room, until they are no longer infectious.How might you incorporate the effect of quarantine in the SIR model? ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day def add_quarantine(system, fraction): tr = 5 * fraction system.gamma = 1 / tr system3 = make_system(beta, gamma) add_immunization(system2, 0.1) add_quarantine(system3, .4) add_hand_washing(system3, spending) run_simulation(system3, update1) calc_total_infected(system3) calc_total_infected(system2) #When the tr number changes and the rate of contact is decreased #to simulate quarantine, the number of total infected decrease ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census - un abs(census - un) abs(census - un) / un abs(census - un) / un * 100 ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1970] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code census[1950] census[2016] t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - 1970 p_0 = census[1970] p_end = get_last_value(census) total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time results = TimeSeries() results[t_0] = census[t_0] - 0.4 results for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') print(census[1970]) print(get_first_value(census)) ###Output 2.557628654 ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2[table2.columns[0]] ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') # savefig('figs/chap03-fig01.pdf') ###Output _____no_output_____ ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code inter_diff = census - un; inter_diff_abs = abs(inter_diff); inter_diff_rel = inter_diff_abs/un; perc_diff = 100 * inter_diff_rel ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code def model_census_data(data, start_year, end_year): avg_growth = (data[end_year] - data[start_year])/(end_year - start_year) results = TimeSeries() results[data.index[0]] = data[start_year] - avg_growth * (start_year - data.index[0]) for i in linspace(data.index[1], end_year, (end_year - data.index[0])): results[i] = results[i-1] + avg_growth plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') model_census_data(census, 1970, census.index[-1]) ###Output _____no_output_____ ###Markdown Personal WorkThe purpose of the following is to redo the models done above using purely base libraries (pandas and numpy, etc., as opposed to using modsim) ###Code import pandas as pd import numpy as np import matplotlib.pyplot as plt def lin_population_model(filename, table_choice_index, fit_data_index, fit_year, fit_data_label, \ comp_data_index, comp_data_label): """ Takes in HTML table data of world population numbers and fits a linear population model to selected data. filename: path to the HTML file containing the table data table_choice_index: Select which table stored in the HTML file to use fit_data_index: Index of the data column within the table to fit the model to fit_year: The year to center the linear model around fit_data_label: Concise descriptor of the data column to which the model is fitted, for plotting comp_data_index: Index of data column to be used to compare model results and original data to comp_data_index: Concise descriptor of the comparison data column, for plotting Plots results of linear model Returns nothing """ # Load the tables tables = read_html(filename, header=0, index_col=0, decimal='M') # Parse tables to find desired data data_table = tables[table_choice_index] data_column_to_fit = data_table.columns[fit_data_index] data_column_to_compare = data_table.columns[comp_data_index] data_to_fit = data_table[data_column_to_fit] data_to_compare = data_table[data_column_to_compare] # Create intermediate index variables end_year = data_to_fit.index[-1] start_year = data_to_fit.index[0] interval = end_year - start_year # Determine average annual population growth avg_growth = (data_to_fit[end_year] - data_to_fit[fit_year])/(end_year - fit_year) # Create blank Series object to hold results results = pd.Series(np.zeros((interval+1)), index=data_to_fit.index) # Create initial value for Series object, centered around year of fit results[start_year] = data_to_fit[fit_year] - avg_growth * (fit_year - start_year) # Increment population values per year, using avg_growth for i in linspace(start_year + 1, end_year, interval): results[i] = results[i-1] + avg_growth # Plot results using matplotlib plt.figure() plt.figure(figsize=[14,11]) # make the plot larger to more easily see results # Use the Series object's plot function to generate a plot via matplotlib data_to_fit.plot() data_to_compare.plot() results.plot() # Add labels, legend, and title plt.xlabel('Year') plt.ylabel('World population (billion)') plt.title('Comparison of Linear World Population Growth Model to measured data') plt.legend([fit_data_label, comp_data_label, 'Linear Population Model']) lin_population_model(filename='data/World_population_estimates.html', table_choice_index=2, fit_data_index=0, \ fit_year=1970, fit_data_label='US Census Data', comp_data_index=2, comp_data_label='UN DESA') ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census - un abs(census - un) abs(census-un)/un (abs(census -un)/un)*100 # Solution goes here # Solution goes here ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] t_0 = 1970 t_end = get_last_label(census) elapsed_time = t_end - t_0 p_0 = census[1970] p_end = get_last_value(census) total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time results = TimeSeries() results[t_0] = census[t_0] results for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth plot(census.loc[1970:2016], ':', label='US Census') plot(un.loc[1970:2016], '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') census[1970] type(census) ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5: DesignCopyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # If you want the figures to appear in the notebook, # and you want to interact with them, use # %matplotlib notebook # If you want the figures to appear in the notebook, # and you don't want to interact with them, use # %matplotlib inline # If you want the figures to appear in separate windows, use # %matplotlib qt5 # To switch from one to another, you have to select Kernel->Restart %matplotlib inline from modsim import * ###Output _____no_output_____ ###Markdown SIR implementationWe'll use a `State` object to represent the number or fraction of people in each compartment. ###Code init = State(S=89, I=1, R=0) init ###Output _____no_output_____ ###Markdown To convert from number of people to fractions, we divide through by the total. ###Code init /= sum(init) init ###Output _____no_output_____ ###Markdown `make_system` creates a `System` object with the given parameters. ###Code def make_system(beta, gamma): """Make a system object for the SIR model. beta: contact rate in days gamma: recovery rate in days returns: System object """ init = State(S=89, I=1, R=0) init /= sum(init) t0 = 0 t_end = 7 * 14 return System(init=init, t0=t0, t_end=t_end, beta=beta, gamma=gamma) ###Output _____no_output_____ ###Markdown Here's an example with hypothetical values for `beta` and `gamma`. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) ###Output _____no_output_____ ###Markdown The update function takes the state during the current time step and returns the state during the next time step. ###Code def update1(state, system): """Update the SIR model. state: State with variables S, I, R system: System with beta and gamma returns: State object """ s, i, r = state infected = system.beta * i * s recovered = system.gamma * i s -= infected i += infected - recovered r += recovered return State(S=s, I=i, R=r) ###Output _____no_output_____ ###Markdown To run a single time step, we call it like this: ###Code state = update1(init, system) state ###Output _____no_output_____ ###Markdown Now we can run a simulation by calling the update function for each time step. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. system: System object update_func: function that updates state returns: State object for final state """ state = system.init for t in linrange(system.t0, system.t_end): state = update_func(state, system) return state ###Output _____no_output_____ ###Markdown The result is the state of the system at `t_end` ###Code run_simulation(system, update1) ###Output _____no_output_____ ###Markdown **Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. After 14 weeks, how many students, total, have been infected?Hint: what is the change in `S` between the beginning and the end of the simulation? ###Code # Solution goes here tc1 = 4 tr1 = 5 beta1 = 1/ tc1 gamma1 = 1/tr1 system1 = make_system(beta1, gamma1) final = run_simulation(system1, update1) final (init - final) ###Output _____no_output_____ ###Markdown Using Series objects If we want to store the state of the system at each time step, we can use one `TimeSeries` object for each state variable. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. Add three Series objects to the System: S, I, R system: System object update_func: function that updates state """ S = TimeSeries() I = TimeSeries() R = TimeSeries() state = system.init t0 = system.t0 S[t0], I[t0], R[t0] = state for t in linrange(system.t0, system.t_end): state = update_func(state, system) S[t+1], I[t+1], R[t+1] = state system.S = S system.I = I system.R = R ###Output _____no_output_____ ###Markdown Here's how we call it. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) run_simulation(system, update1) ###Output _____no_output_____ ###Markdown And then we can plot the results. ###Code def plot_results(S, I, R): """Plot the results of a SIR model. S: TimeSeries I: TimeSeries R: TimeSeries """ plot(S, '--', color='blue', label='Susceptible') plot(I, '-', color='red', label='Infected') plot(R, ':', color='green', label='Recovered') decorate(xlabel='Time (days)', ylabel='Fraction of population') ###Output _____no_output_____ ###Markdown Here's what they look like. ###Code plot_results(system.S, system.I, system.R) savefig('chap05-fig01.pdf') ###Output Saving figure to file chap05-fig01.pdf ###Markdown Using a DataFrame Instead of making three `TimeSeries` objects, we can use one `DataFrame`.We have to use `loc` to indicate which row we want to assign the results to. But then Pandas does the right thing, matching up the state variables with the columns of the `DataFrame`. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. Add a DataFrame to the System: results system: System object update_func: function that updates state """ frame = DataFrame(columns=system.init.index) frame.loc[system.t0] = system.init for t in linrange(system.t0, system.t_end): frame.loc[t+1] = update_func(frame.loc[t], system) system.results = frame ###Output _____no_output_____ ###Markdown Here's how we run it, and what the result looks like. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day sir = make_system(beta, gamma) run_simulation(system, update1) system.results.head() ###Output _____no_output_____ ###Markdown We can extract the results and plot them. ###Code frame = system.results plot_results(frame.S, frame.I, frame.R) ###Output _____no_output_____ ###Markdown **Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. Simulate this scenario for 14 days and plot the results. ###Code # Solution goes here tc = 4 tr = 5 beta = 1 / tc gamma = 1/ tr sir = make_system(beta, gamma) system.t_end = 14 run_simulation(system, update1) system.results.head() frame = system.results plot_results(frame.S, frame.I, frame.R) ###Output _____no_output_____ ###Markdown Metrics Given the results, we can compute metrics that quantify whatever we are interested in, like the total number of sick students, for example. ###Code def calc_total_infected(system): """Fraction of population infected during the simulation. system: System object with results. returns: fraction of population """ frame = system.results return frame.S[system.t0] - frame.S[system.t_end] ###Output _____no_output_____ ###Markdown Here's an example.| ###Code system.beta = 0.333 system.gamma = 0.25 run_simulation(system, update1) print(system.beta, system.gamma, calc_total_infected(system)) ###Output 0.333 0.25 0.0809201122723 ###Markdown **Exercise:** Write functions that take a `System` object as a parameter, extract the `results` object from it, and compute the other metrics mentioned in the book:1. The fraction of students who are sick at the peak of the outbreak.2. The day the outbreak peaks.3. The fraction of students who are sick at the end of the semester.Hint: If you have a `TimeSeries` called `I`, you can compute the largest value of the series like this: I.max()And the index of the largest value like this: I.idxmax()You can read about these functions in the `Series` [documentation](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.html). ###Code # Solution goes here def sick_at_peak(system): frame = system.results return frame.I.max() # Solution goes here system.beta = 0.333 system.gamma = 0.25 run_simulation(system, update1) print(sick_at_peak(system)) # Solution goes here def outbreak_peak(system): frame = system.results return frame.I.idxmax() # Solution goes here system.beta = 0.333 system.gamma = 0.25 run_simulation(system, update1) print(outbreak_peak(system)) # Solution goes here def sick_at_end(system): frame = system.results return frame.I[system.t_end] # Solution goes here system.beta = 0.333 system.gamma = 0.25 run_simulation(system, update1) print(sick_at_end(system)) ###Output 0.0281470380348 ###Markdown What if? We can use this model to evaluate "what if" scenarios. For example, this function models the effect of immunization by moving some fraction of the population from S to R before the simulation starts. ###Code def add_immunization(system, fraction): """Immunize a fraction of the population. Moves the given fraction from S to R. system: System object fraction: number from 0 to 1 """ system.init.S -= fraction system.init.R += fraction ###Output _____no_output_____ ###Markdown Let's start again with the system we used in the previous sections. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) system.beta, system.gamma ###Output _____no_output_____ ###Markdown And run the model without immunization. ###Code run_simulation(system, update1) calc_total_infected(system) ###Output _____no_output_____ ###Markdown Now with 10% immunization. ###Code system2 = make_system(beta, gamma) add_immunization(system2, 0.1) run_simulation(system2, update1) calc_total_infected(system2) ###Output _____no_output_____ ###Markdown 10% immunization leads to a drop in infections of 16 percentage points.Here's what the time series looks like for S, with and without immunization. ###Code plot(system.results.S, '-', label='No immunization') plot(system2.results.S, 'g--', label='10% immunization') decorate(xlabel='Time (days)', ylabel='Fraction susceptible') savefig('chap05-fig02.pdf') ###Output Saving figure to file chap05-fig02.pdf ###Markdown Now we can sweep through a range of values for the fraction of the population who are immunized. ###Code immunize_array = linspace(0, 1, 11) for fraction in immunize_array: system = make_system(beta, gamma) add_immunization(system, fraction) run_simulation(system, update1) print(fraction, calc_total_infected(system)) ###Output 0.0 0.468320811029 0.1 0.30650802854 0.2 0.161365457006 0.3 0.0728155898425 0.4 0.035520216753 0.5 0.0196887157825 0.6 0.0116220579983 0.7 0.00683873780062 0.8 0.00369649625371 0.9 0.00148153267227 1.0 -0.000161212109412 ###Markdown This function does the same thing and stores the results in a `Sweep` object. ###Code def sweep_immunity(immunize_array): """Sweeps a range of values for immunity. immunize_array: array of fraction immunized returns: Sweep object """ sweep = SweepSeries() for fraction in immunize_array: system = make_system(beta, gamma) add_immunization(system, fraction) run_simulation(system, update1) sweep[fraction] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Here's how we run it. ###Code immunize_array = linspace(0, 1, 21) infected_sweep = sweep_immunity(immunize_array) ###Output _____no_output_____ ###Markdown And here's what the results look like. ###Code plot(infected_sweep) decorate(xlabel='Fraction immunized', ylabel='Total fraction infected', title='Fraction infected vs. immunization rate', legend=False) savefig('chap05-fig03.pdf') ###Output Saving figure to file chap05-fig03.pdf ###Markdown If 40% of the population is immunized, less than 4% of the population gets sick. Logistic function To model the effect of a hand-washing campaign, I'll use a [generalized logistic function](https://en.wikipedia.org/wiki/Generalised_logistic_function), which is a convenient function for modeling curves that have a generally sigmoid shape. The parameters of the GLF correspond to various features of the curve in a way that makes it easy to find a function that has the shape you want, based on data or background information about the scenario. ###Code def logistic(x, A=0, B=1, C=1, M=0, K=1, Q=1, nu=1): """Computes the generalize logistic function. A: controls the lower bound B: controls the steepness of the transition C: not all that useful, AFAIK M: controls the location of the transition K: controls the upper bound Q: shift the transition left or right nu: affects the symmetry of the transition returns: float or array """ exponent = -B * (x - M) denom = C + Q * exp(exponent) return A + (K-A) / denom ** (1/nu) ###Output _____no_output_____ ###Markdown The following array represents the range of possible spending. ###Code spending = linspace(0, 1200, 21) spending ###Output _____no_output_____ ###Markdown `compute_factor` computes the reduction in `beta` for a given level of campaign spending.`M` is chosen so the transition happens around \$500.`K` is the maximum reduction in `beta`, 20%.`B` is chosen by trial and error to yield a curve that seems feasible. ###Code def compute_factor(spending): """Reduction factor as a function of spending. spending: dollars from 0 to 1200 returns: fractional reduction in beta """ return logistic(spending, M=300, K=1, B=.05) ###Output _____no_output_____ ###Markdown Here's what it looks like. ###Code percent_reduction = compute_factor(spending) * 100 plot(spending, percent_reduction) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Percent reduction in infection rate', title='Effect of hand washing on infection rate', legend=False) savefig('chap05-fig04.pdf') ###Output Saving figure to file chap05-fig04.pdf ###Markdown **Exercise:** Modify the parameters `M`, `K`, and `B`, and see what effect they have on the shape of the curve. Read about the [generalized logistic function on Wikipedia](https://en.wikipedia.org/wiki/Generalised_logistic_function). Modify the other parameters and see what effect they have. Hand washing Now we can model the effect of a hand-washing campaign by modifying `beta` ###Code def add_hand_washing(system, spending): """Modifies system to model the effect of hand washing. system: System object spending: campaign spending in USD """ factor = compute_factor(spending) system.beta *= (1 - factor) ###Output _____no_output_____ ###Markdown Let's start with the same values of `beta` and `gamma` we've been using. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day beta, gamma ###Output _____no_output_____ ###Markdown Now we can sweep different levels of campaign spending. ###Code spending_array = linspace(0, 1200, 13) for spending in spending_array: system = make_system(beta, gamma) add_hand_washing(system, spending) run_simulation(system, update1) print(spending, system.beta, calc_total_infected(system)) ###Output 0.0 0.333333231366 0.468320457287 100.0 0.33331820071 0.468268310467 200.0 0.331102383025 0.460514096506 300.0 0.166666666667 0.0208697132287 400.0 0.00223095030809 9.89203320988e-05 500.0 1.51326229008e-05 6.65127738886e-07 600.0 1.01967408998e-07 4.48153214538e-09 700.0 6.87051230723e-10 3.01961788907e-11 800.0 4.62933395321e-12 2.03392858111e-13 900.0 3.11602595578e-14 1.22124532709e-15 1000.0 2.22044604925e-16 0.0 1100.0 0.0 0.0 1200.0 0.0 0.0 ###Markdown Here's a function that sweeps a range of spending and stores the results in a `Sweep` object. ###Code def sweep_hand_washing(spending_array): """Run simulations with a range of spending. spending_array: array of dollars from 0 to 1200 returns: Sweep object """ sweep = SweepSeries() for spending in spending_array: system = make_system(beta, gamma) add_hand_washing(system, spending) run_simulation(system, update1) sweep[spending] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Here's how we run it. ###Code spending_array = linspace(0, 1200, 20) infected_sweep = sweep_hand_washing(spending_array) ###Output _____no_output_____ ###Markdown And here's what it looks like. ###Code plot(infected_sweep) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Total fraction infected', title='Effect of hand washing on total infections', legend=False) savefig('chap05-fig05.pdf') ###Output Saving figure to file chap05-fig05.pdf ###Markdown Now let's put it all together to make some public health spending decisions. Optimization Suppose we have \$1200 to spend on any combination of vaccines and a hand-washing campaign. ###Code num_students = 90 budget = 1200 price_per_dose = 50 max_doses = int(budget / price_per_dose) dose_array = linrange(max_doses) max_doses ###Output _____no_output_____ ###Markdown We can sweep through a range of doses from, 0 to `max_doses`, model the effects of immunization and the hand-washing campaign, and run simulations.For each scenario, we compute the fraction of students who get sick. ###Code for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) run_simulation(system, update1) print(doses, system.init.S, system.beta, calc_total_infected(system)) ###Output 0.0 0.988888888889 0.0 0.0 1.0 0.977777777778 0.0 0.0 2.0 0.966666666667 0.0 0.0 3.0 0.955555555556 0.0 0.0 4.0 0.944444444444 2.22044604925e-16 0.0 5.0 0.933333333333 2.59052039079e-15 0.0 6.0 0.922222222222 3.11602595578e-14 1.22124532709e-15 7.0 0.911111111111 3.79992333895e-13 1.52100554374e-14 8.0 0.9 4.62933395321e-12 1.85074178205e-13 9.0 0.888888888889 5.63965911008e-11 2.22810658812e-12 10.0 0.877777777778 6.87051230723e-10 2.68034483497e-11 11.0 0.866666666667 8.36999699179e-09 3.223995515e-10 12.0 0.855555555556 1.01967408998e-07 3.87728060769e-09 13.0 0.844444444444 1.24221309472e-06 4.66215250849e-08 14.0 0.833333333333 1.51326229008e-05 5.60495625912e-07 15.0 0.822222222222 0.000184259545641 6.73749456803e-06 16.0 0.811111111111 0.00223095030809 8.10072554519e-05 17.0 0.8 0.0252860600071 0.000977646325715 18.0 0.788888888889 0.166666666667 0.0121400118185 19.0 0.777777777778 0.308047273326 0.095103145345 20.0 0.766666666667 0.331102383025 0.130925730992 21.0 0.755555555556 0.333149073788 0.124029099319 22.0 0.744444444444 0.33331820071 0.113756010406 23.0 0.733333333333 0.33333209112 0.104005873278 24.0 0.722222222222 0.333333231366 0.0950601556148 ###Markdown The following function wraps that loop and stores the results in a `Sweep` object. ###Code def sweep_doses(dose_array): """Runs simulations with different doses and campaign spending. dose_array: range of values for number of vaccinations return: Sweep object with total number of infections """ sweep = SweepSeries() for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) run_simulation(system, update1) sweep[doses] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Now we can compute the number of infected students for each possible allocation of the budget. ###Code infected_sweep = sweep_doses(dose_array) ###Output _____no_output_____ ###Markdown And plot the results. ###Code plot(infected_sweep) decorate(xlabel='Doses of vaccine', ylabel='Total fraction infected', title='Total infections vs. doses', legend=False) savefig('chap05-fig06.pdf') ###Output Saving figure to file chap05-fig06.pdf ###Markdown **Exercise:** Suppose the price of the vaccine drops to $50 per dose. How does that affect the optimal allocation of the spending? **Exercise:** Suppose we have the option to quarantine infected students. For example, a student who feels ill might be moved to an infirmary, or a private dorm room, until they are no longer infectious.How might you incorporate the effect of quarantine in the SIR model? ###Code # Solution goes here tc = tr # no contact in quarntine until they are recovered tr = 4 beta = 1 / tc gamma = 1 / tr system = make_system(beta, gamma) sir = make_system1(beta, gamma) run_simulation(system, update1) print(system.results) plot_results(frame.S, frame.I, frame.R) ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') tables[2] ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census - un abs(census-un) abs(census-un)/un abs(census - un) / un * 100 ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code p_1 = census[1970] elapsed_time = t_end - 1970 total_growth = p_end - p_1 annual_growth = total_growth / elapsed_time results[t_0] = census[t_0] - abs(results[1970]-census[1970]) for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth plot(census, ':', label='US Census') plot(un, '-', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') census[1970] results[1970] abs(results[1970]-census[1970]) ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census -un abs(census -un) abs(census - un)/un abs(census - un)/un * 100 ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code total_growth = p_end - census[1970] elapsed_time = t_end - 1970 annual_growth = total_growth / elapsed_time results = TimeSeries() results[t_0] = census[t_0]- .4 for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census - un # Solution goes here # Solution goes here # Solution goes here ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code t_0 = get_first_label(census) t_1 = t_0 +20 t_end = get_last_label(census) elapsed_time = t_end - t_1 p_0 = census[1970] p_end = get_last_value(census) total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time results = TimeSeries() results[t_0] = census[t_0] for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown Modeling and Simulation in PythonChapter 5: DesignCopyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # If you want the figures to appear in the notebook, # and you want to interact with them, use # %matplotlib notebook # If you want the figures to appear in the notebook, # and you don't want to interact with them, use # %matplotlib inline # If you want the figures to appear in separate windows, use # %matplotlib qt5 # To switch from one to another, you have to select Kernel->Restart %matplotlib inline from modsim import * ###Output _____no_output_____ ###Markdown SIR implementationWe'll use a `State` object to represent the number or fraction of people in each compartment. ###Code init = State(S=89, I=1, R=0) init ###Output _____no_output_____ ###Markdown To convert from number of people to fractions, we divide through by the total. ###Code init /= sum(init) init ###Output _____no_output_____ ###Markdown `make_system` creates a `System` object with the given parameters. ###Code def make_system(beta, gamma): """Make a system object for the SIR model. beta: contact rate in days gamma: recovery rate in days returns: System object """ init = State(S=89, I=1, R=0) init /= sum(init) t0 = 0 t_end = 7 * 14 return System(init=init, t0=t0, t_end=t_end, beta=beta, gamma=gamma) ###Output _____no_output_____ ###Markdown Here's an example with hypothetical values for `beta` and `gamma`. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) ###Output _____no_output_____ ###Markdown The update function takes the state during the current time step and returns the state during the next time step. ###Code def update1(state, system): """Update the SIR model. state: State with variables S, I, R system: System with beta and gamma returns: State object """ s, i, r = state infected = system.beta * i * s recovered = system.gamma * i s -= infected i += infected - recovered r += recovered return State(S=s, I=i, R=r) ###Output _____no_output_____ ###Markdown To run a single time step, we call it like this: ###Code state = update1(init, system) state ###Output _____no_output_____ ###Markdown Now we can run a simulation by calling the update function for each time step. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. system: System object update_func: function that updates state returns: State object for final state """ state = system.init for t in linrange(system.t0, system.t_end): state = update_func(state, system) return state ###Output _____no_output_____ ###Markdown The result is the state of the system at `t_end` ###Code run_simulation(system, update1) ###Output _____no_output_____ ###Markdown **Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. After 14 weeks, how many students, total, have been infected?Hint: what is the change in `S` between the beginning and the end of the simulation? ###Code # Let's make a system with the right params. Thanks for the good docstrings. system = make_system(.25, .20) initial_S_value = system.init.S projection = run_simulation(system, update1) final_S_value = projection.S difference = initial_S_value - final_S_value difference ###Output _____no_output_____ ###Markdown Using Series objects If we want to store the state of the system at each time step, we can use one `TimeSeries` object for each state variable. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. Add three Series objects to the System: S, I, R system: System object update_func: function that updates state """ S = TimeSeries() I = TimeSeries() R = TimeSeries() state = system.init t0 = system.t0 S[t0], I[t0], R[t0] = state for t in linrange(system.t0, system.t_end): state = update_func(state, system) S[t+1], I[t+1], R[t+1] = state system.S = S system.I = I system.R = R ###Output _____no_output_____ ###Markdown Here's how we call it. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) run_simulation(system, update1) ###Output _____no_output_____ ###Markdown And then we can plot the results. ###Code def plot_results(S, I, R): """Plot the results of a SIR model. S: TimeSeries I: TimeSeries R: TimeSeries """ plot(S, '--', color='blue', label='Susceptible') plot(I, '-', color='red', label='Infected') plot(R, ':', color='green', label='Recovered') decorate(xlabel='Time (days)', ylabel='Fraction of population') ###Output _____no_output_____ ###Markdown Here's what they look like. ###Code plot_results(system.S, system.I, system.R) savefig('chap05-fig01.pdf') ###Output Saving figure to file chap05-fig01.pdf ###Markdown Using a DataFrame Instead of making three `TimeSeries` objects, we can use one `DataFrame`.We have to use `loc` to indicate which row we want to assign the results to. But then Pandas does the right thing, matching up the state variables with the columns of the `DataFrame`. ###Code def run_simulation(system, update_func): """Runs a simulation of the system. Add a DataFrame to the System: results system: System object update_func: function that updates state """ frame = DataFrame(columns=system.init.index) frame.loc[system.t0] = system.init for t in linrange(system.t0, system.t_end): frame.loc[t+1] = update_func(frame.loc[t], system) system.results = frame ###Output _____no_output_____ ###Markdown Here's how we run it, and what the result looks like. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day sir = make_system(beta, gamma) run_simulation(system, update1) system.results.head() ###Output _____no_output_____ ###Markdown We can extract the results and plot them. ###Code frame = system.results plot_results(frame.S, frame.I, frame.R) ###Output _____no_output_____ ###Markdown **Exercise** Suppose the time between contacts is 4 days and the recovery time is 5 days. Simulate this scenario for 14 days and plot the results. ###Code # Solution goes here system = make_system(.25, .20) simulation_results = run_simulation(system, update1) projection = system.results plot_results(projection.S, projection.I, projection.R) ###Output _____no_output_____ ###Markdown Metrics Given the results, we can compute metrics that quantify whatever we are interested in, like the total number of sick students, for example. ###Code def calc_total_infected(system): """Fraction of population infected during the simulation. system: System object with results. returns: fraction of population """ frame = system.results return frame.S[system.t0] - frame.S[system.t_end] ###Output _____no_output_____ ###Markdown Here's an example.| ###Code system.beta = 0.333 system.gamma = 0.25 run_simulation(system, update1) print(system.beta, system.gamma, calc_total_infected(system)) ###Output 0.333 0.25 0.467162931836 ###Markdown **Exercise:** Write functions that take a `System` object as a parameter, extract the `results` object from it, and compute the other metrics mentioned in the book:1. The fraction of students who are sick at the peak of the outbreak.2. The day the outbreak peaks.3. The fraction of students who are sick at the end of the semester.Hint: If you have a `TimeSeries` called `I`, you can compute the largest value of the series like this: I.max()And the index of the largest value like this: I.idxmax()You can read about these functions in the `Series` [documentation](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.html). ###Code # Solution goes here def peak_fraction_sick(system): """ Returns the fraction of infected students when the amount was highest. system : The particular situation under study. """ return system.results.I.max() peak_fraction_sick(system) # Solution goes here def peak_time(system): """ Returns the time at which the fraction of infected students was highest. system: The particular situation under study. """ return system.results.I.idxmax() peak_time(system) # Solution goes here def end_fraction_sick(system): """ Returns the fraction of sick students at the end of the semester. system: The particular situation under study. """ return system.results.I[system.t_end] end_fraction_sick(system) ###Output _____no_output_____ ###Markdown What if? We can use this model to evaluate "what if" scenarios. For example, this function models the effect of immunization by moving some fraction of the population from S to R before the simulation starts. ###Code def add_immunization(system, fraction): """Immunize a fraction of the population. Moves the given fraction from S to R. system: System object fraction: number from 0 to 1 """ system.init.S -= fraction system.init.R += fraction ###Output _____no_output_____ ###Markdown Let's start again with the system we used in the previous sections. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day system = make_system(beta, gamma) system.beta, system.gamma ###Output _____no_output_____ ###Markdown And run the model without immunization. ###Code run_simulation(system, update1) calc_total_infected(system) ###Output _____no_output_____ ###Markdown Now with 10% immunization. ###Code system2 = make_system(beta, gamma) add_immunization(system2, 0.1) run_simulation(system2, update1) calc_total_infected(system2) ###Output _____no_output_____ ###Markdown 10% immunization leads to a drop in infections of 16 percentage points.Here's what the time series looks like for S, with and without immunization. ###Code plot(system.results.S, '-', label='No immunization') plot(system2.results.S, 'g--', label='10% immunization') decorate(xlabel='Time (days)', ylabel='Fraction susceptible') savefig('chap05-fig02.pdf') ###Output Saving figure to file chap05-fig02.pdf ###Markdown Now we can sweep through a range of values for the fraction of the population who are immunized. ###Code immunize_array = linspace(0, 1, 11) for fraction in immunize_array: system = make_system(beta, gamma) add_immunization(system, fraction) run_simulation(system, update1) print(fraction, calc_total_infected(system)) ###Output 0.0 0.468320811029 0.1 0.30650802854 0.2 0.161365457006 0.3 0.0728155898425 0.4 0.035520216753 0.5 0.0196887157825 0.6 0.0116220579983 0.7 0.00683873780062 0.8 0.00369649625371 0.9 0.00148153267227 1.0 -0.000161212109412 ###Markdown This function does the same thing and stores the results in a `Sweep` object. ###Code def sweep_immunity(immunize_array): """Sweeps a range of values for immunity. immunize_array: array of fraction immunized returns: Sweep object """ sweep = SweepSeries() for fraction in immunize_array: system = make_system(beta, gamma) add_immunization(system, fraction) run_simulation(system, update1) sweep[fraction] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Here's how we run it. ###Code immunize_array = linspace(0, 1, 21) infected_sweep = sweep_immunity(immunize_array) ###Output _____no_output_____ ###Markdown And here's what the results look like. ###Code plot(infected_sweep) decorate(xlabel='Fraction immunized', ylabel='Total fraction infected', title='Fraction infected vs. immunization rate', legend=False) savefig('chap05-fig03.pdf') ###Output Saving figure to file chap05-fig03.pdf ###Markdown If 40% of the population is immunized, less than 4% of the population gets sick. Logistic function To model the effect of a hand-washing campaign, I'll use a [generalized logistic function](https://en.wikipedia.org/wiki/Generalised_logistic_function), which is a convenient function for modeling curves that have a generally sigmoid shape. The parameters of the GLF correspond to various features of the curve in a way that makes it easy to find a function that has the shape you want, based on data or background information about the scenario. ###Code def logistic(x, A=0, B=1, C=1, M=1, K=1, Q=1, nu=1): """Computes the generalize logistic function. A: controls the lower bound B: controls the steepness of the transition C: not all that useful, AFAIK M: controls the location of the transition K: controls the upper bound Q: shift the transition left or right nu: affects the symmetry of the transition returns: float or array """ exponent = -B * (x - M) denom = C + Q * exp(exponent) return A + (K-A) / denom ** (1/nu) ###Output _____no_output_____ ###Markdown The following array represents the range of possible spending. ###Code spending = linspace(0, 1200, 21) spending ###Output _____no_output_____ ###Markdown `compute_factor` computes the reduction in `beta` for a given level of campaign spending.`M` is chosen so the transition happens around \$500.`K` is the maximum reduction in `beta`, 20%.`B` is chosen by trial and error to yield a curve that seems feasible. ###Code def compute_factor(spending): """Reduction factor as a function of spending. spending: dollars from 0 to 1200 returns: fractional reduction in beta """ return logistic(spending, M=500, K=0.2, B=0.01) ###Output _____no_output_____ ###Markdown Here's what it looks like. ###Code percent_reduction = compute_factor(spending) * 100 plot(spending, percent_reduction) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Percent reduction in infection rate', title='Effect of hand washing on infection rate', legend=False) savefig('chap05-fig04.pdf') # Played with parameters and then reset everything ###Output Saving figure to file chap05-fig04.pdf ###Markdown **Exercise:** Modify the parameters `M`, `K`, and `B`, and see what effect they have on the shape of the curve. Read about the [generalized logistic function on Wikipedia](https://en.wikipedia.org/wiki/Generalised_logistic_function). Modify the other parameters and see what effect they have. Hand washing Now we can model the effect of a hand-washing campaign by modifying `beta` ###Code def add_hand_washing(system, spending): """Modifies system to model the effect of hand washing. system: System object spending: campaign spending in USD """ factor = compute_factor(spending) system.beta *= (1 - factor) ###Output _____no_output_____ ###Markdown Let's start with the same values of `beta` and `gamma` we've been using. ###Code tc = 3 # time between contacts in days tr = 4 # recovery time in days beta = 1 / tc # contact rate in per day gamma = 1 / tr # recovery rate in per day beta, gamma ###Output _____no_output_____ ###Markdown Now we can sweep different levels of campaign spending. ###Code spending_array = linspace(0, 1200, 13) for spending in spending_array: system = make_system(beta, gamma) add_hand_washing(system, spending) run_simulation(system, update1) print(spending, system.beta, calc_total_infected(system)) ###Output 0.0 0.332887143272 0.466770231236 100.0 0.332134252669 0.464141650401 200.0 0.330171608455 0.457217006313 300.0 0.325386471865 0.439887202912 400.0 0.315403905242 0.401630646271 500.0 0.3 0.33703425949 600.0 0.284596094758 0.267317030568 700.0 0.274613528135 0.22184699046 800.0 0.269828391545 0.200791598416 900.0 0.267865747331 0.192392183393 1000.0 0.267112856728 0.189213207818 1100.0 0.26683150821 0.18803175228 1200.0 0.266727403413 0.187595503995 ###Markdown Here's a function that sweeps a range of spending and stores the results in a `Sweep` object. ###Code def sweep_hand_washing(spending_array): """Run simulations with a range of spending. spending_array: array of dollars from 0 to 1200 returns: Sweep object """ sweep = SweepSeries() for spending in spending_array: system = make_system(beta, gamma) add_hand_washing(system, spending) run_simulation(system, update1) sweep[spending] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Here's how we run it. ###Code spending_array = linspace(0, 1200, 20) infected_sweep = sweep_hand_washing(spending_array) ###Output _____no_output_____ ###Markdown And here's what it looks like. ###Code plot(infected_sweep) decorate(xlabel='Hand-washing campaign spending (USD)', ylabel='Total fraction infected', title='Effect of hand washing on total infections', legend=False) savefig('chap05-fig05.pdf') ###Output Saving figure to file chap05-fig05.pdf ###Markdown Now let's put it all together to make some public health spending decisions. Optimization Suppose we have \$1200 to spend on any combination of vaccines and a hand-washing campaign. ###Code num_students = 90 budget = 1200 price_per_dose = 100 max_doses = int(budget / price_per_dose) dose_array = linrange(max_doses) max_doses ###Output _____no_output_____ ###Markdown We can sweep through a range of doses from, 0 to `max_doses`, model the effects of immunization and the hand-washing campaign, and run simulations.For each scenario, we compute the fraction of students who get sick. ###Code for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) run_simulation(system, update1) print(doses, system.init.S, system.beta, calc_total_infected(system)) ###Output 0.0 0.988888888889 0.266727403413 0.187595503995 1.0 0.977777777778 0.26683150821 0.174580718826 2.0 0.966666666667 0.267112856728 0.162909838349 3.0 0.955555555556 0.267865747331 0.153508349478 4.0 0.944444444444 0.269828391545 0.148565092315 5.0 0.933333333333 0.274613528135 0.152945950611 6.0 0.922222222222 0.284596094758 0.174964415024 7.0 0.911111111111 0.3 0.217343161684 8.0 0.9 0.315403905242 0.259071044488 9.0 0.888888888889 0.325386471865 0.278402884103 10.0 0.877777777778 0.330171608455 0.277914534623 11.0 0.866666666667 0.332134252669 0.267357496693 12.0 0.855555555556 0.332887143272 0.252796945636 ###Markdown The following function wraps that loop and stores the results in a `Sweep` object. ###Code def sweep_doses(dose_array): """Runs simulations with different doses and campaign spending. dose_array: range of values for number of vaccinations return: Sweep object with total number of infections """ sweep = SweepSeries() for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) run_simulation(system, update1) sweep[doses] = calc_total_infected(system) return sweep ###Output _____no_output_____ ###Markdown Now we can compute the number of infected students for each possible allocation of the budget. ###Code infected_sweep = sweep_doses(dose_array) ###Output _____no_output_____ ###Markdown And plot the results. ###Code plot(infected_sweep) decorate(xlabel='Doses of vaccine', ylabel='Total fraction infected', title='Total infections vs. doses', legend=False) savefig('chap05-fig06.pdf') ###Output Saving figure to file chap05-fig06.pdf ###Markdown **Exercise:** Suppose the price of the vaccine drops to $50 per dose. How does that affect the optimal allocation of the spending? **Exercise:** Suppose we have the option to quarantine infected students. For example, a student who feels ill might be moved to an infirmary, or a private dorm room, until they are no longer infectious.How might you incorporate the effect of quarantine in the SIR model? ###Code # Solution goes here num_students = 90 budget = 1200 price_per_dose = 50 max_doses = int(budget / price_per_dose) dose_array = linrange(max_doses) infected_sweep = sweep_doses(dose_array) plot(infected_sweep) decorate(xlabel='Doses of vaccine', ylabel='Total fraction infected', title='Total infections vs. doses', legend=False) # The total fraction of people infected decreases. def add_quarantine(system, fraction_of_sick): """ Modifies system to model the impact of quarantining infected students. system: System object fraction_of_sick: The fraction of sick people actually quarantined """ fraction_quarantined = system.init.I * fraction_of_sick system.beta*= (1 - fraction_quarantined) def sweep_doses(dose_array): """Runs simulations with different doses and campaign spending. dose_array: range of values for number of vaccinations return: Sweep object with total number of infections """ sweep = SweepSeries() for doses in dose_array: fraction = doses / num_students spending = budget - doses * price_per_dose system = make_system(beta, gamma) add_immunization(system, fraction) add_hand_washing(system, spending) add_quarantine(system, fraction) run_simulation(system, update1) sweep[doses] = calc_total_infected(system) return sweep # Solution goes here num_students = 90 budget = 1200 price_per_dose = 50 max_doses = int(budget / price_per_dose) dose_array = linrange(max_doses) infected_sweep = sweep_doses(dose_array) plot(infected_sweep) decorate(xlabel='Doses of vaccine', ylabel='Total fraction infected', title='Total infections vs. doses', legend=False) # TUrns out quarantining people helps too. THat's pretty neat. ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census-un abs(census-un) abs(census-un)/un abs(census - un) / un * 100 ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. ###Code max(abs(census-un)/census) * 100 max(abs(un-census)/un) *100 ###Output _____no_output_____ ###Markdown Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results help(linrange) ###Output Help on function linrange in module modsim: linrange(start=0, stop=None, step=1, **options) Returns an array of evenly-spaced values in the interval [start, stop]. This function works best if the space between start and stop is divisible by step; otherwise the results might be surprising. By default, the last value in the array is `stop-step` (at least approximately). If you provide the keyword argument `endpoint=True`, the last value in the array is `stop`. start: first value stop: last value step: space between values Also accepts the same keyword arguments as np.linspace. See https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html returns: array or Quantity ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code annualGrowth1970toPresentq results3 = TimeSeries() for t in linrange(t_0, t_end): results3[t+1] = results[t] + annualGrowth1970toPresent) results2 = TimeSeries() for t in linrange(t_0, t_end): results2[t+1] = results[t] + (census[t+1]-census[t]) plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results2, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') results2 ###Output _____no_output_____ ###Markdown Modeling and Simulation in PythonChapter 5Copyright 2017 Allen DowneyLicense: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0) ###Code # Configure Jupyter so figures appear in the notebook %matplotlib inline # Configure Jupyter to display the assigned value after an assignment %config InteractiveShell.ast_node_interactivity='last_expr_or_assign' # import functions from the modsim.py module from modsim import * ###Output _____no_output_____ ###Markdown Reading dataPandas is a library that provides tools for reading and processing data. `read_html` reads a web page from a file or the Internet and creates one `DataFrame` for each table on the page. ###Code from pandas import read_html ###Output _____no_output_____ ###Markdown The data directory contains a downloaded copy of https://en.wikipedia.org/wiki/World_population_estimatesThe arguments of `read_html` specify the file to read and how to interpret the tables in the file. The result, `tables`, is a sequence of `DataFrame` objects; `len(tables)` reports the length of the sequence. ###Code filename = 'data/World_population_estimates.html' tables = read_html(filename, header=0, index_col=0, decimal='M') len(tables) ###Output _____no_output_____ ###Markdown We can select the `DataFrame` we want using the bracket operator. The tables are numbered from 0, so `tables[2]` is actually the third table on the page.`head` selects the header and the first five rows. ###Code table2 = tables[2] table2.head() ###Output _____no_output_____ ###Markdown `tail` selects the last five rows. ###Code table2.tail() ###Output _____no_output_____ ###Markdown Long column names are awkard to work with, but we can replace them with abbreviated names. ###Code table2.columns = ['census', 'prb', 'un', 'maddison', 'hyde', 'tanton', 'biraben', 'mj', 'thomlinson', 'durand', 'clark'] ###Output _____no_output_____ ###Markdown Here's what the DataFrame looks like now. ###Code table2.head() ###Output _____no_output_____ ###Markdown The first column, which is labeled `Year`, is special. It is the **index** for this `DataFrame`, which means it contains the labels for the rows.Some of the values use scientific notation; for example, `2.544000e+09` is shorthand for $2.544 \cdot 10^9$ or 2.544 billion.`NaN` is a special value that indicates missing data. SeriesWe can use dot notation to select a column from a `DataFrame`. The result is a `Series`, which is like a `DataFrame` with a single column. ###Code census = table2.census census.head() census.tail() ###Output _____no_output_____ ###Markdown Like a `DataFrame`, a `Series` contains an index, which labels the rows.`1e9` is scientific notation for $1 \cdot 10^9$ or 1 billion. From here on, we will work in units of billions. ###Code un = table2.un / 1e9 un.head() census = table2.census / 1e9 census.head() ###Output _____no_output_____ ###Markdown Here's what these estimates look like. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') decorate(xlabel='Year', ylabel='World population (billion)') savefig('figs/chap03-fig01.pdf') ###Output Saving figure to file figs/chap03-fig01.pdf ###Markdown The following expression computes the elementwise differences between the two series, then divides through by the UN value to produce [relative errors](https://en.wikipedia.org/wiki/Approximation_error), then finds the largest element.So the largest relative error between the estimates is about 1.3%. ###Code max(abs(census - un) / un) * 100 ###Output _____no_output_____ ###Markdown **Exercise:** Break down that expression into smaller steps and display the intermediate results, to make sure you understand how it works.1. Compute the elementwise differences, `census - un`2. Compute the absolute differences, `abs(census - un)`3. Compute the relative differences, `abs(census - un) / un`4. Compute the percent differences, `abs(census - un) / un * 100` ###Code census - un abs(census - un) abs(census - un)/un abs(census - un) / un * 100 ###Output _____no_output_____ ###Markdown `max` and `abs` are built-in functions provided by Python, but NumPy also provides version that are a little more general. When you import `modsim`, you get the NumPy versions of these functions. Constant growth We can select a value from a `Series` using bracket notation. Here's the first element: ###Code census[1950] ###Output _____no_output_____ ###Markdown And the last value. ###Code census[2016] ###Output _____no_output_____ ###Markdown But rather than "hard code" those dates, we can get the first and last labels from the `Series`: ###Code t_0 = get_first_label(census) t_end = get_last_label(census) elapsed_time = t_end - t_0 ###Output _____no_output_____ ###Markdown And we can get the first and last values: ###Code p_0 = get_first_value(census) p_end = get_last_value(census) ###Output _____no_output_____ ###Markdown Then we can compute the average annual growth in billions of people per year. ###Code total_growth = p_end - p_0 annual_growth = total_growth / elapsed_time ###Output _____no_output_____ ###Markdown TimeSeries Now let's create a `TimeSeries` to contain values generated by a linear growth model. ###Code results = TimeSeries() ###Output _____no_output_____ ###Markdown Initially the `TimeSeries` is empty, but we can initialize it so the starting value, in 1950, is the 1950 population estimated by the US Census. ###Code results[t_0] = census[t_0] results ###Output _____no_output_____ ###Markdown After that, the population in the model grows by a constant amount each year. ###Code for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth ###Output _____no_output_____ ###Markdown Here's what the results looks like, compared to the actual data. ###Code plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf ###Markdown The model fits the data pretty well after 1990, but not so well before. Exercises**Optional Exercise:** Try fitting the model using data from 1970 to the present, and see if that does a better job.Hint: 1. Copy the code from above and make a few changes. Test your code after each small change.2. Make sure your `TimeSeries` starts in 1950, even though the estimated annual growth is based on later data.3. You might want to add a constant to the starting value to match the data better. ###Code t_0 = get_first_label(census) t_end = get_last_label(census) p_0 = get_first_value(census) p_end = get_last_value(census) annual_growth = (p_end - census[1970]) / (t_end - 1970) results = TimeSeries() results[t_0] = census[t_0] for t in linrange(t_0, t_end): results[t+1] = results[t] + annual_growth plot(census, ':', label='US Census') plot(un, '--', label='UN DESA') plot(results, color='gray', label='model') decorate(xlabel='Year', ylabel='World population (billion)', title='Constant growth') savefig('figs/chap03-fig02.pdf') ###Output Saving figure to file figs/chap03-fig02.pdf

100_Numpy_exercises_no_solution.ipynb

###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code print(np.__version__) print(np.show_config()) ###Output 1.16.4 mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/usr/local/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/usr/local/anaconda3/include'] blas_mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/usr/local/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/usr/local/anaconda3/include'] blas_opt_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/usr/local/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/usr/local/anaconda3/include'] lapack_mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/usr/local/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/usr/local/anaconda3/include'] lapack_opt_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/usr/local/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/usr/local/anaconda3/include'] None ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code null_ten = np.zeros(10) print(null_ten) ###Output [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code mem_size_null_ten = (null_ten.size * null_ten.itemsize) print(f"The memory size of array null_ten is {mem_size_null_ten} bytes") ###Output The memory size of array null_ten is 80 bytes ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) ###Code np.info(np.add) ###Output add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Add arguments element-wise. Parameters ---------- x1, x2 : array_like The arrays to be added. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or `None`, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`. Returns ------- add : ndarray or scalar The sum of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` + `x2` in terms of array broadcasting. Examples -------- >>> np.add(1.0, 4.0) 5.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.add(x1, x2) array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]]) ###Markdown 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ###Code null_ten[4] = 1 print(null_ten) ###Output [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.] ###Markdown 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code v = np.arange(10,50) print(v) print(type(v)) ###Output [10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49] <class 'numpy.ndarray'> ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code v[::-1] #reverse the array using indexing. :: selects entire array, -1 step ###Output _____no_output_____ ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code t_by_t_matrix = np.array(range(9)).reshape((3,3)) print(t_by_t_matrix) ###Output [[0 1 2] [3 4 5] [6 7 8]] ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code my_array = np.array([1, 2, 0, 0, 0, 4, 0]) my_array_not_null = my_array != 0 print("Indices of non_zero elements:") print(my_array_not_null) ###Output Indices of non_zero elements: [ True True False False False True False] ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code np.eye(3) #OR np.identity(3) ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code np.random.rand(3, 3, 3) ###Output _____no_output_____ ###Markdown 13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆) ###Code ten_by_ten = np.random.rand(10,10) min_ten_by_ten = ten_by_ten.min() print(min_ten_by_ten) max_ten_by_ten = ten_by_ten.max() print(max_ten_by_ten) ###Output 0.008017197920764385 0.9884419266661685 ###Markdown 14. Create a random vector of size 30 and find the mean value (★☆☆) ###Code v30 = np.random.rand(30) v30_mean = v30.mean() print(v30_mean) ###Output 0.5281540898110887 ###Markdown 15. Create a 2d array with 1 on the border and 0 inside (★☆☆) ###Code my_2d_arr = np.ones((5, 5)) print(my_2d_arr) my_2d_arr[1:-1,1:-1] = 0 # [1:-1, 1:-1] references the 2nd through #last rows(non_inclusive), 2nd through #last columns(non_inclusive) setting them = 0 print("\n") print(my_2d_arr) ###Output [[1. 1. 1. 1. 1.] [1. 1. 1. 1. 1.] [1. 1. 1. 1. 1.] [1. 1. 1. 1. 1.] [1. 1. 1. 1. 1.]] [[1. 1. 1. 1. 1.] [1. 0. 0. 0. 1.] [1. 0. 0. 0. 1.] [1. 0. 0. 0. 1.] [1. 1. 1. 1. 1.]] ###Markdown 16. How to add a border (filled with 0's) around an existing array? (★☆☆) ###Code my_array = np.ones((3, 3)) np.pad(my_array, pad_width=1, mode="constant", constant_values=0) ###Output _____no_output_____ ###Markdown 17. What is the result of the following expression? (★☆☆) ###Code #```python print(0 * np.nan) print(np.nan == np.nan) print(np.inf > np.nan) print(np.nan - np.nan) print(np.nan in set([np.nan])) print(0.3 == 3 * 0.1) #``` ###Output nan False False nan True False ###Markdown 18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆) ###Code #five_by_five = np.zeros((5, 5)) five_by_five_diag = np.diagflat([[1,2,3,4]], -1) print(five_by_five_diag) ###Output [[0 0 0 0 0] [1 0 0 0 0] [0 2 0 0 0] [0 0 3 0 0] [0 0 0 4 0]] ###Markdown 19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆) ###Code checker_board = np.ones((8,8)) checker_board[::2, 1::2] = 0 checker_board[1::2, ::2] = 0 print(checker_board) ###Output [[1. 0. 1. 0. 1. 0. 1. 0.] [0. 1. 0. 1. 0. 1. 0. 1.] [1. 0. 1. 0. 1. 0. 1. 0.] [0. 1. 0. 1. 0. 1. 0. 1.] [1. 0. 1. 0. 1. 0. 1. 0.] [0. 1. 0. 1. 0. 1. 0. 1.] [1. 0. 1. 0. 1. 0. 1. 0.] [0. 1. 0. 1. 0. 1. 0. 1.]] ###Markdown 20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? ###Code my_array = np.array(range(336)).reshape((6, 7, 8)) print(my_array) idx_100 = np.where(my_array == 99) print("\n") print(f"The index of the 100th element is {idx_100}") ###Output [[[ 0 1 2 3 4 5 6 7] [ 8 9 10 11 12 13 14 15] [ 16 17 18 19 20 21 22 23] [ 24 25 26 27 28 29 30 31] [ 32 33 34 35 36 37 38 39] [ 40 41 42 43 44 45 46 47] [ 48 49 50 51 52 53 54 55]] [[ 56 57 58 59 60 61 62 63] [ 64 65 66 67 68 69 70 71] [ 72 73 74 75 76 77 78 79] [ 80 81 82 83 84 85 86 87] [ 88 89 90 91 92 93 94 95] [ 96 97 98 99 100 101 102 103] [104 105 106 107 108 109 110 111]] [[112 113 114 115 116 117 118 119] [120 121 122 123 124 125 126 127] [128 129 130 131 132 133 134 135] [136 137 138 139 140 141 142 143] [144 145 146 147 148 149 150 151] [152 153 154 155 156 157 158 159] [160 161 162 163 164 165 166 167]] [[168 169 170 171 172 173 174 175] [176 177 178 179 180 181 182 183] [184 185 186 187 188 189 190 191] [192 193 194 195 196 197 198 199] [200 201 202 203 204 205 206 207] [208 209 210 211 212 213 214 215] [216 217 218 219 220 221 222 223]] [[224 225 226 227 228 229 230 231] [232 233 234 235 236 237 238 239] [240 241 242 243 244 245 246 247] [248 249 250 251 252 253 254 255] [256 257 258 259 260 261 262 263] [264 265 266 267 268 269 270 271] [272 273 274 275 276 277 278 279]] [[280 281 282 283 284 285 286 287] [288 289 290 291 292 293 294 295] [296 297 298 299 300 301 302 303] [304 305 306 307 308 309 310 311] [312 313 314 315 316 317 318 319] [320 321 322 323 324 325 326 327] [328 329 330 331 332 333 334 335]]] The index of the 100th element is (array([1]), array([5]), array([3])) ###Markdown 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆) ###Code eight = np.array([[0,1,0,1],[1,0,1,0]]) checker = np.tile(eight,(4,2)) print(checker) ###Output [[0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0] [0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0] [0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0] [0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0]] ###Markdown 22. Normalize a 5x5 random matrix (★☆☆) ###Code five_by_five = np.random.rand(5, 5) print(f"Array:") print("\n") print(five_by_five) print("\n") five_by_five_stdev = five_by_five.std() print(f"Array Standard Deviation: {five_by_five_stdev}") print("\n") five_by_five_mean = five_by_five.mean() print(f"Array Mean: {five_by_five_mean}") print("\n") five_by_five_norm = (five_by_five - five_by_five_mean) / five_by_five_stdev print("Normalized Array") print("\n") print(five_by_five_norm) ###Output Array: [[4.21808440e-01 6.46443022e-01 2.99143223e-04 9.39625092e-01 8.93558925e-01] [7.98082876e-01 3.86890720e-01 5.08204657e-01 3.22553403e-01 3.71699937e-01] [4.73874931e-01 4.47698673e-01 1.05121838e-01 2.71103062e-01 1.45395282e-01] [2.04830158e-01 8.30331294e-01 7.95105833e-01 9.05266177e-01 5.19794009e-01] [3.52018773e-01 8.54597270e-02 4.25166428e-01 9.03460542e-01 5.93484988e-01]] Array Standard Deviation: 0.2778819815171811 Array Mean: 0.49389111728470375 Normalized Array [[-0.25940033 0.54898092 -1.77626477 1.60404058 1.43826457] [ 1.09467968 -0.38505698 0.05150942 -0.61658447 -0.4397233 ] [-0.07203125 -0.16623044 -1.39904458 -0.80173624 -1.25411455] [-1.04022923 1.21073045 1.08396635 1.48039487 0.09321544] [-0.51054891 -1.46980163 -0.2473161 1.47389702 0.35840349]] ###Markdown 23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆) ###Code rgba = np.dtype([("R", "u1"),("G", "u1"),("B", "u1"),("A", "u1")]) print(type(rgba)) ###Output <class 'numpy.dtype'> ###Markdown 24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆) ###Code a = np.array(range(15)).reshape((5,3)) b = np.array(range(6)).reshape((3, 2)) a_b_prod = a * b ###Output _____no_output_____ ###Markdown 25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆) ###Code arr = np.array(range(12)) arr ###Output _____no_output_____ ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code print(np.__version__) print(np.show_config()) ###Output 1.14.3 mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/anaconda3/include'] blas_mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/anaconda3/include'] blas_opt_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/anaconda3/include'] lapack_mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/anaconda3/include'] lapack_opt_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/anaconda3/include'] None ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code nullVector = np.zeros(10) print(nullVector) ###Output [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.] ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code nullVector.itemsize * nullVector.size ###Output _____no_output_____ ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) ###Code np.info(np.add) ###Output add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Add arguments element-wise. Parameters ---------- x1, x2 : array_like The arrays to be added. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or `None`, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`. Returns ------- add : ndarray or scalar The sum of `x1` and `x2`, element-wise. Returns a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` + `x2` in terms of array broadcasting. Examples -------- >>> np.add(1.0, 4.0) 5.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.add(x1, x2) array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]]) ###Markdown 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ###Code x = np.zeros(10) x[4] = 1 x ###Output _____no_output_____ ###Markdown 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code y = np.arange(10, 50) y ###Output _____no_output_____ ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code y[::-1] ###Output _____no_output_____ ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code #threeByThree = np.array([[0, 1, 2], [3, 4, 5], [6, 7, 8]]) threeByThree = np.arange(9).reshape(3, 3) threeByThree ###Output _____no_output_____ ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code myArr = np.array([1,2,0,0,4,0]) np.nonzero(myArr) ###Output _____no_output_____ ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code -------skippers ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code np.random.random((3, 3, 3)) ###Output _____no_output_____ ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code np.__version__ ###Output _____no_output_____ ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code np.empty((10)) ###Output _____no_output_____ ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code arr = np.array([1,2,3]) arr.size * arr.itemsize ###Output _____no_output_____ ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) ###Code !python -c "import numpy; numpy.info(numpy.add)" ###Output add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Add arguments element-wise. Parameters ---------- x1, x2 : array_like The arrays to be added. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or `None`, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`. Returns ------- add : ndarray or scalar The sum of `x1` and `x2`, element-wise. This is a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` + `x2` in terms of array broadcasting. Examples -------- >>> np.add(1.0, 4.0) 5.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.add(x1, x2) array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]]) ###Markdown 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ###Code arr = np.empty((10)) arr[4] = 1 arr ###Output _____no_output_____ ###Markdown 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code np.arange(10, 50) ###Output _____no_output_____ ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code np.arange(10, 50)[::-1] ###Output _____no_output_____ ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code np.arange(9).reshape(3,3) ###Output _____no_output_____ ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code np.nonzero([1,2,0,0,4,0]) ###Output _____no_output_____ ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code np.eye(3) ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code np.random.random((3, 3, 3)) ###Output _____no_output_____ ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code print(np.__version__) np.show_config() ###Output 1.14.5 blas_mkl_info: NOT AVAILABLE blis_info: NOT AVAILABLE openblas_info: libraries = ['openblas', 'openblas'] library_dirs = ['/usr/local/lib'] language = c define_macros = [('HAVE_CBLAS', None)] blas_opt_info: libraries = ['openblas', 'openblas'] library_dirs = ['/usr/local/lib'] language = c define_macros = [('HAVE_CBLAS', None)] lapack_mkl_info: NOT AVAILABLE openblas_lapack_info: libraries = ['openblas', 'openblas'] library_dirs = ['/usr/local/lib'] language = c define_macros = [('HAVE_CBLAS', None)] lapack_opt_info: libraries = ['openblas', 'openblas'] library_dirs = ['/usr/local/lib'] language = c define_macros = [('HAVE_CBLAS', None)] ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code np.zeros(10) ###Output _____no_output_____ ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code '''This can be done in 2 ways.Firstly we can use the numpy size function and multiply the number of elements with the size of these elements(given by itemsize) Secondly we can also do this by calling nbytes for a numpy array which basically does this job for us ''' sample_arr=np.array([[0,0,0,0],[1,2,3,4],[2,3,4,5]]) print(sample_arr.shape) # ?np.array # np.size(sample_arr)*sample_arr.itemsize sample_arr.nbytes ###Output (3, 4) ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) ###Code # help(np.add) '''We can use the help function provided by python or use the numpy info function which loads the docstring for any given function For Interactive Prompts,both of these return the same output ''' np.info(np.add) ###Output add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Add arguments element-wise. Parameters ---------- x1, x2 : array_like The arrays to be added. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or `None`, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`. Returns ------- add : ndarray or scalar The sum of `x1` and `x2`, element-wise. Returns a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` + `x2` in terms of array broadcasting. Examples -------- >>> np.add(1.0, 4.0) 5.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.add(x1, x2) array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]]) ###Markdown 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ###Code '''Simple Indexing same as python.''' null_vector=np.zeros(10) null_vector[4]=1 print(null_vector) ###Output [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.] ###Markdown 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code '''This Problem can also be done in multiple ways.We can use the arange function given by numpy to do so or we can create a list comprehension in python and pass it to numpy \'s asarray function ''' dynamic_vector=np.arange(10,50) other_vector=np.asarray([i for i in range(10,50)]) # print(dynamic_vector,dynamic_vector.shape) print(other_vector) ###Output [10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49] ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code '''For this,we can use the slicing reverse technique used in python''' dynamic_vector=np.arange(10,50)[::-1] print(dynamic_vector) # ?np.arange ###Output [49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10] ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code '''For this,we can use the reshape method given by numpy.Basically this method can convert the source matrix/vector into a shape of our liking if it is possible.Else it gives us an error''' thby3=np.array(np.arange(0,9)).reshape(3,3) # ?np.array print(thby3,thby3.shape) ###Output [[0 1 2] [3 4 5] [6 7 8]] (3, 3) ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code '''We can do this by using the where function in numpy which gives the indexes based on a given condition or we can use the inbuilt function nonzero which can do the same job''' non_zero=np.array([[1,2,0,0,4,0]]) print(np.where(non_zero !=0)) print(np.nonzero(non_zero)) # ??np.nonzero ###Output (array([0, 0, 0]), array([0, 1, 4])) (array([0, 0, 0]), array([0, 1, 4])) ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code '''Using the ones function we can do this or we can create an array and then reshape it''' idmatrix=np.ones((3,3)) print(idmatrix) ###Output [[1. 1. 1.] [1. 1. 1.] [1. 1. 1.]] ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code '''This can be done in 2 ways.firstly the way that i chose was to create a random number ndarray using m*n*k numbers(27) in this case,and then reshape it into a (m,n,k) matrix.Or we can do this as mentioned in the solutions by directly passing the shape to numpy random classes random method''' new_matrix=np.random.rand(27).reshape((3,3,3)) print(new_matrix) print(np.random.random((3,3,3))) ###Output [[[0.07809135 0.04898578 0.47558162] [0.9993894 0.02910353 0.71019356] [0.25686361 0.27938524 0.69425457]] [[0.6065161 0.10396111 0.52118283] [0.68819857 0.67293342 0.2669946 ] [0.37315374 0.44858262 0.5486767 ]] [[0.69513921 0.2035966 0.69175945] [0.76195683 0.22851447 0.15484736] [0.95394653 0.18001367 0.50401602]]] [[[0.48372124 0.70822352 0.52408378] [0.26950103 0.43656129 0.93014059] [0.78892149 0.09945082 0.64039963]] [[0.06276586 0.00274591 0.90125876] [0.45546816 0.08854011 0.13264544] [0.35511955 0.27476579 0.88672656]] [[0.70766694 0.25992707 0.29547826] [0.35738838 0.61586472 0.61227287] [0.81622363 0.27039751 0.22491028]]] ###Markdown 13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆) ###Code '''This can be done in 2 ways.firstly the way that i chose was to create a random number ndarray by directly passing the shape to numpy random classes random method and passing the created array to the numpy min and max method.Or we can directly call the min and max on the created array itself.''' new_matrix_10=np.random.random((10,10)) # print(new_matrix_10) print(np.min(new_matrix_10),np.max(new_matrix_10)) print(new_matrix_10.min(),new_matrix_10.max()) ###Output 0.024457449668070286 0.9990899170408306 0.024457449668070286 0.9990899170408306 ###Markdown 14. Create a random vector of size 30 and find the mean value (★☆☆) ###Code '''We can do this by calling the mean method on our created numpy array created using the random.random method''' new_array_30=np.random.random(30) print(new_array_30.mean()) ###Output 0.4872822640639497 ###Markdown 15. Create a 2d array with 1 on the border and 0 inside (★☆☆) ###Code '''We can do this via simple indexing logic.For any given matrix of size m X n or m X m or n X n.We need to fill zeroes in rows from the first row and column(Because the border will cover the first row,first column and last row last column) so this should run from the first row and first column to the last row -1 and last column -1''' m,n=10,10 arrayzeroes=np.ones((m,n)) arrayzeroes[1:m-1,1:n-1]=0 print(arrayzeroes) ###Output [[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 0. 0. 0. 0. 0. 0. 0. 0. 1.] [1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]] ###Markdown 16. How to add a border (filled with 0's) around an existing array? (★☆☆) ###Code '''We can do this using the numpy pad function.For this,we can also use methods like insert,vstack and hstack.''' m,n=4,5 outer_border_matrix=np.ones((m,n)) print(outer_border_matrix) np.pad(outer_border_matrix,(1),'constant') ###Output [[1. 1. 1. 1. 1.] [1. 1. 1. 1. 1.] [1. 1. 1. 1. 1.] [1. 1. 1. 1. 1.]] ###Markdown 17. What is the result of the following expression? (★☆☆) ```python0 * np.nannp.nan == np.nannp.inf > np.nannp.nan - np.nannp.nan in set([np.nan])0.3 == 3 * 0.1``` ###Code print(0*np.nan) print(np.nan==np.nan) print(np.inf>np.nan) print(np.nan-np.nan) print(np.nan in set([np.nan])) print(0.3==3*0.1) ###Output nan False False nan True False ###Markdown 18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆) ###Code '''This can be done by using the np.diag method(Just found this function) or we can manually use the indices of the elements to do so.Although this will not work for any other matrix,for this question this is ok''' fivex5matrix=np.arange(25).reshape(5,5) # print(fivex5matrix) fivex5matrix[1,0]=1 fivex5matrix[2,1]=2 fivex5matrix[3,2]=3 fivex5matrix[4,3]=4 print(fivex5matrix) ###Output [[ 0 1 2 3 4] [ 1 6 7 8 9] [10 2 12 13 14] [15 16 3 18 19] [20 21 22 4 24]] ###Markdown 19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆) ###Code '''Hackey Method.Create a 8x8 matrix and then unroll it into one big vector using ravel.Then turn every alternate value into a zero or one(as needed) and then call the reshape command''' checkmatrix=np.ones((8,8)).ravel() checkmatrix[0::2]=0 checkmatrix.reshape((8,8)) ###Output _____no_output_____ ###Markdown 20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? ###Code '''This function basically returns us the index at whihc the elment is to be found.We can also pass a list of indices to search upon also''' newarray=np.random.random((6,7,8)) np.unravel_index(100,(6,7,8)) ###Output _____no_output_____ ###Markdown 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆) ###Code '''The tile function basically repeats a given array n number of times.So for this we can repeat our single row 8 no of times and the column should be just given a single value(1) so that the values are repeated along the columnaxis just once.''' newarray=np.array([0,1,0,1,0,1,0,1]) np.tile(newarray,((8,1))) ###Output _____no_output_____ ###Markdown 22. Normalize a 5x5 random matrix (★☆☆) ###Code '''To normalize a matrix,means to divide the individual elements of a matrix by the determinant of the matrix. The determinant is a special value unique to a matrix.This can be calculated by taking the minors along each row of the matrix.Refer to this link https://en.wikipedia.org/wiki/Determinant''' normalizematrinx=np.random.random((5,5)) determinant=np.linalg.det(normalizematrinx) normalizematrinx/=determinant print(normalizematrinx) ###Output [[0.51099193 0.66140224 0.44830203 0.19321164 0.65814295] [0.20223691 0.34620438 0.02645046 0.78087928 0.37897902] [0.63919224 0.23977047 0.06149836 0.36376474 0.63215891] [0.0155844 0.40818607 0.71835942 0.61074759 0.8811245 ] [0.09774466 0.01534684 0.15358355 0.9697329 0.47281814]] 0.028139673339381156 [[18.15912801 23.50426161 15.93131621 6.86616488 23.38843613] [ 7.18689602 12.30307047 0.93997038 27.75011902 13.46778328] [22.71498447 8.52072694 2.185468 12.92711317 22.46504075] [ 0.55382317 14.50571459 25.5283498 21.70414651 31.31253468] [ 3.47355349 0.54538102 5.45790103 34.46141275 16.80254543]] ###Markdown 23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆) 24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆) ###Code '''We can do this by 2 methods.Firstly we can use the dot method on a given matrix and multiply it with the second matrix as shown.Or we can use the @ operator(overloaded operator) to perform the same operation.This syntax is becoming increasingly common so its good to use this syntax.''' n5X3=np.random.random((5,3)) n3x2=np.random.random((3,2)) print(n5X3 @ n3x2) print(n5X3.dot(n3x2)) ###Output [[0.95661141 0.64514016] [0.66807619 0.31910586] [0.57827602 0.24663639] [0.68355174 0.3410374 ] [0.61122 0.33484139]] [[0.95661141 0.64514016] [0.66807619 0.31910586] [0.57827602 0.24663639] [0.68355174 0.3410374 ] [0.61122 0.33484139]] ###Markdown 25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆) ###Code '''Negation in numpy means that we simply return the multiplication of the value with a single -1.Was trying to solve this usin numpy functions when i realised i did not need those functions.''' onedarray=np.arange(100)[::-1] onedarray[(onedarray>3) & (onedarray<=8)] *=-1 onedarray ###Output _____no_output_____ ###Markdown 26. What is the output of the following script? (★☆☆) ```python Author: Jake VanderPlasprint(sum(range(5),-1))from numpy import *print(sum(range(5),-1))``` ###Code '''The second arg to sum reffers to the starting index from which the summation should take place. But for the np.sum function,the second arg reffers to the axis along which the sum is to be performed and in this case, the axis -1 reffers to a sum along the row hence we get the sum as 10''' print(sum(range(5),-1)) from numpy import * print(sum(range(5),-1)) ###Output 10 10 ###Markdown 27. Consider an integer vector Z, which of these expressions are legal? (★☆☆) ```pythonZ**Z2 > 2Z <- Z1j*ZZ/1/1ZZ``` ###Code intvector=np.array(range(5)) intvector**intvector intvector/1/1 intvector < -intvector intvector<intvector>intvector 2<<intvector>>2 '''THe only expression in this set which is illegal is the 6th expression as we cannot compute less than or greater than operations for an entire array.These operations need to be performed element wise which can be done using & or | operators(and operator or operator)''' ###Output _____no_output_____ ###Markdown 28. What are the result of the following expressions? ```pythonnp.array(0) / np.array(0)np.array(0) // np.array(0)np.array([np.nan]).astype(int).astype(float)``` ###Code np.array(0) / np.array(0) np.array(0) // np.array(0) np.array([np.nan]).astype(int).astype(float) ###Output _____no_output_____ ###Markdown 29. How to round away from zero a float array ? (★☆☆) 30. How to find common values between two arrays? (★☆☆) ###Code # np.lookfor("common") # ?np.intersect1d '''The intersect1d function accepts 2 arrays as parameters and then returns the common elements in both those arrays''' firstarray=np.arange(100) secondarray=np.arange(200) common=np.intersect1d(firstarray,secondarray) common ###Output _____no_output_____ ###Markdown 31. How to ignore all numpy warnings (not recommended)? (★☆☆) 32. Is the following expressions true? (★☆☆) ```pythonnp.sqrt(-1) == np.emath.sqrt(-1)``` ###Code '''The following expression is not true as both these numbers are negative,the sqrt for negative no is not defined for np.sqrt function but is defined for the np.emath.sqrt function.''' # ?np.emath.sqrt # ?np.sqrt ###Output _____no_output_____ ###Markdown 33. How to get the dates of yesterday, today and tomorrow? (★☆☆) ###Code # np.lookfor("today") np.array(['2019-03-31','2019-04-01','2019-04-02'],dtype=datetime64) ###Output _____no_output_____ ###Markdown 34. How to get all the dates corresponding to the month of July 2016? (★★☆) ###Code '''The dtype datetime64 can be used to render the dates for a particular month by providing the np.arange mehtod with the starting and ending dates using which it renders the dates within the given time period''' np.arange('2016-07-01','2016-08-01',dtype=datetime64) ###Output _____no_output_____ ###Markdown 35. How to compute ((A+B)\*(-A/2)) in place (without copy)? (★★☆) 36. Extract the integer part of a random array using 5 different methods (★★☆) 37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆) ###Code '''We can generate an initial matrix using zeros or random module.Then for each row,we can replace it with the arange list values.Or we can append a single list of values ranging from 0,4''' init_matrix=np.zeros((5,5)) init_matrix+=np.arange(5) print(init_matrix) ###Output [[0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.]] ###Markdown 38. Consider a generator function that generates 10 integers and use it to build an array (★☆☆) ###Code '''The np.from iter function allows us to generate an array from a generator expression''' generator_exp=(i for i in range(11)) print(np.fromiter(generator_exp,dtype=int)) ###Output <generator object <genexpr> at 0x7f04bca88f10> [ 0 1 2 3 4 5 6 7 8 9 10] ###Markdown 39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆) ###Code '''Using the np.linspace function we can create random numbers within a given interval range.It has an argument endpoint which specifies whetehr to include the last elment or not.Zero is by default included so we can just start our indexing process from the next element after zero''' np.linspace(0,1,11,endpoint=False)[1:] ###Output _____no_output_____ ###Markdown 40. Create a random vector of size 10 and sort it (★★☆) ###Code '''Create a random matrix using any method and just use the sort method like this or directly on the array.''' np.sort(np.linspace(0,1,10)) ###Output _____no_output_____ ###Markdown 41. How to sum a small array faster than np.sum? (★★☆) ###Code np.lookfor('sum') ###Output Search results for 'sum' ------------------------ numpy.sum Sum of array elements over a given axis. numpy.cumsum Return the cumulative sum of the elements along a given axis. numpy.einsum einsum(subscripts, *operands, out=None, dtype=None, order='K', numpy.nansum Return the sum of array elements over a given axis treating Not a numpy.nancumsum Return the cumulative sum of array elements over a given axis treating Not a numpy.einsum_path Evaluates the lowest cost contraction order for an einsum expression by numpy.trace Return the sum along diagonals of the array. numpy.ma.sum Return the sum of the array elements over the given axis. numpy.polyadd Find the sum of two polynomials. numpy.ma.cumsum Return the cumulative sum of the array elements over the given axis. numpy.logaddexp Logarithm of the sum of exponentiations of the inputs. numpy.matrix.sum Returns the sum of the matrix elements, along the given axis. numpy.logaddexp2 Logarithm of the sum of exponentiations of the inputs in base-2. numpy.chararray.sum Return the sum of the array elements over the given axis. numpy.mask_indices Return the indices to access (n, n) arrays, given a masking function. numpy.chararray.cumsum Return the cumulative sum of the elements along the given axis. numpy.chararray.trace Return the sum along diagonals of the array. numpy.format_float_positional Format a floating-point scalar as a decimal string in positional notation. numpy.format_float_scientific Format a floating-point scalar as a decimal string in scientific notation. numpy.linalg.tensorsolve Solve the tensor equation ``a x = b`` for x. numpy.ma.MaskedArray.sum Return the sum of the array elements over the given axis. numpy.ma.MaskedArray.cumsum Return the cumulative sum of the array elements over the given axis. numpy.PackageLoader.get_pkgdocs Return documentation summary of subpackages. numpy.ma.MaskedArray.trace Return the sum along diagonals of the array. numpy.polynomial.Hermite._add Add one Hermite series to another. numpy.polynomial.HermiteE._add Add one Hermite series to another. numpy.polynomial.Laguerre._add Add one Laguerre series to another. numpy.polynomial.Legendre._add Add one Legendre series to another. numpy.polynomial.Chebyshev._add Add one Chebyshev series to another. numpy.polynomial.Polynomial._add Add one polynomial to another. numpy.AxisError.__class__.__sizeof__ __sizeof__() -> int numpy.fv Compute the future value. numpy.pv Compute the present value. numpy.add Add arguments element-wise. numpy.all Test whether all array elements along a given axis evaluate to True. numpy.any Test whether any array element along a given axis evaluates to True. numpy.cov Estimate a covariance matrix, given data and weights. numpy.dot Dot product of two arrays. Specifically, numpy.irr Return the Internal Rate of Return (IRR). numpy.npv Returns the NPV (Net Present Value) of a cash flow series. numpy.std Compute the standard deviation along the specified axis. numpy.var Compute the variance along the specified axis. numpy.amax Return the maximum of an array or maximum along an axis. numpy.amin Return the minimum of an array or minimum along an axis. numpy.core.setup_common.get_api_versions Return current C API checksum and the recorded checksum. numpy.diag Extract a diagonal or construct a diagonal array. numpy.diff Calculate the n-th discrete difference along the given axis. numpy.in1d Test whether each element of a 1-D array is also present in a second array. numpy.ipmt Compute the interest portion of a payment. numpy.isin Calculates `element in test_elements`, broadcasting over `element` only. numpy.kron Kronecker product of two arrays. numpy.mean Compute the arithmetic mean along the specified axis. numpy.prod Return the product of array elements over a given axis. numpy.cross Return the cross product of two (arrays of) vectors. numpy.inner Inner product of two arrays. numpy.outer Compute the outer product of two vectors. numpy.trapz Integrate along the given axis using the composite trapezoidal rule. numpy.choose Construct an array from an index array and a set of arrays to choose from. numpy.matmul Matrix product of two arrays. numpy.nanstd Compute the standard deviation along the specified axis, while numpy.nanvar Compute the variance along the specified axis, while ignoring NaNs. numpy.nditer Efficient multi-dimensional iterator object to iterate over arrays. numpy.average Compute the weighted average along the specified axis. numpy.nanmean Compute the arithmetic mean along the specified axis, ignoring NaNs. numpy.nanprod Return the product of array elements over a given axis treating Not a numpy.polyfit Least squares polynomial fit. numpy.polyint Return an antiderivative (indefinite integral) of a polynomial. numpy.bincount Count number of occurrences of each value in array of non-negative ints. numpy.blackman Return the Blackman window. numpy.convolve Returns the discrete, linear convolution of two one-dimensional sequences. numpy.diagflat Create a two-dimensional array with the flattened input as a diagonal. numpy.diagonal Return specified diagonals. numpy.gradient Return the gradient of an N-dimensional array. numpy.setxor1d Find the set exclusive-or of two arrays. numpy.correlate Cross-correlation of two 1-dimensional sequences. numpy.histogram Compute the histogram of a set of data. numpy.piecewise Evaluate a piecewise-defined function. numpy.setdiff1d Find the set difference of two arrays. numpy.tensordot Compute tensor dot product along specified axes for arrays >= 1-D. numpy.vectorize vectorize(pyfunc, otypes=None, doc=None, excluded=None, cache=False, numpy.percentile Compute the qth percentile of the data along the specified axis. numpy.histogram2d Compute the bi-dimensional histogram of two data samples. numpy.histogramdd Compute the multidimensional histogram of some data. numpy.intersect1d Find the intersection of two arrays. numpy.ma.add Add arguments element-wise. numpy.array2string Return a string representation of an array. numpy.ma.var Compute the variance along the specified axis. numpy.fft.ifft Compute the one-dimensional inverse discrete Fourier Transform. numpy.nanpercentile Compute the qth percentile of the data along the specified axis, numpy.ma.inner Inner product of two arrays. numpy.ma.outer Compute the outer product of two vectors. numpy.ma.trace a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None) numpy.apply_over_axes Apply a function repeatedly over multiple axes. numpy.ma.average Return the weighted average of array over the given axis. numpy.ma.polyfit Least squares polynomial fit. numpy.linalg.cond Compute the condition number of a matrix. numpy.linalg.norm Matrix or vector norm. numpy.set_printoptions Set printing options. numpy.ma.convolve Returns the discrete, linear convolution of two one-dimensional sequences. numpy.ma.diagflat Create a two-dimensional array with the flattened input as a diagonal. numpy.linalg.lstsq Return the least-squares solution to a linear matrix equation. numpy.ufunc.reduce Reduces `a`'s dimension by one, by applying ufunc along one axis. numpy.bytes0.expandtabs Return a copy of B where all tab characters are expanded using spaces. numpy.ufunc.reduceat Performs a (local) reduce with specified slices over a single axis. numpy.linalg.multi_dot Compute the dot product of two or more arrays in a single function call, numpy.linalg.tensorinv Compute the 'inverse' of an N-dimensional array. numpy.str0.expandtabs Return a copy of S where all tab characters are expanded using spaces. numpy.ufunc.accumulate Accumulate the result of applying the operator to all elements. numpy.linalg.matrix_rank Return matrix rank of array using SVD method numpy.ma.apply_over_axes Apply a function repeatedly over multiple axes. numpy.ma.MaskedArray.var Compute the variance along the specified axis. numpy.distutils.command.sdist.sdist.write_manifest Write the file list in 'self.filelist' (presumably as filled in numpy.core.tests.test_numeric.TestKeepdims.sub_array.sum Return the sum of the array elements over the given axis. numpy.polynomial.Hermite.fit Least squares fit to data. numpy.polynomial.Hermite._fit Least squares fit of Hermite series to data. numpy.polynomial.HermiteE.fit Least squares fit to data. numpy.polynomial.Laguerre.fit Least squares fit to data. numpy.polynomial.Legendre.fit Least squares fit to data. numpy.polynomial.Chebyshev.fit Least squares fit to data. numpy.polynomial.HermiteE._fit Least squares fit of Hermite series to data. numpy.polynomial.Laguerre._fit Least squares fit of Laguerre series to data. numpy.polynomial.Legendre._fit Least squares fit of Legendre series to data. numpy.polynomial.Chebyshev._fit Least squares fit of Chebyshev series to data. numpy.polynomial.Hermite._roots Compute the roots of a Hermite series. numpy.polynomial.Polynomial.fit Least squares fit to data. numpy.polynomial.HermiteE._roots Compute the roots of a HermiteE series. numpy.polynomial.Laguerre._roots Compute the roots of a Laguerre series. numpy.polynomial.Legendre._roots Compute the roots of a Legendre series. numpy.polynomial.Polynomial._fit Least-squares fit of a polynomial to data. numpy.polynomial.Chebyshev._roots Compute the roots of a Chebyshev series. numpy.polynomial.Polynomial._roots Compute the roots of a polynomial. numpy.polynomial.hermite.hermval2d Evaluate a 2-D Hermite series at points (x, y). numpy.polynomial.hermite.hermval3d Evaluate a 3-D Hermite series at points (x, y, z). numpy.polynomial.laguerre.lagval2d Evaluate a 2-D Laguerre series at points (x, y). numpy.polynomial.laguerre.lagval3d Evaluate a 3-D Laguerre series at points (x, y, z). numpy.polynomial.legendre.legval2d Evaluate a 2-D Legendre series at points (x, y). numpy.polynomial.legendre.legval3d Evaluate a 3-D Legendre series at points (x, y, z). numpy.polynomial.hermite.hermgrid2d Evaluate a 2-D Hermite series on the Cartesian product of x and y. numpy.polynomial.hermite.hermgrid3d Evaluate a 3-D Hermite series on the Cartesian product of x, y, and z. numpy.polynomial.laguerre.laggrid2d Evaluate a 2-D Laguerre series on the Cartesian product of x and y. numpy.polynomial.laguerre.laggrid3d Evaluate a 3-D Laguerre series on the Cartesian product of x, y, and z. numpy.polynomial.legendre.leggrid2d Evaluate a 2-D Legendre series on the Cartesian product of x and y. numpy.polynomial.legendre.leggrid3d Evaluate a 3-D Legendre series on the Cartesian product of x, y, and z. numpy.polynomial.chebyshev.chebval2d Evaluate a 2-D Chebyshev series at points (x, y). numpy.polynomial.chebyshev.chebval3d Evaluate a 3-D Chebyshev series at points (x, y, z). numpy.polynomial.chebyshev.chebgrid2d Evaluate a 2-D Chebyshev series on the Cartesian product of x and y. numpy.polynomial.chebyshev.chebgrid3d Evaluate a 3-D Chebyshev series on the Cartesian product of x, y, and z. numpy.polynomial.hermite_e.hermeval2d Evaluate a 2-D HermiteE series at points (x, y). numpy.polynomial.hermite_e.hermeval3d Evaluate a 3-D Hermite_e series at points (x, y, z). numpy.polynomial.polynomial.polyval2d Evaluate a 2-D polynomial at points (x, y). numpy.polynomial.polynomial.polyval3d Evaluate a 3-D polynomial at points (x, y, z). numpy.polynomial.hermite_e.hermegrid2d Evaluate a 2-D HermiteE series on the Cartesian product of x and y. numpy.polynomial.hermite_e.hermegrid3d Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z. numpy.polynomial.polynomial.polygrid2d Evaluate a 2-D polynomial on the Cartesian product of x and y. numpy.polynomial.polynomial.polygrid3d Evaluate a 3-D polynomial on the Cartesian product of x, y and z. numpy.distutils.command.build_clib.build_clib.check_library_list Ensure that the list of libraries is valid. numpy.distutils.command.build_ext.build_ext.check_extensions_list Ensure that the list of extensions (presumably provided as a numpy.distutils.command.develop.develop.create_index.__getitem__ Return a newest-to-oldest list of distributions for `project_name` numpy.testing.nose_tools.noseclasses.NumpyDocTestFinder._find_lineno Return a line number of the given object's docstring. Note: numpy.distutils.misc_util.Configuration.set_options Configure Configuration instance. numpy.distutils.misc_util.Configuration.add_subpackage Add a sub-package to the current Configuration instance. numpy.distutils.misc_util.Configuration.get_subpackage Return list of subpackage configurations. numpy.distutils.misc_util.Configuration.add_npy_pkg_config Generate and install a npy-pkg config file from a template. numpy.core.tests.test_multiarray.TestWritebackIfCopy.subTest Return a context manager that will return the enclosed block numpy.linalg.tests.test_deprecations.test_qr_mode_full_future_warning Check mode='full' FutureWarning. ###Markdown 42. Consider two random array A and B, check if they are equal (★★☆) ###Code '''The np.equal method gives us the element truthwise comparision whereas the np.allclose function gives us the result if all the elements are equal or not. Allclose works it both the matrixes are of the same dimensions(shape) while array equal first compares the shape and then checks the elements.So the array_equal method is better ''' randarray1=np.random.rand(4) randarray2=np.random.rand(5) # print(np.allclose(randarray1,randarray2)) print(np.array_equal(randarray1,randarray2)) # np.lookfor('equal') # ?np.array_equal ###Output False ###Markdown 43. Make an array immutable (read-only) (★★☆) ###Code '''The Simplest Method would be to convert the array into a tuple(immutable object) The other way simple way is to set a writable flag for an array(refer to the above answer) https://stackoverflow.com/questions/5541324/immutable-numpy-array ''' init_array=np.random.rand(10) init_array.setflags(write=False) ###Output _____no_output_____ ###Markdown 44. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆) 45. Create random vector of size 10 and replace the maximum value by 0 (★★☆) ###Code '''Using argmax,we can find the index of the maximum element in the array and then directly assign that index to zero''' init_array=np.random.rand(10) maxval=np.argmax(init_array) # index_max=np.where(maxval,init_array) init_array[maxval]=0 print(init_array) ###Output [0. 0.47079336 0.51235952 0.26298048 0.09889671 0.79884636 0.14280278 0.80566579 0.8795261 0.49992016] ###Markdown 46. Create a structured array with `x` and `y` coordinates covering the \[0,1\]x\[0,1\] area (★★☆) 47. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) 48. Print the minimum and maximum representable value for each numpy scalar type (★★☆) 49. How to print all the values of an array? (★★☆) 50. How to find the closest value (to a given scalar) in a vector? (★★☆) 51. Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆) 52. Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆) 53. How to convert a float (32 bits) array into an integer (32 bits) in place? 54. How to read the following file? (★★☆) ```1, 2, 3, 4, 56, , , 7, 8 , , 9,10,11``` 55. What is the equivalent of enumerate for numpy arrays? (★★☆) 56. Generate a generic 2D Gaussian-like array (★★☆) 57. How to randomly place p elements in a 2D array? (★★☆) 58. Subtract the mean of each row of a matrix (★★☆) ###Code '''Get the mean along the row(axis=1) and create it inot a new array and subtract from the original array''' init_array=np.random.rand(9).reshape(3,3) mean=np.mean(init_array,axis=1) print(init_array) print(init_array-mean) ###Output [[0.15526401 0.36099196 0.95507526] [0.13015837 0.27284659 0.80911787] [0.96565706 0.09242216 0.58342427]] [[-0.33517973 -0.04304898 0.40790743] [-0.36028537 -0.13119436 0.26195004] [ 0.47521332 -0.31161878 0.03625644]] ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code print(np.__version__) ###Output 1.16.5 ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code np.zeros(10) ###Output _____no_output_____ ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code z = np.zeros(10) print(z.size*z.itemsize) ###Output 80 ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code z = np.arange(10,50) z ###Output _____no_output_____ ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code z = np.arange(10) z= z[::-1] print(z) ###Output [9 8 7 6 5 4 3 2 1 0] ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code z = np.arange(0,9).reshape(3,3) z ###Output _____no_output_____ ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code a = np.array([1,2,0,0,4,0]) z = np.nonzero(a) print(z) ###Output (array([0, 1, 4], dtype=int64),) ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code a = np.identity(3) a ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code a = np.random.random((3,3,3)) a ###Output _____no_output_____ ###Markdown 13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆) ###Code a = np.random.random((10,10)) aMax,aMin = a.max(),a.min() print(aMax,aMin) ###Output 0.9894527896688977 0.0033449179792053307 ###Markdown 14. Create a random vector of size 30 and find the mean value (★☆☆) ###Code a = np.random.rand(30) print(a,a.mean()) ###Output [0.1846994 0.41626531 0.3572198 0.94343712 0.82735063 0.45271474 0.78023616 0.18597967 0.21119891 0.8124634 0.67189869 0.73030937 0.38998714 0.52991707 0.55362064 0.72072631 0.20886604 0.78750828 0.18651096 0.01735404 0.7524434 0.87639775 0.86362552 0.8380825 0.33414464 0.92022892 0.28823983 0.57098412 0.4469707 0.10179415] 0.532039173298709 ###Markdown 15. Create a 2d array with 1 on the border and 0 inside (★☆☆) ###Code a = np.ones((10,10)) a[1:-1,1:-1] = 0 a ###Output _____no_output_____ ###Markdown 16. How to add a border (filled with 0's) around an existing array? (★☆☆) ###Code a = np.ones((5,5)) a = np.pad(a,pad_width=1,mode='constant',constant_values=0) a ###Output _____no_output_____ ###Markdown 17. What is the result of the following expression? (★☆☆) ```pythonimport numpy as np0 * np.nannp.nan == np.nannp.inf > np.nannp.nan - np.nannp.nan in set([np.nan])0.3 == 3 * 0.1``` ###Code print(0 * np.nan) print(np.nan == np.nan) print(np.inf > np.nan) print(np.nan - np.nan) print(np.nan in set([np.nan])) print(0.3 == 3 * 0.1) ###Output nan False False nan True False ###Markdown 18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆) ###Code a = np.diag(np.arange(1,5),k = -1) a ###Output _____no_output_____ ###Markdown 19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆) ###Code Z = np.zeros((8,8),dtype=int) Z[1::2,::2] = 1 Z[::2,1::2] = 1 print(Z) ###Output [[0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0] [0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0] [0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0] [0 1 0 1 0 1 0 1] [1 0 1 0 1 0 1 0]] ###Markdown 20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? ###Code a = np.unravel_index(100,(6,7,8)) a ###Output _____no_output_____ ###Markdown 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆) ###Code a = np.tile(([[0,1],[1,0]]),(4,4)) a ###Output _____no_output_____ ###Markdown 22. Normalize a 5x5 random matrix (★☆☆) ###Code a = np.random.random((5,5)) a = (a-a.mean())/a.std() a ###Output _____no_output_____ ###Markdown 23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆) ###Code color = np.dtype([("r", np.ubyte, 1), ("g", np.ubyte, 1), ("b", np.ubyte, 1), ("a", np.ubyte, 1)]) ###Output _____no_output_____ ###Markdown 24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆) ###Code a = np.random.randint(0,10,(5,3)) b = np.random.randint(0,10,(3,2)) c = np.dot(a,b) c ###Output _____no_output_____ ###Markdown 25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆) ###Code Z = np.arange(11) Z[(3 < Z) & (Z <= 8)] *= -1 print(Z) ###Output [ 0 1 2 3 -4 -5 -6 -7 -8 9 10] ###Markdown 26. What is the output of the following script? (★☆☆) ```python Author: Jake VanderPlasprint(sum(range(5),-1))from numpy import *print(sum(range(5),-1))``` ###Code print(sum(range(5),-1)) from numpy import * print(sum(range(5),-1)) ###Output 10 10 ###Markdown 27. Consider an integer vector Z, which of these expressions are legal? (★☆☆) ```pythonZ**Z2 > 2Z <- Z1j*ZZ/1/1ZZ``` ###Code Z**Z 2 << Z >> 2 Z <- Z 1j*Z Z/1/1 Z<Z>Z ###Output _____no_output_____ ###Markdown 28. What are the result of the following expressions? ```pythonimport numpy as npnp.array(0) / np.array(0)np.array(0) // np.array(0)np.array([np.nan]).astype(int).astype(float)``` ###Code print(np.array(0) / np.array(0)) print(np.array(0) // np.array(0)) print(np.array([np.nan]).astype(int).astype(float)) ###Output nan 0 [-2.14748365e+09] ###Markdown 29. How to round away from zero a float array ? (★☆☆) ###Code z = np.random.uniform(-10,+10,10) print(z) a = np.ceil(np.abs(z)) a = np.copysign(a,z) print(a) ###Output [-8.62671653 -7.09880113 -6.89654145 6.46688051 6.58682965 0.35029675 0.86552309 -0.08276563 0.13443567 5.506434 ] [-9. -8. -7. 7. 7. 1. 1. -1. 1. 6.] ###Markdown 30. How to find common values between two arrays? (★☆☆) ###Code a = np.random.randint(0,10,10) b = np.random.randint(0,10,10) print(a) print(b) c = np.intersect1d(a,b) print(c) ###Output [5 2 0 6 4 2 3 7 4 1] [6 7 7 0 3 9 0 2 5 6] [0 2 3 5 6 7] ###Markdown 31. How to ignore all numpy warnings (not recommended)? (★☆☆) 32. Is the following expressions true? (★☆☆) ```pythonimport numpy as npnp.sqrt(-1) == np.emath.sqrt(-1)``` ###Code print(np.sqrt(-1) == np.emath.sqrt(-1)) ###Output False ###Markdown 33. How to get the dates of yesterday, today and tomorrow? (★☆☆) ###Code yesterday = np.datetime64('today', 'D') - np.timedelta64(1, 'D') today = np.datetime64('today', 'D') tomorrow = np.datetime64('today', 'D') + np.timedelta64(1, 'D') ###Output _____no_output_____ ###Markdown 34. How to get all the dates corresponding to the month of July 2016? (★★☆) ###Code a = np.arange('2016-07','2016-08',dtype='datetime64[D]') print(a) ###Output ['2016-07-01' '2016-07-02' '2016-07-03' '2016-07-04' '2016-07-05' '2016-07-06' '2016-07-07' '2016-07-08' '2016-07-09' '2016-07-10' '2016-07-11' '2016-07-12' '2016-07-13' '2016-07-14' '2016-07-15' '2016-07-16' '2016-07-17' '2016-07-18' '2016-07-19' '2016-07-20' '2016-07-21' '2016-07-22' '2016-07-23' '2016-07-24' '2016-07-25' '2016-07-26' '2016-07-27' '2016-07-28' '2016-07-29' '2016-07-30' '2016-07-31'] ###Markdown 35. How to compute ((A+B)\*(-A/2)) in place (without copy)? (★★☆) ###Code A = np.ones(3)*1 B = np.ones(3)*2 C = np.ones(3)*3 np.add(A,B,out=B) np.divide(A,2,out=A) np.negative(A,out=A) np.multiply(A,B,out=A) ###Output [3. 3. 3.] ###Markdown 36. Extract the integer part of a random array using 5 different methods (★★☆) ###Code Z = np.random.uniform(0,10,10) print(Z) print (Z - Z%1) print (np.floor(Z)) print (np.ceil(Z)-1) print (Z.astype(int)) print (np.trunc(Z)) ###Output [5.12587063e-01 6.11417676e+00 4.52278136e+00 7.40439203e+00 1.97934146e+00 7.83186706e+00 9.08705098e+00 2.55233858e-03 5.16819291e+00 8.21004979e+00] [0. 6. 4. 7. 1. 7. 9. 0. 5. 8.] [0. 6. 4. 7. 1. 7. 9. 0. 5. 8.] [0. 6. 4. 7. 1. 7. 9. 0. 5. 8.] [0 6 4 7 1 7 9 0 5 8] [0. 6. 4. 7. 1. 7. 9. 0. 5. 8.] ###Markdown 37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆) ###Code Z = np.zeros((5,5)) Z += np.arange(5) print(Z) ###Output [[0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.] [0. 1. 2. 3. 4.]] ###Markdown 38. Consider a generator function that generates 10 integers and use it to build an array (★☆☆) ###Code def generate(): for x in range(10): yield x z = np.fromiter(generate(),dtype = float) print(z) ###Output _____no_output_____ ###Markdown 39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆) ###Code a = np.linspace(0,1,11,endpoint=False)[1:] print(a) ###Output [0.09090909 0.18181818 0.27272727 0.36363636 0.45454545 0.54545455 0.63636364 0.72727273 0.81818182 0.90909091] ###Markdown 40. Create a random vector of size 10 and sort it (★★☆) ###Code a = np.random.random(10) print(a) b = np.sort(a) print(b) ###Output [4.86757380e-01 1.62914068e-04 2.68263652e-01 3.81264516e-01 4.10301938e-01 6.98630253e-01 3.16398734e-01 6.16344498e-01 7.32390798e-02 2.48836384e-02] [1.62914068e-04 2.48836384e-02 7.32390798e-02 2.68263652e-01 3.16398734e-01 3.81264516e-01 4.10301938e-01 4.86757380e-01 6.16344498e-01 6.98630253e-01] ###Markdown 41. How to sum a small array faster than np.sum? (★★☆) ###Code a = np.random.randint(1,10,10) print(a) x = np.multiply.reduce(a) print(x) ###Output [6 8 9 8 7 1 3 4 8 6] 13934592 ###Markdown 42. Consider two random array A and B, check if they are equal (★★☆) 43. Make an array immutable (read-only) (★★☆) ###Code z = np.zeros(5) z.flags.writeable = False z[0] = 1 ###Output _____no_output_____ ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code print(np.__version__) np.show_config() ###Output 1.14.3 mkl_info: libraries = ['mkl_rt'] library_dirs = ['C:/Apps/Anaconda3\\Library\\lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\lib', 'C:/Apps/Anaconda3\\Library\\include'] blas_mkl_info: libraries = ['mkl_rt'] library_dirs = ['C:/Apps/Anaconda3\\Library\\lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\lib', 'C:/Apps/Anaconda3\\Library\\include'] blas_opt_info: libraries = ['mkl_rt'] library_dirs = ['C:/Apps/Anaconda3\\Library\\lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\lib', 'C:/Apps/Anaconda3\\Library\\include'] lapack_mkl_info: libraries = ['mkl_rt'] library_dirs = ['C:/Apps/Anaconda3\\Library\\lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\lib', 'C:/Apps/Anaconda3\\Library\\include'] lapack_opt_info: libraries = ['mkl_rt'] library_dirs = ['C:/Apps/Anaconda3\\Library\\lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\include', 'C:\\Program Files (x86)\\IntelSWTools\\compilers_and_libraries_2016.4.246\\windows\\mkl\\lib', 'C:/Apps/Anaconda3\\Library\\include'] ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code z=np.zeros(10) z ###Output _____no_output_____ ###Markdown 4. How to find the memory size of any array (★☆☆) 5. How to get the documentation of the numpy add function from the command line? (★☆☆) ###Code np.info(np.add) #command line? ###Output add(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) Add arguments element-wise. Parameters ---------- x1, x2 : array_like The arrays to be added. If ``x1.shape != x2.shape``, they must be broadcastable to a common shape (which may be the shape of one or the other). out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or `None`, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`. Returns ------- add : ndarray or scalar The sum of `x1` and `x2`, element-wise. Returns a scalar if both `x1` and `x2` are scalars. Notes ----- Equivalent to `x1` + `x2` in terms of array broadcasting. Examples -------- >>> np.add(1.0, 4.0) 5.0 >>> x1 = np.arange(9.0).reshape((3, 3)) >>> x2 = np.arange(3.0) >>> np.add(x1, x2) array([[ 0., 2., 4.], [ 3., 5., 7.], [ 6., 8., 10.]]) ###Markdown 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ###Code z=np.zeros(10) z[4]=1 z ###Output _____no_output_____ ###Markdown 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code z=np.arange(10,50) z ###Output _____no_output_____ ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code z=[1,2,4,5] z[::-1] ###Output _____no_output_____ ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code # z=8*np.random.random((3,3)) #not this solution z=np.arange(0,9).reshape((3,3)) z ###Output _____no_output_____ ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code a=np.nonzero([1,2,0,0,4,0]) a ###Output _____no_output_____ ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code z=np.eye(3,3) z ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code z=np.random.random((3,3,3)) z ###Output _____no_output_____ ###Markdown 13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆) ###Code z=np.random.random((10,10)) zmin,zmax=z.min(),z.max() zmin,zmax ###Output _____no_output_____ ###Markdown 14. Create a random vector of size 30 and find the mean value (★☆☆) ###Code z=np.random.random(30) print("the mean is ", z.mean()) ###Output the mean is 0.505523768366917 ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code print(np.__version__) np.show_config() ###Output 1.16.2 mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/home/hoshino/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/home/hoshino/anaconda3/include'] blas_mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/home/hoshino/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/home/hoshino/anaconda3/include'] blas_opt_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/home/hoshino/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/home/hoshino/anaconda3/include'] lapack_mkl_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/home/hoshino/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/home/hoshino/anaconda3/include'] lapack_opt_info: libraries = ['mkl_rt', 'pthread'] library_dirs = ['/home/hoshino/anaconda3/lib'] define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)] include_dirs = ['/home/hoshino/anaconda3/include'] ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code a = np.zeros((10)) ###Output _____no_output_____ ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code a.nbytes ###Output _____no_output_____ ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code np.arange(10, 50) ###Output _____no_output_____ ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code a = np.arange(10, 50) a[::-1] ###Output _____no_output_____ ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code np.arange(9).reshape((3, 3)) ###Output _____no_output_____ ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code np.nonzero([1, 2, 0, 0, 4, 0]) ###Output _____no_output_____ ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code np.eye(3) ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code np.random.random((3,3,3)) ###Output _____no_output_____ ###Markdown 13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆) ###Code a = np.random.random((10, 10)) print(np.max(a)) print(np.min(a)) ###Output 0.9929558396429009 0.007995122448371528 ###Markdown 14. Create a random vector of size 30 and find the mean value (★☆☆) ###Code np.random.random((1000)).mean() ###Output _____no_output_____ ###Markdown 15. Create a 2d array with 1 on the border and 0 inside (★☆☆) ###Code np.pad(np.zeros((3,4)), mode="constant", pad_width=1, constant_values=1) ###Output _____no_output_____ ###Markdown 16. How to add a border (filled with 0's) around an existing array? (★☆☆) ###Code np.pad(a, mode="constant", pad_width=1, constant_values=0) ###Output _____no_output_____ ###Markdown 17. What is the result of the following expression? (★☆☆) ```python0 * np.nannp.nan == np.nannp.inf > np.nannp.nan - np.nannp.nan in set([np.nan])0.3 == 3 * 0.1``` ###Code 0.3 == 3 * 0.1 ###Output _____no_output_____ ###Markdown 18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆) ###Code np.diagflat(range(1,5), -1) ###Output _____no_output_____ ###Markdown 19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆) 20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? ###Code array = np.array([ [11, 22, 33], [77, 88, 99], [44, 55, 66]] ) np.argmax(array) ###Output _____no_output_____ ###Markdown 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆) ###Code np.tile([[0, 1], [1, 0]], (4, 4)) ###Output _____no_output_____ ###Markdown 22. Normalize a 5x5 random matrix (★☆☆) ###Code a = np.random.random((5, 5)) a /= np.sum(a ** 2) a ###Output _____no_output_____ ###Markdown 23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆) ###Code dt = np.dtype(np.uint32) ###Output _____no_output_____ ###Markdown 24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆) ###Code a = np.arange(15).reshape((5, 3)) b = np.arange(6).reshape((3, 2)) np.matmul(a, b) ###Output _____no_output_____ ###Markdown 25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆) ###Code a = np.arange(15) a[np.logical_and(a>3,a<8)] = 0 a ###Output _____no_output_____ ###Markdown 26. What is the output of the following script? (★☆☆) ```python Author: Jake VanderPlasprint(sum(range(5),-1))from numpy import *print(sum(range(5),-1))``` ###Code from numpy import * print(sum(range(5),-1)) ###Output 10 ###Markdown 27. Consider an integer vector Z, which of these expressions are legal? (★☆☆) ```pythonZ**Z2 > 2Z <- Z1j*ZZ/1/1ZZ``` ###Code Z = np.arange(3) Z<Z>Z ###Output _____no_output_____ ###Markdown 28. What are the result of the following expressions? ```pythonnp.array(0) / np.array(0)np.array(0) // np.array(0)np.array([np.nan]).astype(int).astype(float)``` ###Code np.array([np.nan]).astype(int).astype(float) ###Output _____no_output_____ ###Markdown 29. How to round away from zero a float array ? (★☆☆) 30. How to find common values between two arrays? (★☆☆) ###Code a = np.arange(15) b = np.arange(3, 20) np.intersect1d(a, b) ###Output _____no_output_____ ###Markdown 31. How to ignore all numpy warnings (not recommended)? (★☆☆) ###Code np.seterr(all="ignore") ###Output _____no_output_____ ###Markdown 32. Is the following expressions true? (★☆☆) ```pythonnp.sqrt(-1) == np.emath.sqrt(-1)``` ###Code np.sqrt(-1) == np.emath.sqrt(-1) ###Output _____no_output_____ ###Markdown 33. How to get the dates of yesterday, today and tomorrow? (★☆☆) ###Code np.datetime64("today", "D") + np.timedelta64(1, "D") ###Output _____no_output_____ ###Markdown 34. How to get all the dates corresponding to the month of July 2016? (★★☆) ###Code np.arange("2016-06", "2016-07", dtype="datetime64[D]") ###Output _____no_output_____ ###Markdown 35. How to compute ((A+B)\*(-A/2)) in place (without copy)? (★★☆) ###Code a = np.arange(3) b = np.arange(3, 6) (a.__iadd__(b))*(-a/2) ###Output _____no_output_____ ###Markdown 36. Extract the integer part of a random array using 5 different methods (★★☆) 37. Create a 5x5 matrix with row values ranging from 0 to 4 (★★☆) ###Code np.tile(np.arange(5), (5, 1)) ###Output _____no_output_____ ###Markdown 38. Consider a generator function that generates 10 integers and use it to build an array (★☆☆) ###Code np.array(range(10)) ###Output _____no_output_____ ###Markdown 39. Create a vector of size 10 with values ranging from 0 to 1, both excluded (★★☆) ###Code np.linspace(0, 1, 10) ###Output _____no_output_____ ###Markdown 40. Create a random vector of size 10 and sort it (★★☆) ###Code a = np.sort(np.random.random(10)) a ###Output _____no_output_____ ###Markdown 41. How to sum a small array faster than np.sum? (★★☆) ###Code a = np.arange(10).reshape((2, 5)) %timeit np.sum(a) def sumt(a): t = 0 for i in a: t += i %timeit sumt(a) ###Output 2.94 µs ± 51.1 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each) 2.93 µs ± 99.7 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each) ###Markdown 42. Consider two random array A and B, check if they are equal (★★☆) ###Code a = np.random.random(4) b = a c = np.random.random(4) np.array_equal(a, c) ###Output _____no_output_____ ###Markdown 43. Make an array immutable (read-only) (★★☆) ###Code a.flags["WRITEABLE"] = False a a[0] = 1 ###Output _____no_output_____ ###Markdown 44. Consider a random 10x2 matrix representing cartesian coordinates, convert them to polar coordinates (★★☆) ###Code Z = np.random.random((10, 2)) r = np.sqrt(np.sum(Z ** 2, -1)) theta = np.arctan(Z[:, -1]/Z[:, 0]) theta ###Output _____no_output_____ ###Markdown 45. Create random vector of size 10 and replace the maximum value by 0 (★★☆) ###Code Z = np.random.random(10) print(Z) idx = np.unravel_index(np.argmax(Z), Z.shape) Z[idx] = 0 print(Z) ###Output [0.91327621 0.44819014 0.90751922 0.14680165 0.85062559 0.39022343 0.61739459 0.7236832 0.37179418 0.65201644] [0. 0.44819014 0.90751922 0.14680165 0.85062559 0.39022343 0.61739459 0.7236832 0.37179418 0.65201644] ###Markdown 46. Create a structured array with `x` and `y` coordinates covering the \[0,1\]x\[0,1\] area (★★☆) ###Code dt = np.dtype([("x", "<f4"), ("y", "<f4")]) Z = np.array([(0, 0), (0, 1)], dtype=dt) Z["x"] ###Output _____no_output_____ ###Markdown 47. Given two arrays, X and Y, construct the Cauchy matrix C (Cij =1/(xi - yj)) ###Code X = np.random.rand(4) Y = np.random.rand(3) C = 1. / X[:, None] - Y C ###Output _____no_output_____ ###Markdown 48. Print the minimum and maximum representable value for each numpy scalar type (★★☆) ###Code print(np.iinfo(np.int8)) print(np.iinfo(np.int16)) print(np.iinfo(np.int32)) print(np.iinfo(np.int64)) print(np.iinfo(np.uint8)) print(np.iinfo(np.uint16)) print(np.iinfo(np.uint32)) print(np.iinfo(np.uint64)) print(np.finfo(np.float32)) print(np.finfo(np.float64)) ###Output Machine parameters for int8 --------------------------------------------------------------- min = -128 max = 127 --------------------------------------------------------------- Machine parameters for int16 --------------------------------------------------------------- min = -32768 max = 32767 --------------------------------------------------------------- Machine parameters for int32 --------------------------------------------------------------- min = -2147483648 max = 2147483647 --------------------------------------------------------------- Machine parameters for int64 --------------------------------------------------------------- min = -9223372036854775808 max = 9223372036854775807 --------------------------------------------------------------- Machine parameters for uint8 --------------------------------------------------------------- min = 0 max = 255 --------------------------------------------------------------- Machine parameters for uint16 --------------------------------------------------------------- min = 0 max = 65535 --------------------------------------------------------------- Machine parameters for uint32 --------------------------------------------------------------- min = 0 max = 4294967295 --------------------------------------------------------------- Machine parameters for uint64 --------------------------------------------------------------- min = 0 max = 18446744073709551615 --------------------------------------------------------------- Machine parameters for float32 --------------------------------------------------------------- precision = 6 resolution = 1.0000000e-06 machep = -23 eps = 1.1920929e-07 negep = -24 epsneg = 5.9604645e-08 minexp = -126 tiny = 1.1754944e-38 maxexp = 128 max = 3.4028235e+38 nexp = 8 min = -max --------------------------------------------------------------- Machine parameters for float64 --------------------------------------------------------------- precision = 15 resolution = 1.0000000000000001e-15 machep = -52 eps = 2.2204460492503131e-16 negep = -53 epsneg = 1.1102230246251565e-16 minexp = -1022 tiny = 2.2250738585072014e-308 maxexp = 1024 max = 1.7976931348623157e+308 nexp = 11 min = -max --------------------------------------------------------------- ###Markdown 49. How to print all the values of an array? (★★☆) ###Code #np.set_printoptions(threshold=np.inf) Z = np.random.random(1000) print(Z) ###Output [1.39798776e-01 6.69724983e-01 5.87358700e-01 2.66794860e-01 6.04634358e-02 3.75329453e-01 6.70318075e-01 7.76229210e-02 1.83058870e-01 8.73172322e-01 1.80373374e-01 4.23921159e-01 9.43834689e-01 7.77251243e-01 5.00110242e-01 4.48791174e-01 3.13091233e-02 1.61199559e-01 4.40544415e-01 4.87060138e-01 4.50351242e-01 3.21611617e-01 4.95937922e-01 3.49077017e-02 5.67107275e-01 5.36396414e-01 7.27594881e-01 9.17879516e-01 9.63430025e-01 7.26479698e-01 6.62872258e-01 5.36090160e-01 9.34553190e-01 6.72610348e-01 8.79814278e-01 9.61289553e-01 2.10129772e-02 3.85393048e-01 9.34358600e-01 3.06922477e-01 6.72947154e-02 6.42373908e-02 1.84203502e-01 5.08936306e-01 8.82285170e-02 5.74399909e-01 5.58803426e-01 1.14857617e-01 6.52764230e-01 6.04308189e-01 9.67814801e-02 4.32253793e-01 8.13910272e-01 3.69212546e-02 9.19624325e-01 2.07435193e-01 5.01711878e-01 8.49120969e-01 7.22187441e-01 7.41335990e-01 7.27409269e-01 8.63633553e-01 5.73524304e-01 5.31048337e-01 5.98397422e-01 6.71766393e-01 3.36740246e-01 1.95992272e-01 2.48015133e-01 9.84769648e-01 7.81753026e-01 9.39500516e-01 8.94109306e-01 4.77897782e-01 6.61738002e-01 1.08009764e-01 5.90993719e-01 2.40480792e-02 7.40586188e-01 2.67285652e-01 9.36841594e-01 6.75820249e-01 5.62267335e-01 3.98223065e-01 1.28808429e-01 4.42073657e-02 8.19574658e-01 4.40825716e-01 7.11703767e-01 1.80567001e-01 6.36135574e-01 9.30451350e-01 6.70098361e-01 7.12688851e-01 8.21900662e-01 3.62611780e-01 6.80702468e-01 1.94450291e-01 7.15504982e-01 3.34611512e-01 3.68050279e-02 6.75371549e-01 8.66489494e-01 3.12524010e-01 7.86751684e-01 1.15410472e-04 4.61646787e-01 2.09148507e-01 5.38922020e-01 6.27257879e-01 9.32836344e-01 1.12284610e-01 7.05728916e-01 4.26887953e-01 5.59745036e-02 9.00750284e-01 6.84084559e-02 4.62603167e-02 9.00557552e-01 1.27567576e-01 4.87011955e-01 7.95321982e-01 8.75783107e-01 7.86754692e-01 4.72103923e-01 4.12549331e-02 7.23862188e-01 9.62695811e-01 2.75889744e-01 3.69689971e-01 4.40711814e-01 5.83643490e-01 6.05827992e-01 5.35109892e-01 9.31348362e-01 2.34336609e-01 3.26416601e-01 7.82638465e-01 1.31707242e-01 3.40025110e-01 7.00959408e-01 9.53288618e-01 1.31739658e-01 7.74351657e-01 1.80363329e-01 3.03144150e-01 7.22542829e-01 3.81120000e-01 9.23990192e-01 2.67259864e-01 2.01471164e-01 4.54141659e-01 1.16327406e-01 4.98868265e-01 2.92459816e-01 8.26472744e-01 9.05264751e-01 5.72303087e-02 3.34269615e-01 6.84087723e-01 7.28876192e-01 3.78973885e-01 4.67632404e-01 1.43447524e-01 6.02015183e-01 3.61413115e-01 2.29436654e-01 7.56643310e-01 6.35197942e-01 5.55146634e-01 5.67710621e-01 3.65500906e-01 3.50763718e-01 9.48872461e-01 6.53368637e-01 9.42869809e-01 2.88583267e-01 1.02111926e-01 3.29204047e-01 2.45402087e-01 6.27130596e-01 8.75845352e-03 9.43420359e-01 2.55191936e-01 3.02016992e-01 4.12391240e-01 1.21790788e-01 1.65220226e-01 1.46263118e-01 5.50540277e-02 5.43061946e-01 5.96664547e-01 2.58801952e-01 4.44868485e-01 1.80778923e-02 3.30044341e-01 1.99372440e-01 5.42501352e-01 2.71107367e-01 1.86504870e-01 9.01396530e-01 8.67933102e-01 2.48562939e-01 9.70839456e-01 5.72806642e-01 3.62925273e-01 4.00893848e-01 1.03901531e-01 3.43146314e-01 1.18861634e-01 3.32104763e-01 1.24642860e-01 5.17685718e-01 6.14961120e-02 1.02144301e-01 3.40718178e-02 2.33521089e-02 3.92692293e-01 8.13420727e-01 8.88860838e-01 9.28088302e-01 5.38939260e-01 9.38706784e-02 4.47374893e-01 3.46534594e-01 6.05000754e-01 9.42292093e-01 1.07752722e-01 2.92533776e-01 7.50420836e-01 4.84228283e-01 3.47243673e-01 4.09030724e-01 1.34090209e-01 4.16469049e-01 6.08084306e-01 7.76602688e-01 3.12599166e-01 1.84550347e-01 6.17776049e-01 2.25780245e-01 9.87713221e-01 5.95941612e-02 7.30274870e-01 4.65258660e-01 7.33632137e-01 9.95277963e-02 5.48500717e-01 4.45337477e-01 3.25316843e-01 2.44867986e-01 8.53605188e-01 4.35034701e-01 8.80302168e-01 2.65683233e-01 3.67204117e-01 2.15067288e-01 8.56457885e-01 3.41523303e-01 9.71970155e-02 3.20448586e-01 3.45299985e-01 4.73079465e-01 5.22097467e-01 3.53561702e-01 8.11282724e-01 9.34096113e-01 5.15855662e-01 7.40479401e-01 4.14715766e-02 8.63236841e-01 2.37266715e-01 6.82094620e-02 1.17342200e-02 2.45898933e-01 2.75758407e-01 8.99066701e-01 5.06750721e-01 9.81319055e-01 9.48752875e-01 2.37200642e-02 1.75577649e-01 6.83192774e-01 9.94788589e-01 8.04657373e-01 2.76329113e-01 1.09386320e-01 5.97318839e-01 7.86233020e-01 9.07675322e-01 2.24524230e-02 7.87465364e-01 2.33859028e-01 6.63850356e-01 8.83819991e-01 5.60531849e-02 9.07478823e-01 8.39503811e-01 5.65017166e-01 1.20677130e-01 9.64570026e-01 2.61050357e-01 4.16735270e-01 4.83574271e-01 9.73836770e-01 3.14545088e-01 1.57581128e-01 2.86639296e-01 8.35486372e-01 1.26639139e-01 4.35322312e-01 2.24483073e-01 6.97528357e-01 9.97841450e-01 6.23134444e-01 1.83339747e-01 4.46200471e-01 7.61109143e-01 8.40990431e-01 3.18415768e-01 7.08558100e-01 3.10010137e-01 6.67209982e-01 9.93367981e-03 3.92459305e-01 8.85322276e-02 2.18540277e-01 8.36491260e-01 1.88072639e-01 2.17916419e-01 7.44095726e-02 6.56850385e-01 2.33447946e-02 8.79243602e-01 2.63328363e-01 8.86720877e-03 3.92206669e-01 7.05624422e-01 9.00836939e-01 4.38102600e-01 7.14304822e-01 6.59138559e-01 3.26777842e-01 4.99191774e-01 3.16507817e-01 4.95866911e-04 9.91978057e-01 6.76700091e-01 1.89512942e-01 4.93952256e-01 4.17602055e-01 2.15769670e-01 8.32281636e-01 6.99840701e-01 6.73033021e-02 9.43622094e-01 5.04491593e-01 6.72647586e-01 8.84666011e-01 2.88365148e-01 8.67846698e-01 9.03434404e-01 3.53173548e-01 4.45378010e-01 6.92038514e-01 3.41706515e-01 6.11067095e-01 4.84851945e-01 5.23330471e-01 6.99429008e-01 9.88320628e-01 8.09581589e-01 2.96906156e-01 6.00095109e-01 7.98710920e-01 4.67548550e-01 6.90539969e-03 7.67708231e-01 7.81894057e-01 4.43034799e-01 9.15470135e-01 1.25146351e-01 1.17995772e-01 2.49421860e-01 6.88215265e-01 4.85354875e-01 4.15550702e-01 5.09572952e-01 9.51782840e-03 7.73530078e-01 2.01471065e-01 9.68234822e-01 8.18285996e-01 5.14393612e-01 5.49242885e-02 4.73918961e-01 2.20646667e-01 4.21393032e-01 9.39975558e-01 9.25620877e-01 4.24034409e-01 7.60621243e-02 9.87547405e-01 1.25075932e-01 3.31798625e-01 3.66753133e-04 3.82161370e-01 2.80072112e-01 2.43313272e-01 7.36066262e-02 3.59893232e-01 1.95848275e-01 5.94990538e-03 2.73075941e-01 1.99056134e-02 8.95567948e-01 1.06019467e-01 7.11527879e-01 4.53989590e-01 2.60931715e-02 1.06490326e-01 8.31891911e-01 3.98072957e-01 9.28885675e-01 6.64317965e-01 3.71841659e-01 3.09103631e-01 8.67689362e-01 6.17893485e-01 8.33255092e-02 3.62875021e-01 6.95967948e-01 1.45530274e-01 2.71234029e-01 5.60197679e-02 3.88976388e-01 9.79223642e-01 7.27015176e-01 2.61346679e-01 9.75087657e-01 3.20428826e-01 4.98011651e-01 8.22524477e-02 6.80190825e-01 2.57644199e-01 5.84798363e-01 3.85016877e-01 4.69239103e-01 9.40329240e-01 9.84778128e-01 4.38662168e-01 1.10539383e-01 8.04587992e-01 2.84042259e-01 3.62072110e-01 5.56439396e-01 5.69972172e-01 3.41231362e-01 2.17868057e-01 2.47934739e-02 8.79636809e-01 4.15294011e-01 3.73684627e-01 7.37512347e-02 8.75045149e-01 6.98688754e-01 3.50107300e-01 9.09917366e-01 3.51303200e-01 6.80963907e-01 7.52899082e-01 8.88805242e-01 9.94620341e-02 4.77142306e-01 7.53373813e-01 2.92631977e-01 4.59002400e-01 4.63930880e-01 1.88157303e-01 6.71714785e-01 4.94533793e-01 6.13710773e-02 8.96211620e-03 2.26310269e-01 1.13569000e-01 5.94550743e-01 5.56937748e-01 2.99781088e-01 7.11286305e-02 5.19658076e-01 1.72832938e-01 9.52116486e-01 1.38050059e-01 3.04178890e-01 4.02724620e-01 1.87248348e-01 2.83402989e-01 6.47150517e-01 4.53341427e-01 7.10629570e-01 7.37916858e-01 6.83029474e-01 8.07269426e-01 9.46802242e-01 5.35443516e-01 2.62183484e-01 8.90975619e-01 9.07476844e-01 9.40530491e-01 2.06046161e-01 9.70273032e-01 2.09838431e-01 8.89378329e-01 6.84841010e-01 8.26584013e-02 2.46870604e-01 2.59182520e-01 8.20893527e-01 7.19470222e-01 3.22677974e-01 1.69547006e-01 8.49166635e-01 3.54386298e-01 9.44638224e-01 9.33974127e-01 1.44759402e-01 3.57191748e-01 5.05637740e-01 5.95404947e-01 1.95250135e-03 3.05866094e-01 6.29280270e-02 2.94933116e-01 7.01994912e-01 6.04086605e-01 4.52956826e-01 6.42724190e-01 7.81655011e-01 5.99806166e-02 8.36908692e-01 9.41844283e-01 9.57493244e-02 6.40628878e-01 8.85242011e-01 8.82956765e-01 9.70435020e-01 3.58574333e-01 8.94623455e-01 2.92449645e-01 9.59847955e-01 2.29424404e-01 2.19633471e-03 9.95806083e-01 5.94079277e-01 1.79095757e-01 8.20900535e-01 2.41841102e-01 6.49861416e-01 2.98995532e-01 3.60784705e-01 3.04009893e-01 2.75082981e-01 6.46633122e-01 1.79186104e-01 1.13631592e-02 8.15516565e-01 6.19450839e-01 1.60186220e-01 7.42691171e-02 3.45032304e-01 5.41795030e-01 8.61502835e-01 7.92649412e-01 5.92983524e-01 1.68717971e-01 9.09830544e-01 1.06931639e-01 7.88394010e-01 3.33891559e-01 6.23547763e-01 8.04810638e-01 2.08182287e-01 3.08031360e-01 1.17157353e-01 9.17948903e-01 8.14708575e-01 8.87971231e-01 8.08852272e-01 5.64905544e-01 8.39395465e-01 1.55018492e-01 6.49197356e-01 9.93063936e-01 1.67896546e-01 6.79862383e-01 2.05988491e-01 2.88149657e-01 1.10289454e-02 3.13203832e-01 9.65865222e-01 3.13222888e-01 4.39680103e-01 9.77762007e-01 8.67114078e-02 4.93073295e-01 1.43843146e-01 7.30431777e-01 1.07007073e-01 6.26894994e-01 8.31626889e-01 2.42903870e-02 8.54733271e-01 2.53516317e-01 1.85100696e-01 7.06732835e-01 7.11623974e-01 6.94295529e-01 2.29929211e-01 3.44808767e-01 9.04394888e-02 2.52763336e-01 4.50830590e-01 2.92582736e-01 8.16322463e-01 8.20057348e-01 2.47827021e-01 6.03962061e-01 5.88860497e-01 9.23626930e-01 3.03675659e-01 7.70195553e-01 9.52382694e-01 5.87771752e-01 4.45830391e-01 3.17540284e-01 8.17618862e-01 6.57363499e-01 3.76941622e-01 6.92177944e-01 5.83128559e-01 6.42367220e-01 1.55513001e-01 7.72786501e-01 7.63716798e-01 8.83272375e-03 6.23801379e-01 5.52654625e-01 3.57952987e-01 4.02204899e-01 7.66511782e-01 6.72682221e-01 8.62033293e-01 7.15310506e-01 8.43389616e-01 7.67355758e-01 6.53404109e-01 3.87868846e-01 2.15351941e-01 9.53490508e-01 3.68761602e-02 3.79766367e-01 4.25802720e-02 4.99554003e-02 8.56643128e-01 3.26906408e-02 6.16917436e-01 6.59591143e-01 2.09695339e-01 1.62572375e-01 9.84637164e-01 6.30263193e-01 7.77449355e-01 9.11768632e-01 1.71113498e-01 3.94650630e-01 2.93957288e-01 3.62288593e-01 3.24560791e-01 5.90521396e-01 5.73966763e-02 2.80079955e-02 4.00845327e-01 9.22543654e-01 3.17757967e-01 3.82762623e-01 9.20839232e-01 4.74123015e-01 5.13833613e-01 6.45393060e-01 7.76714490e-01 6.68496136e-01 4.84869499e-01 1.30379505e-01 1.91173874e-01 8.08701474e-01 6.40682129e-01 7.80757917e-01 5.96142168e-01 2.58388176e-01 9.45757936e-02 4.95689165e-01 2.15082294e-01 6.39015157e-01 6.01686522e-01 8.50104213e-01 9.29555398e-02 9.45731753e-01 3.28489809e-01 5.26011516e-01 1.93060499e-01 5.69546391e-02 2.18064648e-01 2.67528407e-01 4.02602600e-01 4.72662784e-01 8.99097119e-01 7.23696984e-01 5.82609352e-01 4.60430386e-01 5.50632449e-01 4.38724168e-01 9.35375856e-01 7.41312616e-01 3.80745402e-01 2.40863964e-01 8.98174902e-03 3.44177735e-01 6.46272702e-01 2.27382967e-01 5.26128248e-02 2.84300530e-01 9.44884255e-01 1.32043439e-01 2.00779828e-01 7.99096989e-01 9.47718562e-01 3.27149864e-01 8.36681604e-01 7.28265796e-02 3.46999649e-01 6.19070033e-01 1.48741480e-01 3.09740446e-01 4.80768252e-01 2.17944014e-01 5.12827226e-01 2.15273679e-01 8.11321005e-01 8.74031982e-01 8.63799928e-01 2.36078559e-02 7.68623579e-01 8.73959743e-01 4.99570576e-02 1.60581032e-02 4.10608748e-02 3.00530156e-01 5.28864050e-01 5.56934017e-01 8.62405608e-01 4.48981352e-01 8.87211110e-01 1.48907417e-01 7.55681182e-01 1.89683320e-02 6.97669379e-01 2.65395828e-01 4.60564843e-01 3.18674514e-01 6.67117605e-01 1.47980767e-01 1.10591477e-01 8.09264567e-02 8.40443863e-01 2.19411074e-01 9.59997512e-01 4.72439832e-01 7.70550924e-01 3.87723184e-01 1.99719341e-01 3.00091234e-01 2.02236977e-01 6.11071372e-02 5.53081668e-01 6.79093922e-01 3.21431704e-02 8.55364976e-03 2.36326867e-01 4.03029148e-01 4.44630077e-01 3.05952795e-01 2.69899810e-01 4.97986041e-01 5.36954609e-02 7.70928847e-01 3.52527433e-01 8.52969069e-02 6.32214722e-01 8.54925085e-01 4.47747266e-01 2.31844177e-01 9.84688351e-01 8.40070076e-01 2.25638949e-01 8.41461695e-01 4.69662339e-01 5.04825684e-01 9.16345396e-02 5.41119981e-01 9.96577679e-01 2.84880717e-01 1.44348558e-01 4.02154876e-01 7.10217902e-01 7.73588240e-01 9.53377569e-01 4.41341734e-01 8.57805147e-01 1.96091764e-01 6.18704712e-01 7.25061748e-01 3.09166031e-01 1.43673384e-01 3.69984206e-01 8.13351356e-01 7.23735346e-01 7.24626037e-01 6.41705624e-01 5.11309716e-01 5.90444995e-01 9.31786344e-01 2.05747293e-01 2.12369249e-01 2.27830428e-01 1.57289688e-01 1.68156914e-01 8.77642020e-01 1.49191401e-01 3.74615953e-01 8.69996542e-01 6.54420984e-01 5.02293036e-02 5.49872476e-01 4.18765621e-01 3.41992308e-01 9.05226968e-01 2.40399920e-01 7.36896329e-01 9.92505269e-01 8.26233839e-01 3.29926092e-01 3.37440474e-01 7.60388350e-01 7.35838500e-02 4.10332385e-01 9.50947840e-01 9.08694913e-01 8.70753001e-01 3.34520417e-01 9.50980806e-01 8.93628768e-01 6.42453835e-01 3.94584113e-01 5.26992579e-02 7.57528796e-01 9.28774759e-01 7.25146985e-01 8.43347762e-01 9.36566109e-01 4.48659672e-01 6.16688619e-01 5.38778189e-01 7.29019223e-02 7.06927607e-01 7.03058001e-01 4.99885325e-01 5.69486065e-01 3.11914610e-01 3.91999671e-01 5.87126537e-01 2.40213529e-01 8.77841852e-01 3.48928683e-01 3.76494832e-01 1.32915361e-01 6.12064815e-01 9.59053533e-01 1.07483156e-01 1.39627117e-01 4.77017592e-01 9.23433327e-01 3.36806873e-01 6.63306824e-01 7.39204115e-01 7.28668392e-01 4.62048809e-02 6.60116332e-01 9.18849738e-01 2.60827787e-01 8.01729210e-01 2.37942544e-01 3.44875297e-01 5.01165772e-01 2.65628862e-01 8.45583751e-01 1.43420744e-01 8.21609451e-01 8.20318804e-01 7.41231882e-01 8.73428471e-02 1.82147715e-01 4.94778620e-01 5.88704025e-01 5.81879742e-01 4.38662275e-01 8.41879103e-01 1.06354471e-03 1.97177264e-02 2.77828866e-01 1.41887381e-01 5.93861473e-01 4.93664509e-01 5.49168556e-01 3.66628921e-01 2.54599419e-01 6.55530563e-01 2.53261218e-01 4.32020983e-01 1.25495258e-01 7.09654045e-01 2.94048926e-01 3.12039528e-01 7.11793748e-01 1.27671608e-01 7.09159784e-01 4.21990192e-01 1.90220147e-01 8.75004491e-01 4.19785850e-02 6.69354348e-01 6.17676786e-01 2.38516230e-02 7.57968595e-02 5.37558390e-01 6.51581072e-02 2.12441742e-01 2.51103188e-01 3.91662327e-01 5.24911159e-01 2.45255184e-02 7.45611329e-01 5.64560929e-01 3.66286168e-01 6.67413254e-01 5.12839659e-01 7.01317388e-01 1.93647031e-01 5.56252811e-01 1.30863442e-01 5.81829172e-01 3.79706640e-01 9.90436934e-01 5.34618234e-01 2.15715510e-01 9.27181404e-01 8.33637978e-01 9.57815331e-02 7.70590412e-01 6.56833876e-01 1.46120847e-01 4.20660625e-03 4.84929188e-01 4.91781402e-01 4.30509047e-01 1.57255799e-01 9.32645434e-01 7.46849751e-01 8.07727497e-02 5.48875731e-01 8.80498329e-01 8.51027232e-01 5.36880873e-01 2.62545694e-01 1.22278138e-01 4.33167037e-01 3.70071154e-01 8.98491609e-01 9.70693002e-01 1.03419712e-01 6.31141791e-01 3.08104718e-01 1.79592826e-02 3.97669652e-01 8.03186954e-02 9.67343561e-01 5.03902513e-01 6.03745528e-01 4.54147659e-01 3.91223797e-01 8.38283952e-01] ###Markdown 50. How to find the closest value (to a given scalar) in a vector? (★★☆) ###Code Z = np.random.random((100, 100)) v = 0.61 delta = np.unravel_index(np.argmin(np.abs(Z - v)), Z.shape) Z[delta] ###Output _____no_output_____ ###Markdown 51. Create a structured array representing a position (x,y) and a color (r,g,b) (★★☆) ###Code dt_p = np.dtype([("x", "<f4"), ("y", "<f4")]) dt_c = np.dtype([("r", "u1"), ("g", "u1"), ("b", "u1")]) dt = np.dtype([("position", dt_p), ("color", dt_c)]) ###Output _____no_output_____ ###Markdown 52. Consider a random vector with shape (100,2) representing coordinates, find point by point distances (★★☆) 53. How to convert a float (32 bits) array into an integer (32 bits) in place? 54. How to read the following file? (★★☆) ```1, 2, 3, 4, 56, , , 7, 8 , , 9,10,11``` 55. What is the equivalent of enumerate for numpy arrays? (★★☆) 56. Generate a generic 2D Gaussian-like array (★★☆) 57. How to randomly place p elements in a 2D array? (★★☆) 58. Subtract the mean of each row of a matrix (★★☆) ###Code Z = np.random.random((10, 10)) Z -= np.mean(Z, -1) Z ###Output _____no_output_____ ###Markdown 59. How to sort an array by the nth column? (★★☆) 60. How to tell if a given 2D array has null columns? (★★☆) ###Code Z = np.random.random((10, 10)) np.any(np.all(Z, axis = 0) == 0) ###Output _____no_output_____ ###Markdown 61. Find the nearest value from a given value in an array (★★☆) 62. Considering two arrays with shape (1,3) and (3,1), how to compute their sum using an iterator? (★★☆) 63. Create an array class that has a name attribute (★★☆) 64. Consider a given vector, how to add 1 to each element indexed by a second vector (be careful with repeated indices)? (★★★) 65. How to accumulate elements of a vector (X) to an array (F) based on an index list (I)? (★★★) 66. Considering a (w,h,3) image of (dtype=ubyte), compute the number of unique colors (★★★) 67. Considering a four dimensions array, how to get sum over the last two axis at once? (★★★) ###Code Z = np.random.random((4,3,2,5)) np.add.reduce(Z, axis=(-2, -1)).shape ###Output _____no_output_____ ###Markdown 68. Considering a one-dimensional vector D, how to compute means of subsets of D using a vector S of same size describing subset indices? (★★★) ###Code Z = np.random.random(300) i = np.arange(3, 39) np.mean(Z[i]) ###Output _____no_output_____ ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) 3. Create a null vector of size 10 (★☆☆) ###Code np.zeros(10) ###Output _____no_output_____ ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code np.zeros(10).nbytes ###Output _____no_output_____ ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ###Code z=np.zeros(10) z[4]=1 z ###Output _____no_output_____ ###Markdown 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code np.arange(10,50) ###Output _____no_output_____ ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code z=np.arange(10,20) z[::-1] ###Output _____no_output_____ ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code np.arange(9).reshape(3,3) ###Output _____no_output_____ ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code z=np.array([1,2,0,0,4,0] ) indices=np.where(z==0) indices ###Output _____no_output_____ ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code np.identity(3) np.diag([1,1,1]) ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code np.random.rand(3,3,3) ###Output _____no_output_____ ###Markdown 13. Create a 10x10 array with random values and find the minimum and maximum values (★☆☆) ###Code z=np.random.rand(10,10) print(z) print(z.max(),' ',z.min()) print(z[1].max()) ###Output [[0.3712614 0.95575763 0.14819107 0.80108973 0.84569513 0.97937431 0.20215369 0.32437204 0.24303929 0.93958533] [0.41620807 0.64365167 0.4745426 0.36965147 0.17566429 0.51205804 0.0689625 0.00563769 0.50399285 0.06000029] [0.83960913 0.66418128 0.81703298 0.51205313 0.0044982 0.47765778 0.4818053 0.40927636 0.8423076 0.27300263] [0.05629205 0.62722912 0.32032474 0.28343814 0.92324815 0.60811748 0.34493346 0.61469725 0.35997121 0.17645424] [0.97370631 0.47480215 0.21391344 0.24770859 0.0925012 0.92787275 0.66451203 0.0277279 0.07429704 0.64728567] [0.56666416 0.25349763 0.13890828 0.05992409 0.12811743 0.54884214 0.18408104 0.22798072 0.01613166 0.21992531] [0.61128885 0.29722141 0.67929737 0.08907281 0.39758464 0.68306982 0.01569296 0.82110325 0.23332777 0.22853228] [0.83128901 0.43259131 0.91195003 0.57236809 0.51831628 0.62866361 0.11977837 0.01106123 0.38523137 0.71357097] [0.55594464 0.20224167 0.17916492 0.56852117 0.56548548 0.56195239 0.3333777 0.37051841 0.13042125 0.85249613] [0.5780547 0.83319234 0.43591852 0.4606673 0.83839561 0.93615025 0.17969131 0.15870748 0.90415246 0.44631917]] 0.9793743135139271 0.004498203083211583 0.6436516688904135 ###Markdown 14. Create a random vector of size 30 and find the mean value (★☆☆) ###Code z=np.random.rand(30) print(z) z.mean() ###Output [0.92844801 0.27958059 0.12411883 0.68815552 0.90129838 0.70983942 0.01780177 0.79730927 0.42142924 0.74747304 0.68599151 0.40431038 0.2876902 0.21809605 0.1089472 0.14849823 0.08787999 0.78273632 0.42492549 0.21615617 0.47416501 0.75139107 0.2413429 0.16421622 0.69034998 0.73454215 0.13975545 0.6540834 0.30584496 0.35218465] ###Markdown 15. Create a 2d array with 1 on the border and 0 inside (★☆☆) ###Code z=np.ones(25).reshape(5,5) z[1:-1,1:-1]=0 z ###Output _____no_output_____ ###Markdown 16. How to add a border (filled with 0's) around an existing array? (★☆☆) ###Code z=np.ones((5,5)) np.pad(z,pad_width=1,mode='constant',constant_values=0) ###Output _____no_output_____ ###Markdown 17. What is the result of the following expression? (★☆☆) ```python0 * np.nannp.nan == np.nannp.inf > np.nannp.nan - np.nannp.nan in set([np.nan])0.3 == 3 * 0.1``` ###Code print(0*np.nan) print(np.nan==np.nan) print(np.inf>np.nan) print(np.nan-np.nan) print(np.nan in set([np.nan])) print(0.3 == 3*0.1) print(np.isnan(np.nan)) print(np.isclose(0.3,3*0.1)) ###Output nan False False nan True False True True ###Markdown 18. Create a 5x5 matrix with values 1,2,3,4 just below the diagonal (★☆☆) ###Code z=np.diag(1+np.arange(4),k=-1) z z=np.zeros((5,5)) i=np.arange(4) z[i+1,i]=i+1 z ###Output _____no_output_____ ###Markdown 19. Create a 8x8 matrix and fill it with a checkerboard pattern (★☆☆) ###Code z=np.zeros((8,8)) z[::2,1::2]=1 z[1::2,::2]=1 z ###Output _____no_output_____ ###Markdown 20. Consider a (6,7,8) shape array, what is the index (x,y,z) of the 100th element? ###Code np.arange(6*7*8).reshape(6,7,8).flatten()[99] np.unravel_index(100,(6,7,8)) ###Output _____no_output_____ ###Markdown 21. Create a checkerboard 8x8 matrix using the tile function (★☆☆) ###Code np.tile([[1,0],[0,1]],(4,4)) ###Output _____no_output_____ ###Markdown 22. Normalize a 5x5 random matrix (★☆☆) ###Code z=np.random.rand(5,5) z=(z-np.mean(z))/np.std(z) z ###Output _____no_output_____ ###Markdown 23. Create a custom dtype that describes a color as four unsigned bytes (RGBA) (★☆☆) ###Code color=np.dtype([('r',np.ubyte,1), ('g',np.ubyte,1), ('b',np.ubyte,1), ('a',np.ubyte,1)]) black=np.array([(0,0,0,0),color]) ###Output _____no_output_____ ###Markdown 24. Multiply a 5x3 matrix by a 3x2 matrix (real matrix product) (★☆☆) ###Code a=np.random.rand(5,3) b=np.random.rand(3,2) np.dot(a,b) ###Output _____no_output_____ ###Markdown 25. Given a 1D array, negate all elements which are between 3 and 8, in place. (★☆☆) ###Code a=np.arange(1,15) a[np.where((a>=3) & (a<=8))] *= -1 a a=np.arange(1,15) a[(a>=3)&(a<=8)] *=-1 a ###Output _____no_output_____ ###Markdown 26. What is the output of the following script? (★☆☆) ```python Author: Jake VanderPlasprint(sum(range(5),-1))from numpy import *print(sum(range(5),-1))``` ###Code print(sum(range(5),-1)) print(np.sum(range(5),-1)) ###Output 9 10 ###Markdown 100 numpy exercisesThis is a collection of exercises that have been collected in the numpy mailing list, on stack overflow and in the numpy documentation. The goal of this collection is to offer a quick reference for both old and new users but also to provide a set of exercises for those who teach.If you find an error or think you've a better way to solve some of them, feel free to open an issue at 1. Import the numpy package under the name `np` (★☆☆) ###Code import numpy as np ###Output _____no_output_____ ###Markdown 2. Print the numpy version and the configuration (★☆☆) ###Code np.version.version ###Output _____no_output_____ ###Markdown 3. Create a null vector of size 10 (★☆☆) ###Code v = np.zeros(10) v ###Output _____no_output_____ ###Markdown 4. How to find the memory size of any array (★☆☆) ###Code s = v.size s ###Output _____no_output_____ ###Markdown 5. How to get the documentation of the numpy add function from the command line? (★☆☆) ###Code %run `python -c "import numpy; numpy.info(numpy.add)"` ###Output ERROR:root:File `'`python.py'` not found. ###Markdown 6. Create a null vector of size 10 but the fifth value which is 1 (★☆☆) ###Code nulo = np.zeros(10) nulo[4] = 1 nulo ###Output _____no_output_____ ###Markdown 7. Create a vector with values ranging from 10 to 49 (★☆☆) ###Code seven = np.array(range(10, 50)) seven ###Output _____no_output_____ ###Markdown 8. Reverse a vector (first element becomes last) (★☆☆) ###Code seven[::-1] ###Output _____no_output_____ ###Markdown 9. Create a 3x3 matrix with values ranging from 0 to 8 (★☆☆) ###Code nine = np.arange(0,9).reshape(3,3) nine ###Output _____no_output_____ ###Markdown 10. Find indices of non-zero elements from \[1,2,0,0,4,0\] (★☆☆) ###Code nz = np.nonzero([1,2,0,0,4,0]) nz ###Output _____no_output_____ ###Markdown 11. Create a 3x3 identity matrix (★☆☆) ###Code m = np.identity(3) m ###Output _____no_output_____ ###Markdown 12. Create a 3x3x3 array with random values (★☆☆) ###Code m = np.random.rand(3,3,3) m ###Output _____no_output_____

Data_Preparation.ipynb

###Markdown Import Dependancies ###Code # Initial imports import pandas as pd from pathlib import Path from sklearn.preprocessing import StandardScaler, MinMaxScaler from sklearn.manifold import TSNE from sklearn.decomposition import PCA from sklearn.cluster import KMeans import matplotlib.pyplot as plt train_df = pd.read_csv('crypto_data.csv', index_col= 0) train_df ###Output _____no_output_____ ###Markdown Preprocess Data ###Code # Discard all cryptocurrencies that are not being traded. In other words, filter for #currencies that are currently being traded train_df = train_df.loc[(train_df["IsTrading"] == True)] train_df #drop the IsTrading column from the dataframe. train_df = train_df.drop(["IsTrading"], axis='columns') train_df.head(10) train_df.shape # Find null values for column in train_df.columns: print(f"Column {column} has {train_df[column].isnull().sum()} null values") # Remove all rows that have at least one null value. train_df = train_df.dropna(axis=0, how="any") train_df.shape train_df # Filter for cryptocurrencies that have been mined. Mined should be greater than zero. train_df = train_df.loc[train_df["TotalCoinsMined"] > 0] train_df.shape # Delete the CoinName from the original dataframe. train_df = train_df.drop(["CoinName"], axis='columns') train_df.shape train_df.head(10) train_df['Algorithm'].unique() train_df['ProofType'].unique() train_df['TotalCoinsMined'].unique() train_df['TotalCoinSupply'].unique() train_df.shape train_df.head # convert the remaining features with text values, Algorithm and ProofType, into numerical data. #To accomplish this task, use Pandas to create dummy variables. X = pd.get_dummies(data=train_df, columns=['Algorithm', 'ProofType']) print(X.shape) X.head() #Standardize your dataset scaler = StandardScaler() X_scaled = scaler.fit_transform(X) X_scaled[0] X_scaled.shape #Perform dimensionality reduction with PCA. preserve 90% of the explained variance in dimensionality reduction # How did the number of the features change? # Initialize PCA model pca = PCA(n_components=.90) # Get principal components for the data. crypto_pca = pca.fit_transform(X_scaled) # Fetch the explained variance pca.explained_variance_.sum() crypto_pca.shape # reduce the dataset dimensions with t-SNE and visually inspect the results # run t-SNE on the principal components: the output of the PCA transformation tsne = TSNE(perplexity=50) tsne_features = tsne.fit_transform(crypto_pca) tsne_features.shape # create a scatter plot of the t-SNE output. Observe whether there are distinct clusters or not. x= tsne_features[:,0] y= tsne_features[:,1] plt.scatter(x,y) plt.xlim([-70, 20]) plt.ylim([-20, 50]) plt.show() # Create an elbow plot to identify the best number of clusters. # Use a for-loop to determine the inertia for each k between 1 through 10. inertia = [] k = list(range(1, 11)) # Calculate the inertia for the range of k values for i in k: km = KMeans(n_clusters=i, random_state=0) km.fit(crypto_pca) inertia.append(km.inertia_) # Create the Elbow Curve elbow_df = pd.DataFrame({"k": k, "inertia": inertia}) elbow_df.plot.line(x="k", y="inertia") #if possible, where the elbow of the plot is, and at which value of k it appears. plt.xlabel('Number of clusters') plt.ylabel('Inertia') plt.title('Elbow curve for crypto data') plt.show() ###Output _____no_output_____ ###Markdown Imports ###Code import numpy as np import pandas as pd import datetime as dt import os #scanning folders ###Output _____no_output_____ ###Markdown Load Bidding history Define data load function ###Code def load_bidding_history(directory): bidding_history = pd.DataFrame(columns = ['Itemnumber','Title','Ending Time', 'Timestamp', 'Bidder', 'feedback_score', 'Bid Amount']) for file in os.scandir(directory): bidding_history = bidding_history.append(pd.read_csv(file, usecols=['Itemnumber','Title','Ending Time', 'Timestamp', 'Bidder', 'feedback_score', 'Bid Amount'], parse_dates=['Ending Time', 'Timestamp']), ignore_index=True) return bidding_history ###Output _____no_output_____ ###Markdown Load data ###Code df_bids_antiques = load_bidding_history('biddingdata/antiques') ###Output _____no_output_____ ###Markdown Authors note: eBay only grants public access to auctions within the last several weeks. To increase the number of auctions in the computer category to a suitable scope, I conducted to runs which have to be merged together at this point. ###Code df_bids_computers = load_bidding_history('biddingdata/computers') df_bids_computers = df_bids_computers.append(load_bidding_history('biddingdata/computers2')) ###Output _____no_output_____ ###Markdown Collect Metadata Number of auctions ###Code df_bids_antiques['Itemnumber'].nunique() df_bids_computers['Itemnumber'].nunique() ###Output _____no_output_____ ###Markdown Number of Biddings ###Code len(df_bids_antiques) len(df_bids_computers) ###Output _____no_output_____ ###Markdown Optimize the data structure Exclude items with less than 2 bidders ###Code relevant_itemnumbers = df_bids_antiques.loc[:,['Itemnumber', 'Bidder']].groupby(by=["Itemnumber"]).nunique() relevant_itemnumbers = relevant_itemnumbers.loc[relevant_itemnumbers['Bidder'] > 1] relevant_itemnumbers = relevant_itemnumbers.index.tolist() relevant_itemnumbers df_bids_antiques = df_bids_antiques[df_bids_antiques['Itemnumber'].isin(relevant_itemnumbers)] relevant_itemnumbers = df_bids_computers.loc[:,['Itemnumber', 'Bidder']].groupby(by=["Itemnumber"]).nunique() relevant_itemnumbers = relevant_itemnumbers.loc[relevant_itemnumbers['Bidder'] > 1] relevant_itemnumbers = relevant_itemnumbers.index.tolist() relevant_itemnumbers df_bids_computers = df_bids_computers[df_bids_computers['Itemnumber'].isin(relevant_itemnumbers)] ###Output _____no_output_____ ###Markdown Update metadata after removing auctions with only 1 Bidding ###Code df_bids_antiques['Itemnumber'].nunique() df_bids_computers['Itemnumber'].nunique() ###Output _____no_output_____ ###Markdown Remove timezones from data ###Code df_bids_computers['Ending Time'] = df_bids_computers['Ending Time'].apply(lambda x: x.replace(tzinfo=None)) df_bids_computers['Timestamp'] = df_bids_computers['Timestamp'].apply(lambda x: x.replace(tzinfo=None)) df_bids_computers2['Ending Time'] = df_bids_computers2['Ending Time'].apply(lambda x: x.replace(tzinfo=None)) df_bids_computers2['Timestamp'] = df_bids_computers2['Timestamp'].apply(lambda x: x.replace(tzinfo=None)) ###Output _____no_output_____ ###Markdown Create new column containing the remaining time when the bid was submitted ###Code df_bids_antiques['Time Left'] = df_bids_antiques['Ending Time'] - df_bids_antiques['Timestamp'] df_bids_computers['Time Left'] = df_bids_computers['Ending Time'] - df_bids_computers['Timestamp'] ###Output _____no_output_____ ###Markdown Remove columns not needed anymore ###Code df_bids_antiques = df_bids_antiques.drop(columns=['Ending Time', 'Timestamp']) df_bids_computers = df_bids_computers.drop(columns=['Ending Time', 'Timestamp']) ###Output _____no_output_____ ###Markdown Pickle dataframes for further use ###Code df_bids_antiques.to_pickle("processeddata/bids_antiques.pkl") df_bids_computers.to_pickle("processeddata/bids_computers.pkl") ###Output _____no_output_____ ###Markdown > **How to run this notebook (command-line)?**1. Install the `ReinventCommunity` environment:`conda env create -f environment.yml`2. Activate the environment:`conda activate ReinventCommunity`3. Execute `jupyter`:`jupyter notebook`4. Copy the link to a browser `REINVENT 3.0`: Data Preparation demoThis demo illustrates how data from ChEMBL or other sources be processed, analysed and filtered. To proceed, please update the following code block such that it reflects your system's installation and execute it. Motivation> **There are a number of reasons to pre-process the data used for training a generative model.**1. Removal of invalid or duplicated entries.2. Removal of unusual compounds that are clearly not drug-like (too big, reactive groups and etc.). There is normally no point training model on such examples since that bias will reflected by the generative model. 3. Removal of rare tokens. There are rare compounds that can be seen as outliers. They in turn might contain rare tokens. Excluding them frees a slot in the vocabulary and makes it smaller. Smaller vocabulary means faster training and less memory. As a result removing compounds that introduce rare tokens to the vocabulary speeds up the generative model. ###Code conda list # load dependencieso import os import re import json import tempfile import pyspark #import findspark #findspark.init() ###### assign memory to pyspark #from pyspark import SparkContext #SparkContext.setSystemProperty('spark.executor.memory', '2g') # --------- change these path variables as required DBS_PATH = "./data/chembl.raw.smi" # --------- to be honest this isnt the exact raw version of ChEMBL # it has been already put through some filtering # we should provide the raw version here # so that the actual filtering can be illustrated in the plots below output_dir = os.path.expanduser("~/Desktop/Data_Preparation") parquet_file = f'{output_dir}/chembl.parquet' # --------- do not change # get the notebook's root path try: ipynb_path except NameError: ipynb_path = os.getcwd() # if required, generate a folder to store the results try: os.mkdir(output_dir) except FileExistsError: pass ###Output _____no_output_____ ###Markdown We provide as an alternative a smaller dataset for testing purposesOne can use the cell below just to play with the code.If you intend to process the full dataset dont execute this cell ###Code # DBS_PATH = "./data/chembl.mini.smi" # parquet_file = f'{output_dir}/chembl.mini.parquet' %matplotlib inline import pyspark.sql as ps import pyspark.sql.functions as psf import pyspark.sql.types as pst import rdkit.Chem as rkc import rdkit.Chem.AllChem as rkac import molvs as mv import matplotlib.pyplot as plt import seaborn as sns import pandas as pd %run code/data_preparation.py pd.set_option('display.max_rows', 500) pd.set_option('display.max_columns', 500) pd.set_option('display.width', 1000) pd.set_option('display.max_colwidth', 200) sns.set(style="ticks") SPARK, SC = SparkSessionSingleton.get("clean_db") def to_mol(smi): """ Creates a Mol object from a SMILES string. :param smi: SMILES string. :return: A Mol object or None if it's not valid. """ if smi: return rkc.MolFromSmiles(smi) def to_smiles(mol): """ Converts a Mol object into a canonical SMILES string. :param mol: Mol object. :return: A SMILES string. """ if mol is None: return None return rkc.MolToSmiles(mol, isomericSmiles=False) # standardize molecule STANDARDIZER = mv.Standardizer() ACCEPTED_ATOMS = [6,7,8,9,16,17,35] def _run_reaction(mol, rxn): while True: results = rxn.RunReactants([mol], maxProducts=1) if not results: return mol else: mol = results[0][0] REACTIONS = [ "[S+:1](=[N:3])[OH:2]>>[S+0:1](=[N:3])=[O:2]", "[n+:1][OH:2]>>[n+:1][O-]", "[N:1](=[O:2])=[O:3]>>[N+:1]([O-:2])=[O:3]", "[S+:1]([O:2])[N:3]>>[S+0:1](=[O:2])[N:3]" ] REACTIONS = [rkac.ReactionFromSmarts(rxn) for rxn in REACTIONS] def standardize_mol(mol, standardize=True, min_size=0, max_size=1000): try: if standardize: for rxn in REACTIONS: mol = _run_reaction(mol, rxn) mol = STANDARDIZER.charge_parent(mol, skip_standardize=True) mol = STANDARDIZER.isotope_parent(mol, skip_standardize=True) mol = STANDARDIZER.stereo_parent(mol, skip_standardize=True) mol = STANDARDIZER.standardize(mol) if any([atom.GetAtomicNum() not in ACCEPTED_ATOMS for atom in mol.GetAtoms()]): return None return mol except: return None TOKENIZER = SMILESTokenizer() tokenize_udf = psf.udf(lambda smi: TOKENIZER.tokenize(smi, with_begin_and_end=False), pst.ArrayType(pst.StringType())) def _num_rings(smi): mol = to_mol(smi) if mol: return rkc.GetSSSR(mol) return None num_rings_udf = psf.udf(_num_rings, pst.IntegerType()) def _size_largest_ring(smi): mol = to_mol(smi) if mol: ring_info = mol.GetRingInfo() return max([0] + [len(ring) for ring in ring_info.AtomRings()]) return None size_largest_ring_udf = psf.udf(_size_largest_ring, pst.IntegerType()) num_atoms_udf = psf.udf(lambda smi: to_mol(smi).GetNumHeavyAtoms(), pst.IntegerType()) num_c_atoms_udf = psf.udf(lambda smi: len([atom for atom in to_mol(smi).GetAtoms() if atom.GetAtomicNum() == 6]), pst.IntegerType()) SMARTS_CHAINS = [rkc.MolFromSmarts("-".join(["[CR0H2]"]*i)) for i in range(1, 11)] def _longest_aliphatic_c_chain(smi): mol = to_mol(smi) curr_chain = 0 for chain in SMARTS_CHAINS: if mol.HasSubstructMatch(chain): curr_chain += 1 else: break return curr_chain longest_aliphatic_c_chain = psf.udf(_longest_aliphatic_c_chain, pst.IntegerType()) ###Output _____no_output_____ ###Markdown ChEMBL Remove Invalid SMILES ###Code def _process_rows(row): fields = row.split(" ") mol = to_mol(fields[0]) standardized_smiles = None if mol: standardized_mol = standardize_mol(mol) standardized_smiles = to_smiles(standardized_mol) return ps.Row(original_smiles=fields[0], smiles=standardized_smiles) chembl_df = SPARK.createDataFrame(SC.textFile(DBS_PATH).repartition(5000).map(_process_rows)).distinct().where("smiles is not null") chembl_df.count() ###Output _____no_output_____ ###Markdown Write down to a parquet file as a checkpoint.You can do that at multiple instances where the processing steps take while so that next time can resume from this checkpoint. ###Code chembl_df.write.parquet(parquet_file) ###Output _____no_output_____ ###Markdown Load from the checkpoint ###Code chembl_df = SPARK.read.parquet(parquet_file) ###Output _____no_output_____ ###Markdown Calculate various metrics for each SMILES entry ###Code chembl_annotated_df = chembl_df\ .withColumn("num_atoms", num_atoms_udf("smiles"))\ .withColumn("c_atom_ratio", num_c_atoms_udf("smiles") / psf.col("num_atoms"))\ .withColumn("tokens", tokenize_udf("smiles"))\ .withColumn("num_rings", num_rings_udf("smiles"))\ .withColumn("size_largest_ring", size_largest_ring_udf("smiles"))\ .withColumn("num_tokens", psf.size("tokens"))\ .withColumn("tokens_atom_ratio", psf.col("num_tokens")/psf.col("num_atoms"))\ .withColumn("longest_aliph_c_chain", longest_aliphatic_c_chain("smiles"))\ .persist() ###Output _____no_output_____ ###Markdown Data purgingIn the section below we look at various calculated parameters and apply some arbitrary criteria to eliminate entries that dont meet those. Num atoms distribution ###Code num_atoms_dist = chembl_annotated_df\ .groupBy("num_atoms")\ .agg(psf.count("num_atoms").alias("num"))\ .withColumn("percent", psf.lit(100.0)*psf.col("num")/chembl_annotated_df.count())\ .sort("num_atoms", ascending=False)\ .toPandas() num_atoms_dist.plot(x="num_atoms", y="percent", xlim=(0, 100), lw=3) num_atoms_dist chembl_chemistry_filtered_df = chembl_annotated_df.where("num_atoms >= 6 and num_atoms <= 70") chembl_chemistry_filtered_df.count() ###Output _____no_output_____ ###Markdown Number of rings ###Code num_rings_dist = chembl_chemistry_filtered_df\ .groupBy("num_rings")\ .agg(psf.count("num_atoms").alias("num"))\ .withColumn("percent", psf.lit(100.0)*psf.col("num")/chembl_chemistry_filtered_df.count())\ .sort("num_rings", ascending=False)\ .toPandas() num_rings_dist.plot(x="num_rings", y="percent", lw=3, xticks=num_rings_dist["num_rings"]) num_rings_dist chembl_chemistry_filtered_df = chembl_chemistry_filtered_df.where("num_rings <= 10") chembl_chemistry_filtered_df.count() ###Output _____no_output_____ ###Markdown Size of largest ring ###Code size_largest_ring_dist = chembl_chemistry_filtered_df\ .groupBy("size_largest_ring")\ .agg(psf.count("size_largest_ring").alias("num"))\ .withColumn("percent", psf.lit(100.0)*psf.col("num")/chembl_chemistry_filtered_df.count())\ .sort("size_largest_ring", ascending=False)\ .toPandas() size_largest_ring_dist.plot(x="size_largest_ring", y="percent", lw=3) chembl_chemistry_filtered_df = chembl_chemistry_filtered_df.where("size_largest_ring < 9") chembl_chemistry_filtered_df.count() ###Output _____no_output_____ ###Markdown Long aliphatic C chains ###Code longest_aliph_c_chain = chembl_chemistry_filtered_df\ .groupBy("longest_aliph_c_chain")\ .agg(psf.count("longest_aliph_c_chain").alias("num"))\ .withColumn("percent", psf.lit(100.0)*psf.col("num")/chembl_chemistry_filtered_df.count())\ .sort("longest_aliph_c_chain", ascending=False)\ .toPandas() longest_aliph_c_chain.plot(x="longest_aliph_c_chain", y="percent", lw=3) longest_aliph_c_chain chembl_chemistry_filtered_df = chembl_chemistry_filtered_df.where("longest_aliph_c_chain < 5") chembl_chemistry_filtered_df.count() ###Output _____no_output_____ ###Markdown Heteroatom ratios ###Code c_ratio_dist = chembl_chemistry_filtered_df.sample(False, 0.1).toPandas() c_ratio_dist.hist(column="c_atom_ratio", bins=32) chembl_chemistry_filtered_df = chembl_chemistry_filtered_df.where("c_atom_ratio >= 0.5") chembl_chemistry_filtered_df.count() ###Output _____no_output_____ ###Markdown Number of tokens ###Code num_tokens_dist = chembl_chemistry_filtered_df\ .groupBy("num_tokens")\ .agg(psf.count("num_tokens").alias("num"))\ .withColumn("percent", psf.lit(100.0)*psf.col("num")/chembl_chemistry_filtered_df.count())\ .sort("num_tokens", ascending=False)\ .toPandas() num_tokens_dist.plot(x="num_tokens", y="percent", lw=3) num_tokens_dist chembl_filtered_df = chembl_chemistry_filtered_df.where("num_tokens <= 91") chembl_filtered_df.count() ###Output _____no_output_____ ###Markdown Tokens/atom ratio ###Code tokens_atom_ratio_dist = chembl_filtered_df.sample(False, 0.1).toPandas() tokens_atom_ratio_dist.hist(column="tokens_atom_ratio", bins=32) chembl_filtered_df = chembl_filtered_df.where("tokens_atom_ratio <= 2.0") chembl_filtered_df.count() ###Output _____no_output_____ ###Markdown Token/molecule distribution ###Code token_dist = chembl_filtered_df\ .withColumn("unique_tokens", psf.array_distinct("tokens"))\ .select(psf.explode("unique_tokens").alias("token"))\ .groupBy("token")\ .agg(psf.count("token").alias("num"))\ .withColumn("percent", psf.lit(100.0)*psf.col("num")/chembl_filtered_df.count())\ .sort("percent", ascending=False)\ .toPandas() token_dist tokens_to_remove = token_dist[(token_dist["percent"] < 5E-2) & (token_dist["token"].str.startswith("[")) & ~(token_dist["token"].isin(["[S+]", "[s+]"]))]["token"] query_tokens = psf.lit(False) for token in tokens_to_remove: query_tokens |= psf.array_contains("tokens", token) chembl_filtered_df = chembl_filtered_df.where(~query_tokens).select("original_smiles", "smiles") chembl_filtered_df.count() ###Output _____no_output_____ ###Markdown Write the filtered dataset to diskWe finally write out all SMILES that meet the filtering criteria to a csv file and to a parquet. ###Code filtered_parquet_file = f'{output_dir}/final.filtered.parquet' filtered_csv_file = f'{output_dir}/final.filtered.csv' chembl_filtered_df.write.parquet(filtered_parquet_file) chembl_filtered_df.select("smiles").toPandas().to_csv(filtered_csv_file, index=False, header=False) ###Output _____no_output_____ ###Markdown Scoring.csv ###Code scoring = pd.read_csv(os.path.join("..", "data", "Scoring.csv")) mem_mib(scoring) scoring.shape scoring.columns def recent_nhl_only(df): return df[(df["lgID"] == "NHL") & (df["year"] >= 1980)] scoring = recent_nhl_only(scoring) scoring.shape scoring.columns scoring = scoring.filter(regex="^(?!(Post|PP|SH)).*") scoring.columns scoring = scoring.iloc[:, [0, 1, 3, 6, 7, 8, 9, 14]] scoring.columns make_categorical(scoring, "tmID") scoring.head() scoring.reset_index().head() scoring = scoring.reset_index(drop=True) # Alternatively: scoring.reset_index(drop=True, inplace=True) scoring.head() scoring.to_pickle(os.path.join("..", "scoring.pickle")) ###Output _____no_output_____ ###Markdown Teams.csv ###Code teams = pd.read_csv(os.path.join("..", "data", "Teams.csv")) teams.shape teams.columns teams = recent_nhl_only(teams) teams = teams[["year", "tmID", "name"]] teams.head() teams.nunique() make_categorical(teams, "tmID") teams.to_pickle(os.path.join("..", "teams.pickle")) ###Output _____no_output_____ ###Markdown TeamSplits.csv ###Code team_splits = pd.read_csv(os.path.join("..", "data", "TeamSplits.csv")) team_splits.shape team_splits.columns team_splits = recent_nhl_only(team_splits) cols_to_drop = team_splits.columns[3:11] team_splits = team_splits.drop(columns=cols_to_drop) team_splits.columns # some_data_frame.drop(rows=row_labels) <- to drop rows team_splits = team_splits.drop(columns="lgID") make_categorical(team_splits, "tmID") team_splits.to_pickle(os.path.join("..", "team_splits.pickle")) ###Output _____no_output_____ ###Markdown Entender Problema -- Objetivo do Problema: -- 1.0. Previsao do primeiro destino que um novo usuário irá escolher. -- Porque? -- Qual tipo de modelo de negócio do Airbnb? -- Marketplace ( Conectar pessoas que oferecem acomodacao, com pessoas que estao procurando acomodacao) -- Oferta ( pessoas oferecendo acomodacao ) -- Tamanho do portfólio. -- Diversidade/Densidade de Portfólio. -- Preco Medio -- Demanda ( pessoas procurando acomodacao ) -- Numero de Usuários -- LTV ( Lifetime Value ) -- CAC ( Client Acquisition Cost ) Gross Revenue = ( Fee*Numero cliente ) - CAC -- Proposta da Solucao --- Modelo de Predivao do primeiro destino de um novo usario. --- 1.0. Predicoes e salva em tabela do banco de dados. --- 2.0. API --- Input: usuario e suas caracteristicas --- Output: usuario e suas caracteristicas com a **predicao do destino** --- 16 ciclos 0.0. Imports ###Code import random import numpy as np import pandas as pd import seaborn as sns from matplotlib import pyplot as plt from sklearn import model_selection as ms from sklearn import preprocessing as pp from sklearn import metrics as m from scikitplot import metrics as mt from scipy import stats as ss from imblearn import under_sampling as us from imblearn import over_sampling as oversamp from imblearn import combine as c from category_encoders import TargetEncoder from pandas_profiling import ProfileReport from keras import models as ml from keras import layers as l ###Output _____no_output_____ ###Markdown 0.1. Helper Functions ###Code def cramer_v( x, y ): cm = pd.crosstab( x, y ).values n = cm.sum() r, k = cm.shape chi2 = ss.chi2_contingency( cm )[0] chi2corr = max( 0, chi2 - (k-1)*(r-1)/(n-1) ) kcorr = k - (k-1)**2/(n-1) rcorr = r - (r-1)**2/(n-1) return np.sqrt( (chi2corr/n) / ( min( kcorr-1, rcorr-1 ) ) ) ###Output _____no_output_____ ###Markdown 0.2. Loading Data ###Code df_raw = pd.read_csv( 'dataset/training_users.csv', low_memory=True ) df_raw.shape df_sessions = pd.read_csv( 'dataset/sessions.csv', low_memory=True ) df_sessions.shape ###Output _____no_output_____ ###Markdown 1.0. Data Description ###Code df1 = df_raw.copy() ###Output _____no_output_____ ###Markdown 1.1. Data Dimension ###Code print( 'Number of rows: {}'.format( df1.shape[0] ) ) print( 'Number of columns: {}'.format( df1.shape[1] ) ) print( 'Number of rows: {}'.format( df_sessions.shape[0] ) ) print( 'Number of columns: {}'.format( df_sessions.shape[1] ) ) ###Output Number of rows: 10567737 Number of columns: 6 ###Markdown 1.2. Data Type ###Code df1.dtypes df_sessions.dtypes ###Output _____no_output_____ ###Markdown 1.3. NA Check ###Code df1.isna().sum() / len( df1 ) df_sessions.isna().sum() / len( df_sessions) # remove missing value completly #df1 = df1.dropna() # ========== User ================= # date_first_booking date_first_booking_max = pd.to_datetime( df1['date_first_booking'] ).max().strftime( '%Y-%m-%d' ) df1['date_first_booking'] = df1['date_first_booking'].fillna( date_first_booking_max ) # age df1 = df1[( df1['age'] > 15 ) & ( df1['age'] < 120 )] avg_age = df1['age'].mean().astype( int ) df1['age'] = df1['age'].fillna( avg_age ) # first_affiliate_tracked df1 = df1[~df1['first_affiliate_tracked'].isna()] # ========== Sessions ================= # user_id - 0.3% df_sessions = df_sessions[~df_sessions['user_id'].isna()] # action - 0.7% df_sessions = df_sessions[~df_sessions['action'].isna()] # action_type - 11% df_sessions = df_sessions[~df_sessions['action_type'].isna()] # action_detail - 11% df_sessions = df_sessions[~df_sessions['action_detail'].isna()] # secs_elapsed - 1.2% df_sessions = df_sessions[~df_sessions['secs_elapsed'].isna()] df1.isna().sum() / len( df1 ) df_sessions.isna().sum() / len( df_sessions) ###Output _____no_output_____ ###Markdown 1.4. Change Data Type ###Code df1.dtypes # date_account_created df1['date_account_created'] = pd.to_datetime( df1['date_account_created'] ) # timestamp_first_active df1['timestamp_first_active'] = pd.to_datetime( df1['timestamp_first_active'], format='%Y%m%d%H%M%S' ) # date_first_booking df1['date_first_booking'] = pd.to_datetime( df1['date_first_booking'] ) # age df1['age'] = df1['age'].astype( int ) ###Output _____no_output_____ ###Markdown 1.5. Check Balanced Data ###Code #df1['country_destination'].value_counts( normalize=True ) df1['country_destination'].value_counts() ###Output _____no_output_____ ###Markdown 1.6. Descriptive Analysis ###Code # Users num_attributes = df1.select_dtypes( include=['int64', 'float64'] ) cat_attributes = df1.select_dtypes( exclude=['int64', 'float64', 'datetime64[ns]'] ) time_attributes = df1.select_dtypes( include=['datetime64[ns]'] ) # Sessions num_attributes_sessions = df_sessions.select_dtypes( include=['int64', 'float64'] ) cat_attributes_sessions = df_sessions.select_dtypes( exclude=['int64', 'float64', 'datetime64[ns]'] ) time_attributes_sessions = df_sessions.select_dtypes( include=['datetime64[ns]'] ) ###Output _____no_output_____ ###Markdown 1.6.1. Numerical - Users ###Code # Central Tendency - Mean, Mediana ct1 = pd.DataFrame( num_attributes.apply( np.mean ) ).T ct2 = pd.DataFrame( num_attributes.apply( np.median ) ).T # Dispersions - Std, Min, Max, Range, Skew, Kurtosis d1 = pd.DataFrame( num_attributes.apply( np.std ) ).T d2 = pd.DataFrame( num_attributes.apply( min ) ).T d3 = pd.DataFrame( num_attributes.apply( max ) ).T d4 = pd.DataFrame( num_attributes.apply( lambda x: x.max() - x.min() ) ).T d5 = pd.DataFrame( num_attributes.apply( lambda x: x.skew() ) ).T d6 = pd.DataFrame( num_attributes.apply( lambda x: x.kurtosis() ) ).T # Concatenar ct = pd.concat( [d2, d3, d4, ct1, ct2, d1, d5, d6] ).T.reset_index() ct.columns = ['attributes', 'min', 'max', 'range', 'mean', 'median', 'std', 'skew', 'kurtosis'] ct ###Output _____no_output_____ ###Markdown 1.6.2. Numerical - Sessions ###Code # Central Tendency - Mean, Mediana ct1 = pd.DataFrame( num_attributes_sessions.apply( np.mean ) ).T ct2 = pd.DataFrame( num_attributes_sessions.apply( np.median ) ).T # Dispersions - Std, Min, Max, Range, Skew, Kurtosis d1 = pd.DataFrame( num_attributes_sessions.apply( np.std ) ).T d2 = pd.DataFrame( num_attributes_sessions.apply( min ) ).T d3 = pd.DataFrame( num_attributes_sessions.apply( max ) ).T d4 = pd.DataFrame( num_attributes_sessions.apply( lambda x: x.max() - x.min() ) ).T d5 = pd.DataFrame( num_attributes_sessions.apply( lambda x: x.skew() ) ).T d6 = pd.DataFrame( num_attributes_sessions.apply( lambda x: x.kurtosis() ) ).T # Concatenar ct = pd.concat( [d2, d3, d4, ct1, ct2, d1, d5, d6] ).T.reset_index() ct.columns = ['attributes', 'min', 'max', 'range', 'mean', 'median', 'std', 'skew', 'kurtosis'] ct ###Output _____no_output_____ ###Markdown 1.6.3. Categorial - Users ###Code cat_attributes.drop( 'id', axis=1 ).describe() ###Output _____no_output_____ ###Markdown 1.6.4. Categorial - Sesssions ###Code cat_attributes_sessions.drop( 'user_id', axis=1 ).describe() ###Output _____no_output_____ ###Markdown 1.6.5. Correlation Matrix - Sessions ###Code cat_attributes_list = cat_attributes_sessions.drop( 'user_id', axis=1 ).columns.tolist() corr_dict = {} for i in range( len ( cat_attributes_list ) ): corr_list = [] for j in range( len( cat_attributes_list ) ): ref = cat_attributes_list[i] feat = cat_attributes_list[j] # correlation corr = cramer_v( cat_attributes_sessions[ ref ], cat_attributes_sessions[ feat ] ) # append a list corr_list.append( corr ) # appende a correlation list for each ref attributs corr_dict[ ref ] = corr_list d = pd.DataFrame( corr_dict ) d = d.set_index( d.columns) sns.heatmap( d, annot=True ) ###Output _____no_output_____ ###Markdown 2.0. Feature Engineering ###Code df2 = df1.copy() df2.shape df2.dtypes ###Output _____no_output_____ ###Markdown 2.1. Create New Features ###Code # days from first active up to first booking df2['first_active'] = pd.to_datetime( df2['timestamp_first_active'].dt.strftime( '%Y-%m-%d' ) ) df2['days_from_first_active_until_booking'] = ( df2['date_first_booking'] - df2['first_active'] ).apply( lambda x: x.days ) # days from first active upt to account created df2['days_from_first_active_until_account_created'] = ( df2['date_account_created'] - df2['first_active'] ).apply( lambda x: x.days ) # days from account createad up to first booking df2['days_from_account_created_until_first_booking'] = ( df2['date_first_booking'] - df2['date_account_created'] ).apply( lambda x: x.days ) # ================== First Active ================== # year first active df2['year_first_active'] = df2['first_active'].dt.year # month first active df2['month_first_active'] = df2['first_active'].dt.month # day first active df2['day_first_active'] = df2['first_active'].dt.day # day of week first active df2['day_of_week_first_active'] = df2['first_active'].dt.dayofweek # week of year first active df2['week_of_year_first_active'] = df2['first_active'].dt.weekofyear # ================== First Booking ================== # year first booking df2['year_first_booking'] = df2['date_first_booking'].dt.year # month first booking df2['month_first_booking'] = df2['date_first_booking'].dt.month # day first booking df2['day_first_booking'] = df2['date_first_booking'].dt.day # day of week first booking df2['day_of_week_first_booking'] = df2['date_first_booking'].dt.dayofweek # week of year first booking df2['week_of_year_first_booking'] = df2['date_first_booking'].dt.weekofyear # ================== First Account Created ================= # year first booking df2['year_account_created'] = df2['date_account_created'].dt.year # month account_created df2['month_account_created'] = df2['date_account_created'].dt.month # day account_created df2['day_account_created'] = df2['date_account_created'].dt.day # day of week account_created df2['day_of_week_account_created'] = df2['date_account_created'].dt.dayofweek # week of year account_created df2['week_of_year_account_created'] = df2['date_account_created'].dt.weekofyear df2.shape df2[['id', 'date_account_created', 'day_account_created', 'day_first_booking']].sample(10) ###Output _____no_output_____ ###Markdown 3.0. Data Filtering ###Code a = [2100, 3500, 4000, 8000, 10000, 16000] b = [19, 28, 29, 30, 31, 32] ( 19 - np.mean( b ) ) / np.std( b ) np.mean( b ) np.std( b ) df3 = df2.copy() df3.shape ###Output _____no_output_____ ###Markdown 3.1. Filtering Rows ###Code # Filtering rows: # age - greater than 15 and lower than 120 - There are few people over 12O year old df3 = df3[( df3['age'] > 15 ) & ( df3['age'] < 120 )] # secs_elapsed - there is no possible 0 secs elapsed on website #df3 = df3[df3['secs_elapsed'] > 0] ###Output _____no_output_____ ###Markdown 3.2. Columns Selection ###Code cols = ['date_account_created', 'date_account_created', 'date_first_booking', 'timestamp_first_active', 'first_active'] # original datetime ###Output _____no_output_____ ###Markdown 4.0. Balanced Dataset ###Code df4 = df3.drop( cols, axis=1 ) df4.shape # Encoder Categorical Variables ohe = pp.OneHotEncoder() # Numerical col_num = df4.select_dtypes( include=['int64', 'float64'] ).columns.tolist() # Categorical col_cat = df4.select_dtypes( exclude=['int64', 'float64', 'datetime64[ns]'] ).drop( ['id', 'country_destination'], axis=1 ).columns.tolist() # encoding df4_dummy = pd.DataFrame( ohe.fit_transform( df4[ col_cat] ).toarray(), index=df4.index ) # join numerical and categorical df42 = pd.concat( [df4[col_num], df4_dummy], axis=1 ) df42.shape ###Output _____no_output_____ ###Markdown 4.1. Random Undersampling ###Code # ratio_balanced ratio_balanced = {'NDF': 10000 } # define sampler undersampling = us.RandomUnderSampler( sampling_strategy=ratio_balanced, random_state=32 ) # apply sampler X_under, y_under = undersampling.fit_resample( df42, df4['country_destination'] ) df4['country_destination'].value_counts() y_under.value_counts() ###Output _____no_output_____ ###Markdown 4.2. Random Oversampling ###Code # ratio_balanced #ratio_balanced = {'NDF': 10000 } # define sampler oversampling = oversamp.RandomOverSampler( sampling_strategy='all', random_state=32 ) # apply sampler X_over, y_over = oversampling.fit_resample( df42, df4['country_destination'] ) df4['country_destination'].value_counts() y_over.value_counts() ###Output _____no_output_____ ###Markdown 4.3. SMOTE + TOMEKLINK ###Code ratio_balanced = {'NDF': 54852, 'US': 48057, 'other': 6*7511, 'FR': 12*3669, 'IT': 20*2014, 'GB': 30*1758, 'ES': 30*1685, 'CA': 40*1064, 'DE': 45*841, 'NL': 80*595, 'AU': 85*433, 'PT': 300*157} # define sampler smt = c.SMOTETomek( sampling_strategy=ratio_balanced, random_state=32, n_jobs=-1 ) # apply sampler X_smt, y_smt = smt.fit_resample( df42, df4['country_destination'] ) df4['country_destination'].value_counts() y_smt.value_counts() # numerical data df43 = X_smt[ col_num ] # categorical data df44 = X_smt.drop( col_num, axis=1 ) df45 = pd.DataFrame( ohe.inverse_transform( df44 ), columns=col_cat, index=df44.index ) # join numerical categorical df46 = pd.concat( [df43, df45], axis=1 ) df46['country_destination'] = y_smt ###Output _____no_output_____ ###Markdown 5.0. Exploratory Data Analysis ( EDA ) 5.1. Hypothesys Validation ( Unbalanced Dataset ) ###Code df51 = df4.copy() ###Output _____no_output_____ ###Markdown **H01.** Em todos os destinos, os usuários levam 15 dias, em média, para fazer a primeira reserva no Airbnb, desde sua primeira ativacao.**Verdadeiro.** Em todos os destinos, os usuários até 6 dias para reservar o primeiro Airbnb ###Code plt.figure( figsize=(20, 12)) plt.subplot( 3, 1, 1 ) aux01 = df51[['days_from_first_active_until_booking', 'country_destination']].groupby( 'country_destination' ).median().reset_index() sns.barplot( x='country_destination', y='days_from_first_active_until_booking', data=aux01.sort_values( 'days_from_first_active_until_booking' ) ) # remove outlier plt.subplot( 3, 1, 2 ) aux02 = df51[df51['country_destination'] != 'NDF'] aux02 = aux02[['days_from_first_active_until_booking', 'country_destination']].groupby( 'country_destination' ).median().reset_index() sns.barplot( x='country_destination', y='days_from_first_active_until_booking', data=aux02.sort_values( 'days_from_first_active_until_booking' ) ) ###Output _____no_output_____ ###Markdown **H02.** Em todos os destinos, os usuários levam 3 dias, em média, para fazer o cadastro no site.**Verdadeira**. Em todos os destinos, os usuários levam até 2 dias para finalizar o cadastro ###Code plt.figure( figsize=(20, 12)) aux01 = df51[['days_from_first_active_until_account_created', 'country_destination']].groupby( 'country_destination' ).mean().reset_index() sns.barplot( x='country_destination', y='days_from_first_active_until_account_created', data=aux01.sort_values( 'days_from_first_active_until_account_created' ) ) ###Output _____no_output_____ ###Markdown **H03.** O volume de reservas anual feitas durante o verão aumentaram 20% para destinos dentro dos USA. **False**. O Volume de reservas aumenta durante o verão entre os anos de 2010 até 2013. ###Code aux01 = df51[['year_first_booking', 'month_first_booking', 'country_destination']].\ groupby( ['year_first_booking', 'month_first_booking', 'country_destination'] ). \ size().reset_index().rename( columns={0:'count'}) # select only summer aux01 = aux01[( aux01['month_first_booking'].isin( [6, 7, 8, 9] ) ) & (aux01['country_destination'] == 'US')] aux02 = aux01[['year_first_booking', 'count']].groupby( 'year_first_booking' ).sum().reset_index() aux02['delta'] = 100*aux02['count'].pct_change().fillna( 0 ) plt.figure( figsize=(20,12)) sns.barplot( x='year_first_booking', y='delta', data=aux02) ###Output _____no_output_____ ###Markdown **H04.** Usuários do sexo feminino fazem 10% mais reservas para países fora dos USA. **H05.** O canal de Marketing Google representa 40% das reservas para países fora dos USA. **H06.** O destino dos USA representam mais de 20% em todos os canais. **H07.** A idade média das pessoas é de 35 anos em todos os destinos. **H08.** A porcentagem de usuários que usam o site na lingua inglês-americano para reservar acomodações em qualquer destino é maior que 90% **H09.** O número de reservas do Airbnb é crescente ou decrescente ao longo dos anos? **H10.** O número de reservas do Airbnb é crescente ao longo dos anos. 5.2. Variables Impact ( Balanced Dataset ) ###Code df52 = df4.copy() ###Output _____no_output_____ ###Markdown 5.2.1. Univariate Analysis ###Code profile = ProfileReport( df52, title='Airbnb Booking' ) #profile.to_notebook_iframe() profile.to_file( output_file='airbnb_booking_statistics_after_cleaning.html' ) # ===================== High Correlation ===================== # days_from_first_active_until_booking x days_from_account_created_until_first_booking # Remove: days_from_first_active_until_booking # year_first_active x year_account_created # Remove: year_first_active # month_first_active x month_account_created # Remove: month_first_active # day_first_active x day_account_created # Remove: day_first_active # day_of_week_first_active x day_of_week_account_created # Remove: day_of_week_first_active # week_of_year_first_active x week_of_year_account_created # Remove: week_of_year_first_active # month_first_booking x week_of_year_first_booking # Remove: month_first_booking # month_account_created x week_of_year_account_created # Remove: month_account_created # year_first_booking x year_account_created # Remove: year_first_booking # week_of_year_first_booking x week_of_year_account_created # Remove: week_of_year_first_booking # affiliate_channel x affiliate_provider # Remove: affiliate_provider # first_device_type x first_browser # Remove: first_browser #first_device_type x sigup_app #Remove: first_device_type ###Output _____no_output_____ ###Markdown 5.2.2. Bivariate Analysis 5.2.3. Multivariate Analysis ###Code cols = ['days_from_first_active_until_booking', 'year_first_active', 'month_first_active', 'day_first_active', 'day_of_week_first_active', 'week_of_year_first_active', 'month_first_booking', 'month_account_created', 'year_first_booking', 'week_of_year_first_booking', 'affiliate_provider', 'first_browser', 'first_device_type', 'language'] # high correlation ###Output _____no_output_____ ###Markdown 6.0. Data Preparation ###Code df6 = df46.drop( cols, axis=1 ) df6.shape df6.dtypes ###Output _____no_output_____ ###Markdown 6.1. Rescaling ###Code ss = pp.StandardScaler() rs = pp.RobustScaler() mms = pp.MinMaxScaler() # age - Standardization df6['age'] = ss.fit_transform( df6[['age']].values ) # signup_flow - Robust Scaler df6['signup_flow'] = rs.fit_transform( df6[['signup_flow']].values ) # days_from_first_active_until_account_created - Robust Scaler df6['days_from_first_active_until_account_created'] = rs.fit_transform( df6[['days_from_first_active_until_account_created']].values ) # days_from_account_created_until_first_booking - Robust Scaler df6['days_from_account_created_until_first_booking'] = rs.fit_transform( df6[['days_from_account_created_until_first_booking']].values ) # year_account_created - MinMax Scaler df6['year_account_created'] = mms.fit_transform( df6[['year_account_created']].values ) ###Output _____no_output_____ ###Markdown 6.2. Encoding ###Code te = TargetEncoder() # gender - One Hot Encoder df6 = pd.get_dummies( df6, prefix=['gender'], columns=['gender'] ) # signup_method - One Hot Encoder df6 = pd.get_dummies( df6, prefix=['signup_method'], columns=['signup_method'] ) # signup_app - One Hot Encoder df6 = pd.get_dummies( df6, prefix=['signup_app'], columns=['signup_app'] ) # affiliate_channel - Target Encoder c = {'NDF':0, 'US':1, 'other':2, 'CA':3, 'FR':4, 'IT':5, 'ES':6, 'GB':7, 'NL':8, 'DE':9, 'AU':10, 'PT':11} df6['affiliate_channel'] = te.fit_transform( df6[['affiliate_channel']].values, df6['country_destination'].map( c ) ) # first_affiliate_tracked - Target Encoder df6['first_affiliate_tracked'] = te.fit_transform( df6[['first_affiliate_tracked']].values, df6['country_destination'].map( c ) ) ###Output /Users/meigarom.lopes/.pyenv/versions/3.8.0/envs/airbnbpredictfirstbooking/lib/python3.8/site-packages/category_encoders/utils.py:21: FutureWarning: is_categorical is deprecated and will be removed in a future version. Use is_categorical_dtype instead elif pd.api.types.is_categorical(cols): /Users/meigarom.lopes/.pyenv/versions/3.8.0/envs/airbnbpredictfirstbooking/lib/python3.8/site-packages/category_encoders/utils.py:21: FutureWarning: is_categorical is deprecated and will be removed in a future version. Use is_categorical_dtype instead elif pd.api.types.is_categorical(cols): ###Markdown 6.3. Transformation ###Code # week_of_year_account_created df6['week_of_year_account_created_sin'] = df6['week_of_year_account_created'].apply( lambda x: np.sin( x * (2*np.pi/52 ) ) ) df6['week_of_year_account_created_cos'] = df6['week_of_year_account_created'].apply( lambda x: np.cos( x * (2*np.pi/52 ) ) ) # day_of_week_first_booking df6['day_of_week_first_booking_sin'] = df6['day_of_week_first_booking'].apply( lambda x: np.sin( x * (2*np.pi/7 ) ) ) df6['day_of_week_first_booking_cos'] = df6['day_of_week_first_booking'].apply( lambda x: np.cos( x * (2*np.pi/7 ) ) ) # day_account_created df6['day_account_created_sin'] = df6['day_account_created'].apply( lambda x: np.sin( x * (2*np.pi/31 ) ) ) df6['day_account_created_cos'] = df6['day_account_created'].apply( lambda x: np.cos( x * (2*np.pi/31 ) ) ) # day_of_week_account_created df6['day_of_week_account_created_sin'] = df6['day_of_week_account_created'].apply( lambda x: np.sin( x * (2*np.pi/7 ) ) ) df6['day_of_week_account_created_cos'] = df6['day_of_week_account_created'].apply( lambda x: np.cos( x * (2*np.pi/7 ) ) ) ###Output _____no_output_____ ###Markdown 7.0. Feature Selection ###Code df7 = df6.copy() X = df6.drop( 'country_destination', axis=1 ) y = df6['country_destination'].copy() # Split dataset into training and test x_train, x_test, y_train, y_test = ms.train_test_split( X, y, test_size=0.2, random_state=32 ) ###Output _____no_output_____ ###Markdown 8.0. Machine Learning Model 8.1. Baseline Model ###Code country_destination_list = df1['country_destination'].drop_duplicates().sort_values().tolist() k_num = y_test.shape[0] country_destination_weights = df1['country_destination'].value_counts( normalize=True ).sort_index().tolist() yhat_random = random.choices( population=country_destination_list, weights=country_destination_weights, k=k_num ) ###Output _____no_output_____ ###Markdown 8.1.1. Baseline Model Performance ###Code # Accuracy acc_random = m.accuracy_score( y_test, yhat_random ) print( 'Accuracy: {}'.format( acc_random ) ) # Balanced Accuray balanced_acc_random = m.balanced_accuracy_score( y_test, yhat_random ) print( 'Balanced Accuracy:{}'.format( balanced_acc_random ) ) # Kappa Metrics kappa_random = m.cohen_kappa_score( y_test, yhat_random ) print( 'Kappa Score: {}'.format( kappa_random ) ) # Classification report print( m.classification_report( y_test, yhat_random ) ) # Confusion Matrix mt.plot_confusion_matrix( y_test, yhat_random, normalize=False, figsize=(12,12)) ###Output Accuracy: 0.09213223987698616 Balanced Accuracy:0.08310397046943117 Kappa Score: -0.00020319419528025406 precision recall f1-score support AU 0.06 0.00 0.00 7470 CA 0.08 0.01 0.02 8517 DE 0.06 0.01 0.01 7462 ES 0.10 0.01 0.02 10003 FR 0.08 0.03 0.05 8741 GB 0.10 0.01 0.03 10489 IT 0.07 0.02 0.03 7962 NDF 0.10 0.45 0.17 11058 NL 0.08 0.00 0.01 9675 PT 0.10 0.00 0.00 9465 US 0.09 0.39 0.14 9435 other 0.08 0.06 0.07 8979 accuracy 0.09 109256 macro avg 0.08 0.08 0.04 109256 weighted avg 0.08 0.09 0.05 109256 ###Markdown 8.2. Neural Network - MLP ###Code ohe = pp.OneHotEncoder() y_train_nn = ohe.fit_transform( y_train.values.reshape( -1, 1 ) ).toarray() print( 'Number of Rows: {}'.format( x_train.shape[0] ) ) print( 'Number of Features: {}'.format( x_train.shape[1] ) ) print( 'Number of Classes: {}'.format( y_train.nunique() ) ) # model definition model = ml.Sequential() model.add( l.Dense( 64, input_dim=x_train.shape[1], activation='relu' ) ) model.add( l.Dense( 12, activation='softmax') ) # model compile model.compile( loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] ) # train model model.fit( x_train, y_train_nn, epochs=100 ) ###Output Epoch 1/100 13657/13657 [==============================] - 10s 753us/step - loss: 2.1184 - accuracy: 0.2448 Epoch 2/100 13657/13657 [==============================] - 10s 766us/step - loss: 2.0116 - accuracy: 0.2881 Epoch 3/100 13657/13657 [==============================] - 10s 739us/step - loss: 1.9689 - accuracy: 0.3042 Epoch 4/100 13657/13657 [==============================] - 10s 746us/step - loss: 1.9419 - accuracy: 0.3145 Epoch 5/100 13657/13657 [==============================] - 10s 703us/step - loss: 1.9246 - accuracy: 0.3212 Epoch 6/100 13657/13657 [==============================] - 10s 698us/step - loss: 1.9136 - accuracy: 0.3246 Epoch 7/100 13657/13657 [==============================] - 10s 700us/step - loss: 1.9059 - accuracy: 0.3264 Epoch 8/100 13657/13657 [==============================] - 10s 728us/step - loss: 1.9000 - accuracy: 0.3283 Epoch 9/100 13657/13657 [==============================] - 10s 710us/step - loss: 1.8959 - accuracy: 0.3295 Epoch 10/100 13657/13657 [==============================] - 10s 706us/step - loss: 1.8914 - accuracy: 0.3302 Epoch 11/100 13657/13657 [==============================] - 10s 720us/step - loss: 1.8886 - accuracy: 0.3313 Epoch 12/100 13657/13657 [==============================] - 10s 711us/step - loss: 1.8859 - accuracy: 0.3320 Epoch 13/100 13657/13657 [==============================] - 10s 706us/step - loss: 1.8829 - accuracy: 0.3336 Epoch 14/100 13657/13657 [==============================] - 10s 723us/step - loss: 1.8799 - accuracy: 0.3349 Epoch 15/100 13657/13657 [==============================] - 10s 712us/step - loss: 1.8789 - accuracy: 0.3351 Epoch 16/100 13657/13657 [==============================] - 10s 711us/step - loss: 1.8758 - accuracy: 0.3362 Epoch 17/100 13657/13657 [==============================] - 10s 728us/step - loss: 1.8748 - accuracy: 0.3369 Epoch 18/100 13657/13657 [==============================] - 10s 714us/step - loss: 1.8728 - accuracy: 0.3368 Epoch 19/100 13657/13657 [==============================] - 10s 729us/step - loss: 1.8709 - accuracy: 0.3380s - loss: 1.8706 - accu Epoch 20/100 13657/13657 [==============================] - 10s 755us/step - loss: 1.8699 - accuracy: 0.3377 Epoch 21/100 13657/13657 [==============================] - 10s 709us/step - loss: 1.8688 - accuracy: 0.3385 Epoch 22/100 13657/13657 [==============================] - 10s 717us/step - loss: 1.8672 - accuracy: 0.3392 Epoch 23/100 13657/13657 [==============================] - 10s 717us/step - loss: 1.8662 - accuracy: 0.3391 Epoch 24/100 13657/13657 [==============================] - 10s 723us/step - loss: 1.8652 - accuracy: 0.3396 Epoch 25/100 13657/13657 [==============================] - 10s 721us/step - loss: 1.8639 - accuracy: 0.3395 Epoch 26/100 13657/13657 [==============================] - 10s 725us/step - loss: 1.8628 - accuracy: 0.3403 Epoch 27/100 13657/13657 [==============================] - 10s 717us/step - loss: 1.8626 - accuracy: 0.3396 Epoch 28/100 13657/13657 [==============================] - 10s 744us/step - loss: 1.8610 - accuracy: 0.3409 Epoch 29/100 13657/13657 [==============================] - 10s 760us/step - loss: 1.8608 - accuracy: 0.3414 Epoch 30/100 13657/13657 [==============================] - 10s 769us/step - loss: 1.8607 - accuracy: 0.3416 Epoch 31/100 13657/13657 [==============================] - 10s 762us/step - loss: 1.8592 - accuracy: 0.3417 Epoch 32/100 13657/13657 [==============================] - 10s 755us/step - loss: 1.8583 - accuracy: 0.3416 Epoch 33/100 13657/13657 [==============================] - 10s 755us/step - loss: 1.8578 - accuracy: 0.3411 Epoch 34/100 13657/13657 [==============================] - 10s 718us/step - loss: 1.8569 - accuracy: 0.3411 Epoch 35/100 13657/13657 [==============================] - 10s 715us/step - loss: 1.8565 - accuracy: 0.3417 Epoch 36/100 13657/13657 [==============================] - 10s 725us/step - loss: 1.8560 - accuracy: 0.3414 Epoch 37/100 13657/13657 [==============================] - 10s 716us/step - loss: 1.8549 - accuracy: 0.3427 Epoch 38/100 13657/13657 [==============================] - 10s 746us/step - loss: 1.8542 - accuracy: 0.3426 Epoch 39/100 13657/13657 [==============================] - 10s 719us/step - loss: 1.8537 - accuracy: 0.3426 Epoch 40/100 13657/13657 [==============================] - 11s 783us/step - loss: 1.8532 - accuracy: 0.3421 Epoch 41/100 13657/13657 [==============================] - 11s 822us/step - loss: 1.8531 - accuracy: 0.3425 Epoch 42/100 13657/13657 [==============================] - 11s 838us/step - loss: 1.8522 - accuracy: 0.3426 Epoch 43/100 13657/13657 [==============================] - 12s 869us/step - loss: 1.8516 - accuracy: 0.3433 Epoch 44/100 13657/13657 [==============================] - 12s 866us/step - loss: 1.8505 - accuracy: 0.3432 Epoch 45/100 13657/13657 [==============================] - 12s 871us/step - loss: 1.8503 - accuracy: 0.3430 Epoch 46/100 13657/13657 [==============================] - 12s 852us/step - loss: 1.8504 - accuracy: 0.3428 Epoch 47/100 13657/13657 [==============================] - 11s 814us/step - loss: 1.8506 - accuracy: 0.3431 Epoch 48/100 13657/13657 [==============================] - 12s 852us/step - loss: 1.8492 - accuracy: 0.3441 Epoch 49/100 13657/13657 [==============================] - 11s 841us/step - loss: 1.8486 - accuracy: 0.3444 Epoch 50/100 13657/13657 [==============================] - 12s 853us/step - loss: 1.8487 - accuracy: 0.3436 Epoch 51/100 13657/13657 [==============================] - 12s 879us/step - loss: 1.8482 - accuracy: 0.3442 Epoch 52/100 13657/13657 [==============================] - 12s 868us/step - loss: 1.8473 - accuracy: 0.3445 Epoch 53/100 13657/13657 [==============================] - 12s 909us/step - loss: 1.8467 - accuracy: 0.3446 Epoch 54/100 13657/13657 [==============================] - 13s 918us/step - loss: 1.8467 - accuracy: 0.3445 Epoch 55/100 13657/13657 [==============================] - 12s 906us/step - loss: 1.8465 - accuracy: 0.3445 Epoch 56/100 13657/13657 [==============================] - 13s 917us/step - loss: 1.8463 - accuracy: 0.3449 Epoch 57/100 13657/13657 [==============================] - 12s 913us/step - loss: 1.8468 - accuracy: 0.3447 Epoch 58/100 13657/13657 [==============================] - 13s 988us/step - loss: 1.8464 - accuracy: 0.3451 Epoch 59/100 13657/13657 [==============================] - 14s 1ms/step - loss: 1.8453 - accuracy: 0.3453 Epoch 60/100 13657/13657 [==============================] - 15s 1ms/step - loss: 1.8456 - accuracy: 0.3447 Epoch 61/100 13657/13657 [==============================] - 15s 1ms/step - loss: 1.8445 - accuracy: 0.3454 Epoch 62/100 13657/13657 [==============================] - 15s 1ms/step - loss: 1.8444 - accuracy: 0.3451 Epoch 63/100 13657/13657 [==============================] - 16s 1ms/step - loss: 1.8436 - accuracy: 0.3456 Epoch 64/100 13657/13657 [==============================] - 16s 1ms/step - loss: 1.8436 - accuracy: 0.3449 Epoch 65/100 13657/13657 [==============================] - 16s 1ms/step - loss: 1.8437 - accuracy: 0.3458 Epoch 66/100 13657/13657 [==============================] - 12s 896us/step - loss: 1.8445 - accuracy: 0.3454 Epoch 67/100 13657/13657 [==============================] - 11s 811us/step - loss: 1.8436 - accuracy: 0.3458 Epoch 68/100 13657/13657 [==============================] - 10s 716us/step - loss: 1.8425 - accuracy: 0.3453 Epoch 69/100 13657/13657 [==============================] - 9s 687us/step - loss: 1.8421 - accuracy: 0.3457 Epoch 70/100 13657/13657 [==============================] - 9s 648us/step - loss: 1.8421 - accuracy: 0.3455 Epoch 71/100 13657/13657 [==============================] - 9s 638us/step - loss: 1.8421 - accuracy: 0.3461 Epoch 72/100 13657/13657 [==============================] - 9s 640us/step - loss: 1.8417 - accuracy: 0.3457 Epoch 73/100 13657/13657 [==============================] - 8s 621us/step - loss: 1.8419 - accuracy: 0.3461 Epoch 74/100 13657/13657 [==============================] - 9s 623us/step - loss: 1.8424 - accuracy: 0.3459 Epoch 75/100 13657/13657 [==============================] - 8s 616us/step - loss: 1.8409 - accuracy: 0.3471 Epoch 76/100 13657/13657 [==============================] - 9s 640us/step - loss: 1.8415 - accuracy: 0.3468 Epoch 77/100 13657/13657 [==============================] - 9s 644us/step - loss: 1.8409 - accuracy: 0.3462 Epoch 78/100 13657/13657 [==============================] - 9s 667us/step - loss: 1.8411 - accuracy: 0.3468 Epoch 79/100 13657/13657 [==============================] - 9s 665us/step - loss: 1.8411 - accuracy: 0.3466 Epoch 80/100 13657/13657 [==============================] - 9s 672us/step - loss: 1.8404 - accuracy: 0.3464 Epoch 81/100 13657/13657 [==============================] - 9s 668us/step - loss: 1.8406 - accuracy: 0.3471 Epoch 82/100 13657/13657 [==============================] - 9s 676us/step - loss: 1.8412 - accuracy: 0.3475 Epoch 83/100 13657/13657 [==============================] - 9s 680us/step - loss: 1.8407 - accuracy: 0.3464 Epoch 84/100 13657/13657 [==============================] - 9s 693us/step - loss: 1.8394 - accuracy: 0.3469 Epoch 85/100 13657/13657 [==============================] - 9s 694us/step - loss: 1.8396 - accuracy: 0.3473 Epoch 86/100 13657/13657 [==============================] - 9s 692us/step - loss: 1.8396 - accuracy: 0.3467 Epoch 87/100 13657/13657 [==============================] - 9s 685us/step - loss: 1.8402 - accuracy: 0.3469 Epoch 88/100 13657/13657 [==============================] - 9s 667us/step - loss: 1.8391 - accuracy: 0.3472 Epoch 89/100 13657/13657 [==============================] - 9s 663us/step - loss: 1.8388 - accuracy: 0.3477 Epoch 90/100 13657/13657 [==============================] - 9s 665us/step - loss: 1.8388 - accuracy: 0.3470 Epoch 91/100 13657/13657 [==============================] - 9s 663us/step - loss: 1.8386 - accuracy: 0.3470 Epoch 92/100 13657/13657 [==============================] - 9s 684us/step - loss: 1.8390 - accuracy: 0.3478 Epoch 93/100 13657/13657 [==============================] - 10s 704us/step - loss: 1.8389 - accuracy: 0.3476 Epoch 94/100 13657/13657 [==============================] - 10s 706us/step - loss: 1.8387 - accuracy: 0.3466 Epoch 95/100 13657/13657 [==============================] - 10s 755us/step - loss: 1.8381 - accuracy: 0.3480 Epoch 96/100 13657/13657 [==============================] - 10s 761us/step - loss: 1.8385 - accuracy: 0.3482 Epoch 97/100 13657/13657 [==============================] - 12s 852us/step - loss: 1.8379 - accuracy: 0.3474 Epoch 98/100 13657/13657 [==============================] - 16s 1ms/step - loss: 1.8377 - accuracy: 0.3476 0s - loss: 1.8376 - accuracy Epoch 99/100 13657/13657 [==============================] - 13s 983us/step - loss: 1.8384 - accuracy: 0.3480 Epoch 100/100 13657/13657 [==============================] - 13s 956us/step - loss: 1.8381 - accuracy: 0.3473 ###Markdown 7.2.1. NN Performance ###Code # prediction pred_nn = model.predict( x_test ) # invert prediction yhat_nn = ohe.inverse_transform( pred_nn ) # prediction prepare y_test_nn = y_test.to_numpy() yhat_nn = yhat_nn.reshape( 1, -1 )[0] # Accuracy acc_nn = m.accuracy_score( y_test_nn, yhat_nn ) print( 'Accuracy: {}'.format( acc_nn ) ) # Balanced Accuray balanced_acc_nn = m.balanced_accuracy_score( y_test_nn, yhat_nn ) print( 'Balanced Accuracy:{}'.format( balanced_acc_nn ) ) # Kappa Metrics kappa_nn = m.cohen_kappa_score( y_test_nn, yhat_nn ) print( 'Kappa Score: {}'.format( kappa_nn ) ) # Classification report print( m.classification_report( y_test_nn, yhat_nn ) ) # Confusion Matrix mt.plot_confusion_matrix( y_test_nn, yhat_nn, normalize=False, figsize=(12,12)) ###Output Accuracy: 0.35109284615947867 Balanced Accuracy:0.33314777646607335 Kappa Score: 0.29028000162482237 precision recall f1-score support AU 0.32 0.37 0.34 7470 CA 0.20 0.21 0.20 8517 DE 0.21 0.14 0.17 7462 ES 0.20 0.19 0.19 10003 FR 0.15 0.07 0.10 8741 GB 0.19 0.15 0.17 10489 IT 0.16 0.08 0.10 7962 NDF 1.00 1.00 1.00 11058 NL 0.24 0.50 0.32 9675 PT 0.60 0.92 0.73 9465 US 0.26 0.30 0.28 9435 other 0.17 0.07 0.10 8979 accuracy 0.35 109256 macro avg 0.31 0.33 0.31 109256 weighted avg 0.32 0.35 0.32 109256 ###Markdown 7.2.2. NN Performance - Cross-Validation ###Code # generate k-fold num_folds = 5 kfold = ms.StratifiedKFold( n_splits=num_folds, shuffle=True, random_state=32 ) balanced_acc_list = [] kappa_acc_list = [] i = 1 for train_ix, val_ix in kfold.split( x_train, y_train ): print( 'Fold Number: {}/{}'.format( i, num_folds ) ) # get fold x_train_fold = x_train.iloc[train_ix] y_train_fold = y_train.iloc[train_ix] x_val_fold = x_train.iloc[val_ix] y_val_fold = y_train.iloc[val_ix] # target hot-encoding ohe = pp.OneHotEncoder() y_train_fold_nn = ohe.fit_transform( y_train_fold.values.reshape( -1, 1 ) ).toarray() # model definition model = ml.Sequential() model.add( l.Dense( 256, input_dim=x_train.shape[1], activation='relu' ) ) model.add( l.Dense( 12, activation='softmax') ) # compile model model.compile( loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'] ) # training model model.fit( x_train_fold, y_train_fold_nn, epochs=100, batch_size=32, verbose=0 ) # prediction pred_nn = model.predict( x_val_fold ) yhat_nn = ohe.inverse_transform( pred_nn ) # prepare data y_test_nn = y_val_fold.to_numpy() yhat_nn = yhat_nn.reshape( 1, -1 )[0] # metrics ## Balanced Accuracy balanced_acc_nn = m.balanced_accuracy_score( y_test_nn, yhat_nn ) balanced_acc_list.append( balanced_acc_nn ) ## Kappa Metrics kappa_acc_nn = m.cohen_kappa_score( y_test_nn, yhat_nn ) kappa_acc_list.append( kappa_acc_nn ) i += 1 print( 'Avg Balanced Accuracy: {} +/- {}'.format( np.round( np.mean( balanced_acc_list ), 4 ), np.round( np.std( balanced_acc_list ), 4 ) ) ) print( 'Avg Kappa: {} +/- {}'.format( np.round( np.mean( kappa_acc_list ), 4 ), np.round( np.std( kappa_acc_list ), 4 ) ) ) ###Output Avg Balanced Accuracy: 0.1666 +/- 0.0001 Avg Kappa: 0.724 +/- 0.0006 ###Markdown DATA PREPARATION Unduh Data : https://github.com/realpython/python-data-cleaning/blob/master/Datasets/BL-Flickr-Images-Book.csv 1. import library yang dibutuhkan ###Code import pandas as pd import numpy as np df = pd.read_csv('BL-Flickr-Images-Book.csv') data.head() yg_dihapus = ['Edition Statement','Corporate Author'] df.drop(yg_dihapus, inplace=True, axis=1) df.head() data['Identifier'].is_unique df = df.set_index('Identifier') df.head() df.loc[472] ###Output _____no_output_____ ###Markdown 3. merapikan fields ###Code df.dtypes.value_counts() df.loc[1905:,'Date of Publication'].head(15) ###Output _____no_output_____ ###Markdown ~ hilangkan tgl lain dalam kurung siku~ hilangkan rentang tanggal~ hilangkan tanggal yang gajelas[1897?]--> NaN~ konversi NaN ###Code regex = r'^(\d{4})' ekstrak = df['Date of Publication'].str.extract(r'^(\d{4})',expand=False) df.loc[667] df.loc[4157862] df['Place of Publication'].tail(15) df.loc[4115138] publikasi = df['Place of Publication'] london = publikasi.str.contains('London') london[:5] oxford = publikasi.str.contains ('Oxford') df['Place of Publication'] = np.where(london,'London', np.where(oxford, 'Oxford', publikasi.str.replace ('-', ' '))) df['Place of Publication'].head(15) ###Output _____no_output_____ ###Markdown DATA SET BARU 5. membersihkan dataset dengan applymap ###Code university_town = [] with open("university_towns.txt") as file: for line in file: if '[edit]'in line: state = line else: university_town.append((state,line)) university_town[:5] df_kota = pd.DataFrame(university_town, columns=['State','RegionName']) df_kota.head(15) def get_citystate(item): if '(' in item: return item[:item.find('(')] elif '[' in item: return item[:item.find('[')] else: return item df_kota = df_kota.applymap(get_citystate) df_kota.head ###Output _____no_output_____ ###Markdown ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns %matplotlib inline movies = pd.read_csv('https://github.com/JuanPabloMF/datasets-platzi-course/blob/master/datasets/peliculas.csv?raw=true',encoding='utf-8') movies.head() movies.shape movies.columns movies.index columna1 = movies['movie_title'] columna1.head() line = movies.loc[10,:] line movies.loc[:,'movie_title'].head() movies.info() movies.dtypes == float movies.dtypes == int movies.dtypes == object num = (movies.dtypes == float) | (movies.dtypes == int) num num.index for i in num.index: print(i) num_cols = [x for x in num.index if num[x]] num_cols movies.dtypes == object obj = (movies.dtypes == object) obj_cols = [c for c in obj.index if obj[c]] obj_cols num_cols movies_num = movies[num_cols] movies_num.describe() movies_num['duration'].hist() movies_num['imdb_score'].hist() movies_num['budget'].hist() mask = (movies_num['budget'] > 1e9) movies[mask] financial = pd.read_csv('https://github.com/JuanPabloMF/datasets-platzi-course/blob/master/datasets/thenumbers.csv?raw=true',encoding='utf-8') financial.head(5) financial = financial[['movie_title','production_budget','worldwide_gross']] gross_opening = pd.read_csv('https://github.com/JuanPabloMF/datasets-platzi-course/blob/master/datasets/opening_df.csv?raw=true') financial.shape movies.shape movies['movie_title'] movies_num movies_num = movies_num.loc[:,~movies_num.columns.duplicated()] movies_num = pd.concat([movies_num, movies['movie_title']],axis=1) gross_opening = gross_opening.drop('Unnamed: 0',axis=1) movies_v2 = pd.merge(financial,movies_num,on='movie_title',how='left') movies_v2 = pd.merge(movies_v2,gross_opening,on='movie_title',how='left') movies_v2.shape movies_v2.notnull().apply(pd.Series.value_counts) (movies_v2 != 0).apply(pd.Series.value_counts) available = ((movies_v2 != 0) & (movies_v2.notnull())) available.all(axis=1).value_counts() mask = available['worldwide_gross'] movies_v2 = movies_v2[mask] ((movies_v2 != 0) & (movies_v2.notnull())).worldwide_gross.value_counts() movies_v2 = movies_v2.drop('movie_title',axis=1) movies_v2 = movies_v2.drop('duration',axis=1) movies_v2 = movies_v2.drop('gross',axis=1) movies_v2.head() movies_v2 = movies_v2[available.screens] len(movies_v2) from sklearn.impute import SimpleImputer imputer = SimpleImputer(missing_values=np.nan, strategy='mean') values = imputer.fit_transform(movies_v2) X = pd.DataFrame(values) X.columns = movies_v2.columns X.index = movies_v2.index X.head() len(X) movies_v2.values values X.to_csv('/content/drive/My Drive/Colab Notebooks/db/X_opening.csv',index=False) ###Output _____no_output_____ ###Markdown VUmc Research Project - Reinforcement Learning for Sepsis Prevention Data PreparationAmsterdamUMCdb version 1.0.2 March 2020 Copyright &copy; 2003-2022 Amsterdam UMC - Amsterdam Medical Data Science 1. Clustering ###Code Sum_of_squared_distances = [] K = range(2,500, 5) for k in K: km = KMeans(n_clusters=k) km = km.fit(space[['Kalium (bloed)', 'ABP gemiddeld', 'Kreatinine (bloed)', 'Natrium (bloed)', 'UrineCAD', 'UrineSupraPubis', 'UrineSpontaan', 'UrineUP', 'Kreatinine', 'Nefrodrain re Uit', 'Nefrodrain li Uit', 'UrineIncontinentie', 'gender_Vrouw', 'agegroup', 'AKI']]) Sum_of_squared_distances.append(km.inertia_) plt.plot(K, Sum_of_squared_distances, 'b-') plt.xlabel('k') plt.ylabel('Sum_of_squared_distances') plt.title('Elbow Method For Optimal k') plt.show() from sklearn.cluster import KMeans from sklearn.metrics import silhouette_samples, silhouette_score def k_means_over_instances(dataset, cols, k, max_iters, n_inits): # Take the appropriate columns. temp_dataset = dataset[cols] # Now apply the k-means algorithm kmeans = KMeans(n_clusters=k, max_iter=max_iters, n_init=n_inits, random_state=0).fit(temp_dataset) # Add the labels to the dataset dataset['cluster'] = kmeans.labels_ # Compute the solhouette and add it as well. silhouette_avg = silhouette_score(temp_dataset, kmeans.labels_) silhouette_per_inst = silhouette_samples(temp_dataset, kmeans.labels_) dataset['silhouette'] = silhouette_per_inst return dataset, silhouette_avg # Use k=50 based on previous runs new_d, sil = k_means_over_instances(space, ['Kalium (bloed)', 'ABP gemiddeld', 'Kreatinine (bloed)', 'Natrium (bloed)', 'UrineCAD', 'UrineSupraPubis', 'UrineSpontaan', 'UrineUP', 'Kreatinine', 'Nefrodrain re Uit', 'Nefrodrain li Uit', 'UrineIncontinentie', 'gender_Vrouw', 'agegroup', 'AKI'], 50, 20, 10) ###Output _____no_output_____ ###Markdown 2. Bin Values ###Code # Binning Values binsv = [-np.inf, 0, new_d['Noradrenaline (Norepinefrine)'].median(), np.inf] binsf = [-np.inf, 250, new_d['NaCl 0,45%/Glucose 2,5%'].median(), np.inf] labels = [0, 1, 2] new_d['vasop'] = pd.cut(new_d['Noradrenaline (Norepinefrine)'], bins=binsv, labels=labels) new_d['fluid'] = pd.cut(new_d['NaCl 0,45%/Glucose 2,5%'], bins=binsf, labels=labels) # 0 = no vasop, no fluid # 1 = no vasop, low fluid # 2 = no vasop, high fluid # 3 = low vasop, no fluid # 4 = low vasop, low fluid # 5 = low vasop, high fluid # 6 = high vasop, no fluid # 7 = high vasop, low fluid # 8 = high vasop, high fluid act = [] for v, f in zip(new_d['vasop'], new_d['fluid']): if v == 0 and f == 0: act.append('0') elif v == 0 and f == 1: act.append('1') elif v == 0 and f == 2: act.append('2') elif v == 1 and f == 0: act.append('3') elif v == 1 and f == 1: act.append('4') elif v == 1 and f == 2: act.append('5') elif v == 2 and f == 0: act.append('6') elif v == 2 and f == 1: act.append('7') elif v == 2 and f == 2: act.append('8') new_d['action'] = act new_d['reward'] = -new_d['AKI'] new_d['next'] = new_d['cluster'].shift(-1) final = new_d.dropna() ###Output _____no_output_____

notebook/Workshop_Practical_Python.ipynb

###Markdown Introduction to Python Author: Shaowu Pan Date: 11/16/2016 ###Code import this ###Output _____no_output_____ ###Markdown 1. *Let's start with working in a single Python file* 1.1 Basic variable int long float complex str bool ###Code # signed integer x = 1 type(x) # long integer y = 1000L # float z = 1.0 ###Output _____no_output_____ ###Markdown Python is case-sensetive ###Code # string varaible: using quotes single or double is fine X = 'good!' X[0:4] Y = True # false ###Output _____no_output_____ ###Markdown Useful function print - print out printable variable ###Code print x print y print X print z print Y ###Output 1 1000 good! 1.0 True ###Markdown raw_input- input value from keyboard ###Code name = raw_input("My name is ") print name ###Output My name is Shaowu Shaowu ###Markdown type - check type of unknown variable ###Code print type(x) print type(y) print type(X) print type(z) print type(Y) ###Output <type 'int'> <type 'long'> <type 'str'> <type 'float'> <type 'bool'> ###Markdown [Jupyter Notebook ONLY]check method/attribute of a object- ENTER . then just PRESS 'tab' example: find the capitalize function ###Code X.capitalize() ###Output _____no_output_____ ###Markdown [Jupyter Notebook ONLY]find how to use this function- X.method?then PRESS ENTEREXTREMELY USEFUL when using a third party library ###Code X.capitalize? ###Output _____no_output_____ ###Markdown range- return a list of ordered index array- example: get a integer list [0, 1, 2]while in Matlab: 0:2 ###Code range(3) range(0,3) ###Output _____no_output_____ ###Markdown - demenstration 2 1.2 Compound sequence type list- designed to be flexible: dynamic array- most frequenty type in Python- can be accessed using index ###Code a_list = [1,2,'d'] ###Output _____no_output_____ ###Markdown Popular method:- Append ###Code aa_list = [] for i in range(10): aa_list.append(i*i) a_list.append(3) a_list ###Output _____no_output_____ ###Markdown list comprehensions - task: obtain a new list contains dype of each element in a_list ###Code a_list [type(element) for element in a_list] ###Output _____no_output_____ ###Markdown tuple- everything is fixed at initialization, nothing can be changed- can be accessed using index- generate a tuple is fast than list ###Code a_tuple=(1,2,'d') ###Output _____no_output_____ ###Markdown set- no duplicates element- usually used when set operation involved in your algorithm- no order, so cannot access using index- can remove or add elements freely- check membership value in set is very fast ###Code a_set = {1,2,3} b_set = {1,2,2} ###Output _____no_output_____ ###Markdown - set operation ###Code a_set.union(b_set) a_set.intersection(b_set) ###Output _____no_output_____ ###Markdown set is faster for searching membership ###Code hugelist = range(4000000) hugetuple = tuple(hugelist) hugeset = set(hugelist); %timeit (1000000-1) in hugelist %timeit (1000000-1) in hugetuple %timeit (1000000-1) in hugeset ###Output The slowest run took 39.95 times longer than the fastest. This could mean that an intermediate result is being cached. 10000000 loops, best of 3: 53.7 ns per loop ###Markdown special note for timeit-n N, --number=N how many times to execute ‘statement’-r N, --repeat=N how many times to repeat the timer (default 3) dict- a data structure like a dictionary: key-value pair- extreme expressiveness- one key points to one value- value can be anything- key cannot be compound sequence type ###Code a_dict={1:1, 2:2, 3:'d'} print a_dict # in a more verbose way... a_dict[1] = 1 a_dict[2] = 2 a_dict[3] = 'd' a_dict ###Output _____no_output_____ ###Markdown Popular method:- update: merge to dict ###Code a_dict b_dict = {11:11} c_dict = {1:11} a_dict.update(b_dict) a_dict.update(c_dict) a_dict ###Output _____no_output_____ ###Markdown - get(): to check if a key existed in the dict, if not return None by default - **very useful for computing a histogram**, much simpler than C++/C ###Code # example: count the letter in this string my_string = "I want to get the counts for each letter in this sentence" # step 1: create an empty dictionary counts = {} # step 2: loop over the string for letter in my_string: counts[letter] = counts.get(letter, 0) + 1 print counts a = 5 if a == 5: print a ###Output 5 ###Markdown - break/continue ###Code a_list = [1,2] for a in a_list: if a ==1: continue print a a_list = [1,2] q = 2 while q > 0: if a ==1: continue print a q = q -1 ###Output 2 2 ###Markdown Very important Slicing: a:b -> contains a, up to b-1- Slicing operatior [ ] ;(while Matlab: ( ) ) ###Code print X ###Output good! ###Markdown - Python is 0-index ###Code print X[0:2] # here a = 0, b = 2 # [0:2] = [0,2) print X[:-1] ###Output good ###Markdown Useful function zip- create a list of tuples, each tuple is the i-th element of each argument sequence ###Code a = [1,2] b = ['a','b'] print zip(a,b) print zip(a,b,b) dict(zip(a,b)) ###Output _____no_output_____ ###Markdown - Let's see the magic of object oriented programming- This combination of python build-in function is often seen in pythonic code ###Code dict([[1,'a'],[2,'b']]) dict(((1,'a'),(2,'b'))) dict({(1,'a'),(2,'b')}) ###Output _____no_output_____ ###Markdown Question: Will the following work? ###Code dict(({1,'a'},{2,'b'})) # undefined behavior ###Output _____no_output_____ ###Markdown enumerate- python for loop is not designed fro indexing number looping. ###Code a_list for n, item in enumerate(a_list): print n, item ###Output 0 1 1 2 2 d ###Markdown 1.3 User-defined Function 1.3.1 classic way to define function ###Code def square(x): q = x**2 return q z = square(3) print z ###Output 9 ###Markdown 1.3.2 inline function ###Code g = lambda x: x**2 print g(3) ###Output 9 ###Markdown 1.3.3 map ###Code a_list map(lambda x: type(x),a_list) ###Output _____no_output_____ ###Markdown 1.4 File input/output - Task: convert example.txt file into numpy array ###Code %cat example.txt fh=open('example.txt','rw') data=fh.readlines(); data l_data=[]; for line in data: line=line.strip() # remove whitespace on head and tail print line print '--' line=line.split(',') # split the string to form a list by ',' print line l_data.append(line) fh.close() l_data ###Output _____no_output_____ ###Markdown - convert list to number with int type ###Code l_data_int=[map(lambda x: int(x),line) for line in l_data] l_data_int ###Output _____no_output_____ ###Markdown 2. *How to work with multiple python files/functions?* 2.1 Import - This is how to the python file know where to search for another python file- Python code in one module gains access to the code in another module by the process of importing it- module = file consisting of Python code example:1 import whole file- import moduleName- import moduleName as mN2 import only one function in the file- from moduleName import subFunction_1 Popurlar modules- numpy- matplotlib- scipy- pandas- sklearn- sys- ... Numpy- basic type: "numpy.ndarray" - for matlab users: this subclass is more friendly: "numpy.matrixlib.defmatrix.matrix"- multidimensional array of the same type ###Code import numpy as np ###Output _____no_output_____ ###Markdown - usually create numpy array by transforming list to ndarray ###Code b = np.array([1,2,3]) np.arange(15) a = np.arange(15).reshape(3, 5) print a b.shape a.shape a[0] a[0][0] a.ndim a.shape a.dtype type(a) ###Output _____no_output_____ ###Markdown - condition slicing: VERY POWERFUL ###Code a print a>3 print a<11 (a>3)&(a<11) c=a[(a>3)&(a<11)] # or (a>3)*(a<11) print c print c.shape ###Output [ 4 5 6 7 8 9 10] (7,) ###Markdown - summation to reduce the matrix to 1D array along i-th axis- 0: row-wise- 1: column-wise ###Code a a.sum(axis=0) ###Output _____no_output_____ ###Markdown - attention: like C/C++, sqrt and exp, math functions are all not built-in, but imported ###Code np.exp(3) ###Output _____no_output_____ ###Markdown - ATTENTION TO MATLAB USERS - using space to divide element (e.g., [1 2 3]) works in matlab but do not work here - operator * in ndarray is element-wise product and produce the ndarray in the largest dimension of the two - ref: https://docs.scipy.org/doc/numpy-dev/user/numpy-for-matlab-users.html ###Code a=np.array([1,2,3]) b=np.array([4,5,6]) print a*b print '--' print a.T*b print '--' print a.reshape(1,3) print '--' print a.reshape(3,1)*b # when .reshape, the dimensionality is altered print 'number of [] means the dimensions' print a.reshape(1,3) print '--' print b.reshape(3,1) ###Output number of [] means the dimensions [[1 2 3]] -- [[4] [5] [6]] ###Markdown in ndarray: * is element-wise product ###Code a.reshape(3,1)*b.reshape(1,3) # looks like two vector spans a matrix, but it is not print a.reshape(1,3)*b.reshape(3,1) print 'do not return dot product' a.reshape(3,1)*b.reshape(3,1) a.reshape(1,3)*b.reshape(1,3) ###Output _____no_output_____ ###Markdown to solve the pain for ndarray for matrix production, one can look for matrix subclass ###Code ## attentation..change mb to ma ma = np.matrix(a) ma*ma.T ma = np.mat(a) ma ma*ma.transpose() ###Output _____no_output_____ ###Markdown Matplotlib ###Code from matplotlib import pyplot as plt %matplotlib inline ### add this line!!! a=np.arange(4).reshape(2,2) plt.figure(figsize=(12,8)) plt.plot(a[0],a[1]) plt.title('example figure') plt.xlabel('x') plt.ylabel('y') plt.savefig('./example.png') ###Output _____no_output_____ ###Markdown 3. *How to debug?* pdb- import pdb- pdb.set_trace() useful pdb command:- n: nextline- c: continue to end- l: show current line in the code- r: jump to return- s: step into- p: print - !python command - change the python code on the fly embedded detection in your code- try + exception - An exception is a Python object that represents an error. - common exception - https://www.tutorialspoint.com/python/python_exceptions.htm sanity-check- assert try + exception - example: ZeroDivisionError situation: doubt element in b could be zero and it leads to error ###Code a = 1.0 b = [0, 0.1 ,0.2, 0.3, 0, 32, 0, 3.4] for b_iter in b: try: print a/b_iter except ZeroDivisionError: print '--' print 'Divide Zero...Find..' print '--' ###Output -- Divide Zero...Find.. -- 10.0 5.0 3.33333333333 -- Divide Zero...Find.. -- 0.03125 -- Divide Zero...Find.. -- 0.294117647059 ###Markdown assert ###Code for b_iter in b: assert b_iter != 0 ###Output _____no_output_____ ###Markdown 4. *How to profiling the code?* - time profiling- memory profiling example code ###Code %cat ../code/speed_profile.py ###Output #@profile def main(): num = 50000000 s=0; for i in range(num): s = s + i return def sub(): num = 50000000 s = 0 for i in range(num): s = s+i return main() sub() ###Markdown time profiling cProfile ###Code #python -m cProfile speed_profile.py %run -m cProfile ../code/speed_profile.py ###Output 6 function calls in 5.494 seconds Ordered by: standard name ncalls tottime percall cumtime percall filename:lineno(function) 1 0.000 0.000 5.494 5.494 speed_profile.py:2(<module>) 1 2.017 2.017 2.731 2.731 speed_profile.py:2(main) 1 2.079 2.079 2.764 2.764 speed_profile.py:9(sub) 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects} 2 1.398 0.699 1.398 0.699 {range} ###Markdown line proflier and kernprof ###Code # pip install line_profiler ###Output _____no_output_____ ###Markdown kernprof -l -v kern_speed_profile.py Wrote profile results to kern_speed_profile.py.lprofTimer unit: 1e-06 sTotal time: 26.9222 sFile: kern_speed_profile.pyFunction: main at line 1Line Hits Time Per Hit % Time Line Contents============================================================== 1 @profile 2 def main(): 3 1 1 1.0 0.0 num = 50000000 4 1 1 1.0 0.0 s=0; 5 50000001 13561380 0.3 50.4 for i in range(num): 6 50000000 13360858 0.3 49.6 s = s + i 7 1 3 3.0 0.0 returnTotal time: 27.0697 sFile: kern_speed_profile.pyFunction: sub at line 8Line Hits Time Per Hit % Time Line Contents============================================================== 8 @profile 9 def sub(): 10 1 0 0.0 0.0 num = 50000000 11 1 0 0.0 0.0 s = 0 12 50000001 13581265 0.3 50.2 for i in range(num): 13 50000000 13488440 0.3 49.8 s = s+i 14 1 4 4.0 0.0 return optimization- replace range with xrange ###Code %cat ../code/opti_speed_profile.py %run -m cProfile ../code/opti_speed_profile.py ###Output 4 function calls in 2.980 seconds Ordered by: standard name ncalls tottime percall cumtime percall filename:lineno(function) 1 0.000 0.000 2.980 2.980 opti_speed_profile.py:2(<module>) 1 1.514 1.514 1.514 1.514 opti_speed_profile.py:2(main) 1 1.466 1.466 1.466 1.466 opti_speed_profile.py:9(sub) 1 0.000 0.000 0.000 0.000 {method 'disable' of '_lsprof.Profiler' objects} ###Markdown kernprof -l -v ../code/opti_kern_speed_profile.py ###Code Wrote profile results to opti_kern_speed_profile.py.lprof Timer unit: 1e-06 s Total time: 31.2482 s File: opti_kern_speed_profile.py Function: main at line 1 Line # Hits Time Per Hit % Time Line Contents #============================================================== 1 @profile 2 def main(): 3 1 1 1.0 0.0 num = 50000000 4 1 1 1.0 0.0 s=0; 5 50000001 15159694 0.3 48.5 for i in xrange(num): 6 50000000 16088469 0.3 51.5 s = s + i 7 1 1 1.0 0.0 return Total time: 32.3526 s File: opti_kern_speed_profile.py Function: sub at line 8 Line # Hits Time Per Hit % Time Line Contents #============================================================== 8 @profile 9 def sub(): 10 1 1 1.0 0.0 num = 50000000 11 1 1 1.0 0.0 s = 0 12 50000001 15705699 0.3 48.5 for i in xrange(num): 13 50000000 16646855 0.3 51.5 s = s+i 14 1 1 1.0 0.0 return ###Output _____no_output_____ ###Markdown explanation - range vs xrange range creates a list, so if you do range(1, 10000000) it creates a list in memory with 9999999 elements. xrange is a sequence object that evaluates lazily. memory profiling ###Code # pip install memory_profiler #python -m memory_profiler ../code/mem_profiling.py Filename: mem_profiling.py Line # Mem usage Increment Line Contents ================================================ 1 30.965 MiB 0.000 MiB @profile 2 def main(): 3 30.965 MiB 0.000 MiB num = 500000 4 30.965 MiB 0.000 MiB s=0; 5 46.367 MiB 15.402 MiB for i in range(num): 6 46.367 MiB 0.000 MiB s = s + i 7 42.734 MiB -3.633 MiB return #python -m memory_profiler ../code/opti_mem_profiling.py Filename: opti_mem_profiling.py Line # Mem usage Increment Line Contents ================================================ 1 30.848 MiB 0.000 MiB @profile 2 def main(): 3 30.848 MiB 0.000 MiB num = 500000 4 30.848 MiB 0.000 MiB s=0; 5 30.848 MiB 0.000 MiB for i in xrange(num): 6 30.848 MiB 0.000 MiB s = s + i 7 30.848 MiB 0.000 MiB return ###Output _____no_output_____

Model_Building/Collaborative_Filtering_ML_ALS_vs_BigDL_NCF_20m.ipynb

###Markdown Notebook for Collaborative Filtering with both ALS and NCF models for 20M rows In this notebook, we implement ALS and NCF models for Movie Recommendation System for 1M movie ratings. The 20M reviews dataset contains 20 million reviews made by 138,000 users on 27,000 movies. ###Code # Intialization import os import time import datetime as dt import warnings warnings.filterwarnings("ignore", message="numpy.dtype size changed") # spark sql imports from pyspark.sql import SparkSession, SQLContext, Row from pyspark.sql.functions import UserDefinedFunction, explode, desc, rank, col, row_number from pyspark.sql.types import * from pyspark.sql.window import Window # spark ml imports from pyspark.ml.recommendation import ALS, ALSModel from pyspark.ml.linalg import Vectors from pyspark.ml.tuning import ParamGridBuilder, CrossValidator from pyspark.ml.evaluation import RegressionEvaluator # spark bigdl, analytics zoo imports from zoo.models.recommendation import UserItemFeature from zoo.models.recommendation import NeuralCF from zoo.common.nncontext import init_nncontext from bigdl.nn.criterion import * from bigdl.optim.optimizer import * from bigdl.util.common import * # data science imports import math import numpy as np import pandas as pd from sklearn import metrics from operator import itemgetter data_path = 'hdfs:///user/andrew/' sc = init_nncontext("NCF Example") ###Output _____no_output_____ ###Markdown Data Preparation ###Code # Initialize the SQLContext for reading in parquet files as Spark dataframes sqlContext = SQLContext(sc) # Load in the ratings data and format such that it has 3 columns - userId, movieId, rating # The ratings data will be used for modeling and making recommendations ratings = sqlContext.read.parquet(data_path + 'ratings_20m') ratings = ratings.drop('timestamp') ratings = ratings.withColumn("userId", ratings["userId"].cast("int")) ratings = ratings.withColumn("rating", ratings["rating"] * 2) #Multiply by 2 so that values are whole numbers -> values 1 to 10 # Load in the movies data and format such that it contains 3 columns - movieId, title, genres # The movies data will be used in the final step to understand what items have been recommended movies = sqlContext.read.parquet(data_path + 'movies_20m') movies = movies.drop('imdbId') ratings.show(5) movies.show(5) ratings_train, ratings_val = ratings.randomSplit([0.8, 0.2], seed = 42) print('The random split results in %s reviews in the training dataset and %s reviews in the validation dataset.' % (ratings_train.count(), ratings_val.count())) ratings_train.take(3) # Format the training and validation datasets into RDDs of Sample. This is the distributed format # used in Analytics Zoo and BigDL to speed up processing time. def build_sample(user_id, item_id, rating): sample = Sample.from_ndarray(np.array([user_id, item_id]), np.array([rating])) return UserItemFeature(user_id, item_id, sample) fullPairFeatureRdds = ratings.rdd.map(lambda x: build_sample(x[0], x[1], x[2])) trainPairFeatureRdds = ratings_train.rdd.map(lambda x: build_sample(x[0], x[1], x[2])) valPairFeatureRdds = ratings_val.rdd.map(lambda x: build_sample(x[0], x[1], x[2])) full_rdd = fullPairFeatureRdds.map(lambda pair_feature: pair_feature.sample) train_rdd = trainPairFeatureRdds.map(lambda pair_feature: pair_feature.sample) val_rdd = valPairFeatureRdds.map(lambda pair_feature: pair_feature.sample) # Visualize the first three rows of the training data to better understand what a RDD of Sample looks like. train_rdd.take(3) ###Output _____no_output_____ ###Markdown ALS and NCF Model Training and Validation on Training dataTrain ALS and NCF models and compare the Mean Absolte Error (MAE) for each on the validation set. With the parameter settings set below, the ALS model has slightly lower validation error, but also takes far less time to train. However, when comparing the training and validation error for each model, the ALS model is more over fit. ###Code %%time als = ALS(seed = 42, regParam = 0.1, maxIter = 15, rank = 12, userCol = "userId", itemCol = "movieId", ratingCol = "rating") evaluator = RegressionEvaluator(metricName="mae", labelCol="rating", predictionCol="prediction") als_model = als.fit(ratings_train) %%time print 'Training Error (MAE):', evaluator.evaluate(als_model.transform(ratings_train)) print 'Validation Error (MAE):', evaluator.evaluate(als_model.transform(ratings_val).fillna(0)) # Save ALS model (trained on all 20M reviews) als_model.write().overwrite().save(path = data_path + 'ALS_Model_test.h5') als_model_test = ALSModel.load(path = data_path + 'ALS_Model_test.h5') print 'Training Error (MAE):', evaluator.evaluate(als_model_test.transform(ratings_train)) print 'Validation Error (MAE):', evaluator.evaluate(als_model_test.transform(ratings_val).fillna(0)) %%time batch_size = 92160 max_user_id = ratings.agg({'userId': 'max'}).collect()[0]['max(userId)'] max_movie_id = ratings.agg({'movieId': 'max'}).collect()[0]['max(movieId)'] ncf = NeuralCF(user_count = max_user_id, item_count = max_movie_id, class_num = 10, hidden_layers = [20, 10], include_mf = False) optimizer = Optimizer( model=ncf, training_rdd=train_rdd, criterion=ClassNLLCriterion(), end_trigger=MaxEpoch(10), batch_size=batch_size, # 16 executors, 16 cores each optim_method=Adam(learningrate=0.001)) optimizer.set_validation( batch_size=batch_size, # 16 executors, 16 cores each val_rdd=val_rdd, trigger=EveryEpoch(), val_method=[MAE(), Loss(ClassNLLCriterion())] ) optimizer.optimize() %%time train_res = ncf.evaluate(train_rdd, batch_size, [MAE()]) val_res = ncf.evaluate(val_rdd, batch_size, [MAE()]) print 'Training Error (MAE):', train_res[0] print 'Validation Error (MAE):', val_res[0] # Save NCF model (trained on all 20M reviews) ncf.save_model(path = data_path + 'NCF_Model_test.bigdl', weight_path = data_path + 'NCF_Model_test_weights.bin', over_write = True) # Load NCF model - compare loaded model results to trained model results ncf_test = NeuralCF.load_model(path = data_path + 'NCF_Model_test.bigdl', weight_path = data_path + 'NCF_Model_test_weights.bin') train_res = ncf_test.evaluate(train_rdd, batch_size, [MAE()]) val_res = ncf_test.evaluate(val_rdd, batch_size, [MAE()]) print 'Training Error (MAE):', train_res[0] print 'Validation Error (MAE):', val_res[0] ###Output creating: createMAE creating: createMAE Training Error (MAE): Evaluated result: 1.23713171482, total_num: 44580, method: MAE Validation Error (MAE): Evaluated result: 1.27953600883, total_num: 11238, method: MAE ###Markdown ALS and NCF Model Training and Validation on the entire dataset ###Code %%time als = ALS(seed = 42, regParam = 0.1, maxIter = 15, rank = 12, # coldStartStrategy = 'drop', # drops userIds/movieIds from the validation set or test set so that NaNs are not returned userCol = "userId", itemCol = "movieId", ratingCol = "rating") evaluator = RegressionEvaluator(metricName="mae", labelCol="rating", predictionCol="prediction") als_model = als.fit(ratings) print 'Model Error (MAE):', evaluator.evaluate(als_model.transform(ratings)) # Save ALS model (trained on all 20M reviews) als_model.write().overwrite().save(path = data_path + 'ALS_Model_20m.h5') %%time max_user_id = ratings.agg({'userId': 'max'}).collect()[0]['max(userId)'] max_movie_id = ratings.agg({'movieId': 'max'}).collect()[0]['max(movieId)'] ncf = NeuralCF(user_count=max_user_id, item_count=max_movie_id, class_num=10, hidden_layers=[20, 10], include_mf = False) optimizer = Optimizer( model=ncf, training_rdd=full_rdd, criterion=ClassNLLCriterion(), end_trigger=MaxEpoch(10), batch_size=batch_size, # 16 executors, 16 cores each optim_method=Adam(learningrate=0.001)) optimizer.optimize() full_res = ncf.evaluate(full_rdd, batch_size, [MAE()]) print 'Model Error (MAE):', full_res[0] # Save NCF model (trained on all 20M reviews) ncf.save_model(path = data_path + 'NCF_Model_20m.bigdl', weight_path = data_path + 'NCF_Model_20m_weights.bin', over_write = True) ###Output _____no_output_____ ###Markdown Predictions Comparison Compare the prediction between ALS and NCF for one specific user. The user id is specified in the final two cells ###Code %%time # Create a sparse matrix of all combinations of items ratings_df = ratings.toPandas() ratings_matrix = ratings_df.pivot(index='userId',columns='movieId',values='rating').fillna(0) # Melt sparse matrix to dataframe of 3 columns containing userId, movieId, and rating ratings_matrix['userId'] = ratings_matrix.index ratings_df_2 = pd.melt(ratings_matrix, id_vars = ['userId'], value_vars = list(ratings_matrix.columns).remove('userId')) ratings_df_2.columns = ['userId', 'movieId', 'rating'] ratings_df_2.shape %%time # Predict for specified user pred_userId = 25643 # keep only the userId, movieId pairs that do not have ratings ratings_blanks_df = ratings_df_2.iloc[np.where((ratings_df_2.rating == 0) & (ratings_df_2.userId == pred_userId))] # Convert to spark dataframe ratings_blanks = sqlContext.createDataFrame(ratings_blanks_df) # Create RDD of Sample from the spark dataframe blankPairFeatureRdds = ratings_blanks.rdd.map(lambda x: build_sample(x[0], x[1], x[2])) %%time als_pair_preds = als_model.transform(ratings_blanks) ncf_pair_preds = ncf.recommend_for_user(blankPairFeatureRdds, 10).toDF() als_preds = als_pair_preds.select('userId', 'movieId', 'prediction').toDF('userId', 'movieId', 'als_pred') ncf_preds_topN = ncf_pair_preds.select('user_id', 'item_id', 'prediction').toDF('userId', 'movieId', 'ncf_pred') del als_pair_preds, ncf_pair_preds %%time window = Window.partitionBy(als_preds['userId']).orderBy(als_preds['als_pred'].desc()) als_preds_topN = als_preds.select(col('*'), row_number().over(window).alias('row_number')).where(col('row_number') <= 10) als_preds_topN_labeled = als_preds_topN.join(movies, how = 'left', on = 'movieId') ncf_preds_topN_labeled = ncf_preds_topN.join(movies, how = 'left', on = 'movieId') als_final = als_preds_topN_labeled.select('userId', 'movieId', 'als_pred', 'title').sort(col("userId")).toPandas() ncf_final = ncf_preds_topN_labeled.select('userId', 'movieId', 'ncf_pred', 'title').sort(col("userId")).toPandas() del window, als_preds, als_preds_topN, ncf_preds_topN, als_preds_topN_labeled, ncf_preds_topN_labeled als_final ncf_final ###Output _____no_output_____

2016/tutorial_final/3/PyAlgoTrade-checkpoint.ipynb

###Markdown PyAlgoTradeIntroduction PyAlgoTrade is a Python Algorithmic Trading Library mainly used to backtest any user devised strategy. It also provides support for paper trading and live trading. Quantitative estimation of the accuracy of new trading algorithms on historical market data is the prime use of PyAlgoTrade. In this tutorial we will learn how to use pyalgotrade, create a simple user strategy, understand the features using a simple strategy and explore features to backtest and analyse the same strategy.Getting PyalgoTrade You can install PyAlgoTrade using pip like this: ###Code pip install pyalgotrade ###Output _____no_output_____ ###Markdown Main features1. Event driven.2. Supports Market, Limit, Stop and StopLimit orders. These are essentially when we would sell and buy.3. Supports Yahoo! Finance, Google Finance and NinjaTrader CSV files. These are the market feed data.4. Bitcoin trading support through Bitstamp.5. Technical indicators and filters like SMA, WMA, EMA, RSI, Bollinger Bands, Hurst exponent and others.6. Performance metrics like Sharpe ratio, trade and drawdown analysis.7. Handling Twitter events in realtime.8. Event profiler.PyAlgoTrade has 6 main components:StrategiesThese are classes which contain the business logic of the trading algorithm: buying time, selling time etc...FeedsThese are data providing abstractions. It can be a CSV feed that loads bars to a strategy or a Twitter feed that allows incorporating Twitter events into trading decisions. This data is the one on which the business logic is written.BrokersThis is the executing section which carries out the orders.DataSeriesA data series is an abstraction used to manage time series data.TechnicalsThese are a set of filters that you use to make calculations on top of DataSeries. For example SMA (Simple Moving Average), RSI (Relative Strength Index), etc. These filters are modeled as DataSeries decorators.OptimizerThese are a set of classes that allow you to distribute backtesting among different computers, or different processes running in the same computer, or a combination of both. They make horizontal scaling easy. Getting DataThe first thing that we’ll need to test our strategies is some data. Let’s use Mirosoft’s stock prices for year 2000, which we’ll download with the following command: ###Code from pyalgotrade.tools import yahoofinance yahoofinance.download_daily_bars('msft', 2000, 'msft-2000.csv') The pyalgotrade.tools.yahoofinance package downloads CSV formatted data from Yahoo! Finance. The msft-2000.csv file should look like this: Date,Open,High,Low,Close,Volume,Adj Close 2000-12-29,30.87,31.31,28.69,29.06,31655500,28.35 2000-12-28,30.56,31.12,30.37,31.06,25055600,30.30 2000-12-27,30.37,31.06,29.37,30.69,26441700,29.94 . . 2000-01-04,115.50,118.62,105.00,107.69,116850000,26.26 2000-01-03,124.62,125.19,111.62,118.12,98122000,28.81 ###Output _____no_output_____ ###Markdown Creating first strategyPresented below is an illustration of the simple moving average algorithm. This solves the purpose of understanding the architecture and flow of the PyAlgoTrade module. PyAlgoTrade provides us with a skeleton of a base strategy in the form of BaseStrategy class. The class has the following format:class pyalgotrade.strategy.BaseStrategy(barFeed, broker)Parameters: barFeed (pyalgotrade.barfeed.BaseBarFeed.) – The bar feed that will supply the bars.broker (pyalgotrade.broker.Broker.) – The broker that will handle orders.Methods:onBars(bars)Override (mandatory) to get notified when new bars are available. The default implementation raises an Exception.This is the method to override to enter your trading logic and enter/exit positions.Parameters: bars (pyalgotrade.bar.Bars.) – The current bars.run()Call once (and only once) to run the strategy.stop()Stops a running strategy.onStart()Override (optional) to get notified when the strategy starts executing. The default implementation is empty.onFinish(bars)Override (optional) to get notified when the strategy finished executing. The default implementation is empty.Parameters: bars (pyalgotrade.bar.Bars.) – The last bars processed.These are the basic functions in the BaseStrategy class which contains a bunch of functions, which we will capture as we go ahead. There is also a class called BacktestStrategy explicitly inherited from BaseStrategy and useful in backtesting a trading logic. ###Code from pyalgotrade import strategy from pyalgotrade.barfeed import yahoofeed from pyalgotrade.technical import ma class FirstStrategy(strategy.BacktestingStrategy): def __init__(self, feed, instrument): super(FirstStrategy, self).__init__(feed) self.__sma = ma.SMA(feed[instrument].getCloseDataSeries(), 10) self.__instrument = instrument def onBars(self, bars): bar = bars[self.__instrument] self.info("%s %s" % (bar.getClose(), self.__sma[-1])) ###Output _____no_output_____ ###Markdown To test our strategy let us load the data for Microsoft and check the output. ###Code feed = yahoofeed.Feed() feed.addBarsFromCSV("msft", "msft-2000.csv") myStrategy = FirstStrategy(feed, "msft") myStrategy.run() ###Output _____no_output_____ ###Markdown In the above code we declare a new strategy. We need to override the onBars callback which gets fired whenever a feed is available. We load the feeds from a csv file and then run it with our strategy which for now just prints the slosing prices and simple moving averages.To get a brief insight into the short and long positions of trading, the different types of orders which can be placed, here is a good start. This will help us understand the APIs better.http://www.investopedia.com/ask/answers/100314/whats-difference-between-long-and-short-position-market.asphttp://www.investopedia.com/university/intro-to-order-types/limit-orders.aspLet’s move on with a simple strategy, this time simulating actual trading. The idea is very simple:If the adjusted close price is above the SMA() for the given period we enter a long position (we place a buy market order). If a long position is in place, and the adjusted close price drops below the SMA() we exit the long position (we place a sell market order). We are defining the rules of trading, our buying and selling strategies based on SMA values in this part of the tutorial. This is just an illustration, ofcourse there are trading algorithms which make use of much more fancy parameters and do a bunch of computations before deciding. ###Code from pyalgotrade import strategy from pyalgotrade.barfeed import yahoofeed from pyalgotrade.technical import ma class FirstStrategy(strategy.BacktestingStrategy): def __init__(self, feed, instrument, smaPeriod): super(FirstStrategy, self).__init__(feed, 1000) self.__position = None self.__instrument = instrument self.setUseAdjustedValues(True) self.__sma = ma.SMA(feed[instrument].getPriceDataSeries(), smaPeriod) def getSMA(self): return self.__sma def onEnterOk(self, position): execInfo = position.getEntryOrder().getExecutionInfo() self.info("BUY at $%.2f" % (execInfo.getPrice())) def onEnterCanceled(self, position): self.__position = None def onExitOk(self, position): execInfo = position.getExitOrder().getExecutionInfo() self.info("SELL at $%.2f" % (execInfo.getPrice())) self.__position = None def onExitCanceled(self, position): self.__position.exitMarket() def onBars(self, bars): if self.__sma[-1] is None: return bar = bars[self.__instrument] if self.__position is None: if bar.getPrice() > self.__sma[-1]: self.__position = self.enterLong(self.__instrument, 10, True) elif bar.getPrice() < self.__sma[-1] and not self.__position.exitActive(): self.__position.exitMarket() def run_strategy(feed, instrument, smaPeriod): first_strategy = FirstStrategy(feed, instrument, smaPeriod) first_strategy.run() print "Final value: $%.2f" % first_strategy.getBroker().getEquity() return first_strategy feed = yahoofeed.Feed() feed.addBarsFromCSV("msft", "msft-2000.csv") first_strategy = run_strategy(feed, "msft", 10) ###Output 2000-01-18 00:00:00 strategy [INFO] BUY at $38.22 2000-01-20 00:00:00 strategy [INFO] SELL at $36.59 2000-02-02 00:00:00 strategy [INFO] BUY at $35.01 2000-02-03 00:00:00 strategy [INFO] SELL at $34.88 2000-02-04 00:00:00 strategy [INFO] BUY at $35.67 2000-02-14 00:00:00 strategy [INFO] SELL at $34.60 2000-03-06 00:00:00 strategy [INFO] BUY at $32.81 2000-03-07 00:00:00 strategy [INFO] SELL at $32.86 2000-03-08 00:00:00 strategy [INFO] BUY at $32.06 2000-03-15 00:00:00 strategy [INFO] SELL at $32.32 2000-03-20 00:00:00 strategy [INFO] BUY at $33.75 2000-03-31 00:00:00 strategy [INFO] SELL at $36.23 2000-04-03 00:00:00 strategy [INFO] BUY at $32.28 2000-04-04 00:00:00 strategy [INFO] SELL at $31.30 2000-05-02 00:00:00 strategy [INFO] BUY at $24.89 2000-05-03 00:00:00 strategy [INFO] SELL at $24.05 2000-05-08 00:00:00 strategy [INFO] BUY at $24.25 2000-05-09 00:00:00 strategy [INFO] SELL at $23.99 2000-05-16 00:00:00 strategy [INFO] BUY at $23.78 2000-05-18 00:00:00 strategy [INFO] SELL at $23.26 2000-06-02 00:00:00 strategy [INFO] BUY at $22.56 2000-06-30 00:00:00 strategy [INFO] SELL at $26.34 2000-07-03 00:00:00 strategy [INFO] BUY at $27.24 2000-07-06 00:00:00 strategy [INFO] SELL at $26.96 2000-07-07 00:00:00 strategy [INFO] BUY at $27.78 2000-07-11 00:00:00 strategy [INFO] SELL at $26.94 2000-07-13 00:00:00 strategy [INFO] BUY at $26.94 2000-07-17 00:00:00 strategy [INFO] SELL at $26.75 2000-08-04 00:00:00 strategy [INFO] BUY at $23.73 2000-08-07 00:00:00 strategy [INFO] SELL at $23.99 2000-08-08 00:00:00 strategy [INFO] BUY at $23.95 2000-08-17 00:00:00 strategy [INFO] SELL at $24.31 2000-08-29 00:00:00 strategy [INFO] BUY at $24.33 2000-08-30 00:00:00 strategy [INFO] SELL at $24.16 2000-10-20 00:00:00 strategy [INFO] BUY at $20.96 2000-11-13 00:00:00 strategy [INFO] SELL at $22.79 2000-11-16 00:00:00 strategy [INFO] BUY at $23.73 2000-11-17 00:00:00 strategy [INFO] SELL at $23.73 2000-11-27 00:00:00 strategy [INFO] BUY at $24.42 2000-11-29 00:00:00 strategy [INFO] SELL at $22.84 2000-12-13 00:00:00 strategy [INFO] BUY at $20.68 2000-12-15 00:00:00 strategy [INFO] SELL at $17.45 ###Markdown Technicals: Technicals will return None when the value can’t be calculated at a given time.Technicals can be cascaded. That is because they’re modeled as DataSeries as well. An example below combines RSI and SMA filters. These are parameters which will be used in dedcision making. ###Code def __init__(self, feed, instrument): super(MyStrategy, self).__init__(feed) self.__rsi = rsi.RSI(feed[instrument].getCloseDataSeries(), 14) self.__sma = ma.SMA(self.__rsi, 15) self.__instrument = instrument ###Output _____no_output_____ ###Markdown OptimizationTrading algorithm are computationally intensive considering the volume of data they work on. More importantly they need to be very fast in procecssing the data and giving out results. Also depending on the strategy we choose, and the parameters we use for the strategy there would be enormous possibilities. We would want to do processing of the entire data on all these possibilties. This is when we think of parallel execution. Fortunately, Pyalgotrade has an option to parallelize our algorithm by setting up a server, which manages the intense computation by distributing it across multiple workers. The server is configured to test a strategy for different set of parameter combinations (of the order of 10^6). It waits for worker processes to subscribe for some load. Many or one workers (other machines) can subscribe to the server, which assigns a part of the computation (say some subset of parameter range). Once the workers have completed computation, they share their results with the server which aggregates them and filters out the best combination for the chosen strategy. ###Code from pyalgotrade.tools import yahoofinance yahoofinance.download_daily_bars('msft', 2009, 'msft-2009.csv') yahoofinance.download_daily_bars('msft', 2010, 'msft-2010.csv') yahoofinance.download_daily_bars('msft', 2011, 'msft-2011.csv') import itertools from pyalgotrade.technical import ma from pyalgotrade.optimizer import server from pyalgotrade.technical import rsi def parameters_generator(): instrument = "msft" rsiPeriod = range(2, 11) entrySMA = range(150, 251) exitSMA = range(5, 16) return itertools.product(instrument, entrySMA, exitSMA, rsiPeriod) feed = yahoofeed.Feed() feed.addBarsFromCSV("msft", "msft-2009.csv") feed.addBarsFromCSV("msft", "msft-2010.csv") feed.addBarsFromCSV("msft", "msft-2011.csv") server.serve(feed, parameters_generator(), 'localhost', 5000) ###Output _____no_output_____ ###Markdown The above sections of code downloads necessary files for 3 years worth of data and configures a server to generate 100x10x10 = 10000 possible configurations to be tested on that data. It waits on the port 5000 for active workers which request a subset of these parameters for a strategy they would be testing. ###Code from pyalgotrade.optimizer import worker worker.run(FooStrategy, 'localhost', 5000) #FooStrategy is just a place holder ###Output _____no_output_____ ###Markdown The above code registers the worker with the above created server for some strategy called 'FooStrategy'. Analyzing a strategyStrategy analyzers provide an extensible way to attach different calculations to strategy executions. It surfaces routines to extract profit/loss statements, commissions, evaluate returns using which we could converge to optimal levels.Different investors use moving averages for different reasons. Some use them as their primary analytical tool, while others simply use them as a confidence builder to back up their investment decisions. A crossover is the most basic type of signal and is favored among many traders because it removes all emotion. The most basic type of crossover is when the price of an asset moves from one side of a moving average and closes on the other. Price crossovers are used by traders to identify shifts in momentum and can be used as a basic entry or exit strategy. ###Code from pyalgotrade import strategy from pyalgotrade.technical import ma from pyalgotrade.technical import cross class SMACrossOver(strategy.BacktestingStrategy): def __init__(self, feed, instrument, smaPeriod): super(SMACrossOver, self).__init__(feed) self.__instrument = instrument self.__position = None self.setUseAdjustedValues(True) self.__prices = feed[instrument].getPriceDataSeries() self.__sma = ma.SMA(self.__prices, smaPeriod) def getSMA(self): return self.__sma def onEnterCanceled(self, position): self.__position = None def onExitOk(self, position): self.__position = None def onExitCanceled(self, position): self.__position.exitMarket() def onBars(self, bars): if self.__position is None: if cross.cross_above(self.__prices, self.__sma) > 0: shares = int(self.getBroker().getCash() * 0.75 / bars[self.__instrument].getPrice()) #compute the number of shares with which you would want to enter a long position self.__position = self.enterLong(self.__instrument, shares, True) elif not self.__position.exitActive() and cross.cross_below(self.__prices, self.__sma) > 0: self.__position.exitMarket() from pyalgotrade.barfeed import yahoofeed from pyalgotrade.stratanalyzer import returns from pyalgotrade.stratanalyzer import sharpe from pyalgotrade.stratanalyzer import drawdown from pyalgotrade.stratanalyzer import trades feed = yahoofeed.Feed() feed.addBarsFromCSV("msft", "msft-2000.csv") myStrategy = SMACrossOver(feed, "msft", 20) retAnalyzer = returns.Returns() myStrategy.attachAnalyzer(retAnalyzer) drawDownAnalyzer = drawdown.DrawDown() myStrategy.attachAnalyzer(drawDownAnalyzer) tradesAnalyzer = trades.Trades() myStrategy.attachAnalyzer(tradesAnalyzer) myStrategy.run() print "Final portfolio value: " + str(myStrategy.getResult()) print "Cumulative returns: " + str(retAnalyzer.getCumulativeReturns()[-1] * 100) print "Longest drawdown duration: " + str((drawDownAnalyzer.getLongestDrawDownDuration())) ###Output _____no_output_____ ###Markdown VisualizationThe pyalgotrader also provides a plotter to capture the changes in any kind of matrices. When the below code is run, a plotter window pops up with the requested graphs generated. It also has options to zoom-in, copy etc.. for a thorough analysis. ###Code from pyalgotrade import plotter from pyalgotrade.stratanalyzer import returns returnsAnalyzer = returns.Returns() first_strategy.run() first_strategy.info("Final portfolio value: $%.2f" % first_strategy.getResult()) first_strategy.attachAnalyzer(returnsAnalyzer) plt = plotter.StrategyPlotter(first_strategy) plt.getInstrumentSubplot("msft").addDataSeries("SMA", first_strategy.getSMA()) plt.getOrCreateSubplot("returns").addDataSeries("Simple returns", returnsAnalyzer.getReturns()) plt.plot() ###Output _____no_output_____ ###Markdown Please note that the visualizer is still in the raw form. Since this library is new and undergoing changes there might be chances when the visualizer does not pick up data. The work around code for that is very straighforward. We can just use the SMA values from first_strategy.getSMA() and use matpoltlib to generate our own visualizations. The graph might come as a pop up window please check for that. ###Code import matplotlib.pyplot as plt smas = [] for sma in first_strategy.getSMA(): if sma!=None: smas.append(sma) plt.hist(smas, 50, normed=1, facecolor='green', alpha=0.75) plt.xlabel('sma values') plt.show() ###Output _____no_output_____

resources/useful_repos/ORIGINAL_intuitive-deep-learning-master/Part 2: Image Recognition CIFAR-10/Coding Companion to Intuitive Deep Learning Part 2 (Annotated).ipynb

###Markdown Coding Companion for Intuitive Deep Learning Part 2 (Annotated) The medium post for this notebook is [here](https://medium.com/@josephleeweien/build-your-first-convolutional-neural-network-to-recognize-images-84b9c78fe0ce).In this notebook, we'll go through the code for the coding companion for [Intuitive Deep Learning Part 2](https://medium.com/intuitive-deep-learning/intuitive-deep-learning-part-2-cnns-for-computer-vision-24992d050a27) to create your very first Convolutional neural network to predict what is contained within the image (airplane, automobile, bird, cat, deer, dog, frog, horse, ship, and truck). We will go through the following in this notebook:- Exploring and Processing the Data- Building and Training our Convolutional Neural Network- Testing out with your own imagesNote that the results you get might differ slightly from the blogpost as there is a degree of randomness in the way we split our dataset as well as the initialization of our neural network. Exploring and Processing the Data We will first have to download our dataset, CIFAR-10. The details of the dataset are as follows:- Images to be recognized: Tiny images of 32 * 32 pixels- Labels: 10 possible labels (airplane, automobile, bird, cat, deer, dog, frog, horse, ship, and truck)- Dataset size: 60000 images, split into 50000 for training and 10000 for testing ###Code from keras.datasets import cifar10 (x_train, y_train), (x_test, y_test) = cifar10.load_data() print('x_train shape:', x_train.shape) print('y_train shape:', y_train.shape) ###Output y_train shape: (50000, 1) ###Markdown We will now take a look at an individual image. If we print out the first image of our training dataset (x_train[0]): ###Code print(x_train[0]) ###Output [[[ 59 62 63] [ 43 46 45] [ 50 48 43] ... [158 132 108] [152 125 102] [148 124 103]] [[ 16 20 20] [ 0 0 0] [ 18 8 0] ... [123 88 55] [119 83 50] [122 87 57]] [[ 25 24 21] [ 16 7 0] [ 49 27 8] ... [118 84 50] [120 84 50] [109 73 42]] ... [[208 170 96] [201 153 34] [198 161 26] ... [160 133 70] [ 56 31 7] [ 53 34 20]] [[180 139 96] [173 123 42] [186 144 30] ... [184 148 94] [ 97 62 34] [ 83 53 34]] [[177 144 116] [168 129 94] [179 142 87] ... [216 184 140] [151 118 84] [123 92 72]]] ###Markdown In order to see the image as an image rather than a series of pixel value numbers, we will use a function from matplotlib: ###Code import matplotlib.pyplot as plt %matplotlib inline img = plt.imshow(x_train[0]) print('The label is:', y_train[0]) ###Output The label is: [6] ###Markdown Let's explore one more image, the second image (with index 1 instead of 0) in our training dataset: ###Code img = plt.imshow(x_train[1]) print('The label is:', y_train[1]) ###Output The label is: [9] ###Markdown What we really want is the probability of each of the 10 different classes. For that, we need 10 output neurons in our neural network. Since we have 10 output neurons, our labels must match this as well. To do this, we convert the label into a set of 10 numbers where each number represents if the image belongs to that class or not. So if an image belongs to the first class, the first number of this set will be a 1 and all other numbers in this set will be a 0. To convert our labels to our one-hot encoding, we use a function in Keras: ###Code import keras y_train_one_hot = keras.utils.to_categorical(y_train, 10) y_test_one_hot = keras.utils.to_categorical(y_test, 10) print('The one hot label is:', y_train_one_hot[1]) ###Output The one hot label is: [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.] ###Markdown A common step we do is to let the values to be between 0 and 1, which will aid in the training of our neural network. Since our pixel values already take the values between 0 and 255, we simply need to divide by 255. ###Code x_train = x_train.astype('float32') x_test = x_test.astype('float32') x_train = x_train / 255 x_test = x_test / 255 x_train[0] ###Output _____no_output_____ ###Markdown Building and Training our Convolutional Neural Network Similar to our first notebook, we need to define the architecture (template) first before fitting the best numbers into this architecture by learning from the data. In summary, the architecture we will build in this post is this:- Conv Layer (Filter size 3x3, Depth 32)- Conv Layer (Filter size 3x3, Depth 32)- Max Pool Layer (Filter size 2x2)- Dropout Layer (Prob of dropout 0.25)- Conv Layer (Filter size 3x3, Depth 64)- Conv Layer (Filter size 3x3, Depth 64)- Max Pool Layer (Filter size 2x2)- Dropout Layer (Prob of dropout 0.25)- FC Layer (512 neurons)- Dropout Layer (Prob of dropout 0.5)- FC Layer, Softmax (10 neurons)For an intuition behind these layers, please refer to Intuitive Deep Learning [Part 2](https://medium.com/intuitive-deep-learning/intuitive-deep-learning-part-2-cnns-for-computer-vision-24992d050a27).We will be using Keras to build our architecture. Let's import the code from Keras that we will need to use: ###Code from keras.models import Sequential from keras.layers import Dense, Dropout, Flatten, Conv2D, MaxPooling2D ###Output _____no_output_____ ###Markdown We then call an empty Sequential model and 'add' to this model layer by layer: ###Code model = Sequential() ###Output _____no_output_____ ###Markdown The first layer is a conv layer with filter size 3x3, stride size 1 (in both dimensions), and depth 32. The padding is the 'same' and the activation is 'relu' (these two settings will apply to all layers in our CNN). We add this layer to our empty sequential model using the function model.add().The first number 32 refers to the depth. The next pair of numbers (3,3) refer to the filter width and size. Then, we specify activation which is 'relu' and padding which is 'same'. Notice that we did not specify stride. This is because stride=1 is a default setting, and unless we want to change this setting, we need not specify it.If you recall, we also need to specify an input size for our first layer; subsequent layers does not have this specification since they can infer the input size from the output size of the previous layer.All that being said, our first layer in code looks like this: ###Code model.add(Conv2D(32, (3, 3), activation='relu', padding='same', input_shape=(32,32,3))) ###Output _____no_output_____ ###Markdown Our second layer looks like this in code (we don't need to specify the input size): ###Code model.add(Conv2D(32, (3, 3), activation='relu', padding='same')) ###Output _____no_output_____ ###Markdown The next layer is a max pooling layer with pool size 2 x 2 and stride 2 (in both dimensions). The default for a max pooling layer stride is the pool size, so we don't have to specify the stride: ###Code model.add(MaxPooling2D(pool_size=(2, 2))) ###Output _____no_output_____ ###Markdown Lastly, we add a dropout layer with probability 0.25 of dropout so as to prevent overfitting: ###Code model.add(Dropout(0.25)) ###Output _____no_output_____ ###Markdown And there we have it, our first four layers in code. The next four layers look really similar (except the depth of the conv layer is 64 instead of 32): ###Code model.add(Conv2D(64, (3, 3), activation='relu', padding='same')) model.add(Conv2D(64, (3, 3), activation='relu', padding='same')) model.add(MaxPooling2D(pool_size=(2, 2))) model.add(Dropout(0.25)) ###Output _____no_output_____ ###Markdown Lastly, we have to code in our fully connected layer, which is similar to what we've done in our previous post, [Build your first Neural Network](https://medium.com/intuitive-deep-learning/build-your-first-neural-network-to-predict-house-prices-with-keras-eb5db60232c). However, at this point, our neurons are spatially arranged in a cube-like format rather than in just one row. To make this cube-like format of neurons into one row, we have to first flatten it. We do so by adding a Flatten layer: ###Code model.add(Flatten()) ###Output _____no_output_____ ###Markdown Now, we have a dense (FC) layer of 512 neurons with relu activation: ###Code model.add(Dense(512, activation='relu')) ###Output _____no_output_____ ###Markdown We add another dropout of probability 0.5: ###Code model.add(Dropout(0.5)) ###Output _____no_output_____ ###Markdown And lastly, we have a dense (FC) layer with 10 neurons and softmax activation: ###Code model.add(Dense(10, activation='softmax')) ###Output _____no_output_____ ###Markdown And we're done with specifying our architecture! To see a summary of the full architecture, we run the code: ###Code model.summary() ###Output _________________________________________________________________ Layer (type) Output Shape Param # ================================================================= conv2d_1 (Conv2D) (None, 32, 32, 32) 896 _________________________________________________________________ conv2d_2 (Conv2D) (None, 32, 32, 32) 9248 _________________________________________________________________ max_pooling2d_1 (MaxPooling2 (None, 16, 16, 32) 0 _________________________________________________________________ dropout_1 (Dropout) (None, 16, 16, 32) 0 _________________________________________________________________ conv2d_3 (Conv2D) (None, 16, 16, 64) 18496 _________________________________________________________________ conv2d_4 (Conv2D) (None, 16, 16, 64) 36928 _________________________________________________________________ max_pooling2d_2 (MaxPooling2 (None, 8, 8, 64) 0 _________________________________________________________________ dropout_2 (Dropout) (None, 8, 8, 64) 0 _________________________________________________________________ flatten_1 (Flatten) (None, 4096) 0 _________________________________________________________________ dense_1 (Dense) (None, 512) 2097664 _________________________________________________________________ dropout_3 (Dropout) (None, 512) 0 _________________________________________________________________ dense_2 (Dense) (None, 10) 5130 ================================================================= Total params: 2,168,362 Trainable params: 2,168,362 Non-trainable params: 0 _________________________________________________________________ ###Markdown We now fill in the best numbers after we've specified our architecture. We'll compile the model with our settings below.The loss function we use is called categorical cross entropy, which is applicable for a classification problem of many classes. The optimizer we use here is Adam. We haven't gone through the intuition of Adam yet, but know that Adam is simply a type of stochastic gradient descent (with a few modifications) so that it trains better. Lastly, we want to track the accuracy of our model. ###Code model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy']) ###Output _____no_output_____ ###Markdown And now, it's time to run our training.We train our model with batch size 32 and 20 epochs. We use the setting validation_split=0.2 instead of validation_data. With this shortcut, we did not need to split our dataset into a train and validation set at the start! Instead, we simply specify how much of our dataset will be used as a validation set. In this case, 20% of our dataset is used as a validation set. This will take a while on a CPU, so you might want to start training and get some coffee before coming back. ###Code hist = model.fit(x_train, y_train_one_hot, batch_size=32, epochs=20, validation_split=0.2) ###Output Train on 40000 samples, validate on 10000 samples Epoch 1/20 40000/40000 [==============================] - 256s 6ms/step - loss: 1.5844 - acc: 0.4176 - val_loss: 1.1586 - val_acc: 0.5848 Epoch 2/20 40000/40000 [==============================] - 263s 7ms/step - loss: 1.1519 - acc: 0.5897 - val_loss: 0.9885 - val_acc: 0.6494 Epoch 3/20 40000/40000 [==============================] - 259s 6ms/step - loss: 0.9921 - acc: 0.6502 - val_loss: 0.8804 - val_acc: 0.6901 Epoch 4/20 40000/40000 [==============================] - 250s 6ms/step - loss: 0.8872 - acc: 0.6847 - val_loss: 0.8371 - val_acc: 0.6995 Epoch 5/20 40000/40000 [==============================] - 251s 6ms/step - loss: 0.8172 - acc: 0.7109 - val_loss: 0.7716 - val_acc: 0.7261 Epoch 6/20 40000/40000 [==============================] - 251s 6ms/step - loss: 0.7544 - acc: 0.7335 - val_loss: 0.7429 - val_acc: 0.7422 Epoch 7/20 40000/40000 [==============================] - 251s 6ms/step - loss: 0.7086 - acc: 0.7504 - val_loss: 0.7441 - val_acc: 0.7477 Epoch 8/20 40000/40000 [==============================] - 251s 6ms/step - loss: 0.6676 - acc: 0.7639 - val_loss: 0.7214 - val_acc: 0.7492 Epoch 9/20 40000/40000 [==============================] - 250s 6ms/step - loss: 0.6327 - acc: 0.7776 - val_loss: 0.7185 - val_acc: 0.7555 Epoch 10/20 40000/40000 [==============================] - 248s 6ms/step - loss: 0.6016 - acc: 0.7888 - val_loss: 0.6891 - val_acc: 0.7656 Epoch 11/20 40000/40000 [==============================] - 249s 6ms/step - loss: 0.5660 - acc: 0.7996 - val_loss: 0.6867 - val_acc: 0.7626 Epoch 12/20 40000/40000 [==============================] - 248s 6ms/step - loss: 0.5476 - acc: 0.8064 - val_loss: 0.6849 - val_acc: 0.7698 Epoch 13/20 40000/40000 [==============================] - 248s 6ms/step - loss: 0.5316 - acc: 0.8115 - val_loss: 0.6887 - val_acc: 0.7678 Epoch 14/20 40000/40000 [==============================] - 248s 6ms/step - loss: 0.5002 - acc: 0.8246 - val_loss: 0.6931 - val_acc: 0.7731 Epoch 15/20 40000/40000 [==============================] - 245s 6ms/step - loss: 0.4917 - acc: 0.8246 - val_loss: 0.7365 - val_acc: 0.7660 Epoch 16/20 40000/40000 [==============================] - 248s 6ms/step - loss: 0.4690 - acc: 0.8374 - val_loss: 0.7153 - val_acc: 0.7693 Epoch 17/20 40000/40000 [==============================] - 245s 6ms/step - loss: 0.4592 - acc: 0.8377 - val_loss: 0.6857 - val_acc: 0.7755 Epoch 18/20 40000/40000 [==============================] - 248s 6ms/step - loss: 0.4519 - acc: 0.8416 - val_loss: 0.6918 - val_acc: 0.7741 Epoch 19/20 40000/40000 [==============================] - 246s 6ms/step - loss: 0.4330 - acc: 0.8461 - val_loss: 0.6926 - val_acc: 0.7739 Epoch 20/20 40000/40000 [==============================] - 246s 6ms/step - loss: 0.4242 - acc: 0.8493 - val_loss: 0.7026 - val_acc: 0.7785 ###Markdown After you've done training, we can visualize the model training and validation loss as well as training / validation accuracy over the number of epochs using the below code: ###Code plt.plot(hist.history['loss']) plt.plot(hist.history['val_loss']) plt.title('Model loss') plt.ylabel('Loss') plt.xlabel('Epoch') plt.legend(['Train', 'Val'], loc='upper right') plt.show() plt.plot(hist.history['acc']) plt.plot(hist.history['val_acc']) plt.title('Model accuracy') plt.ylabel('Accuracy') plt.xlabel('Epoch') plt.legend(['Train', 'Val'], loc='lower right') plt.show() ###Output _____no_output_____ ###Markdown Once we are done with tweaking our hyperparameters, we can run it on our test dataset below: ###Code model.evaluate(x_test, y_test_one_hot)[1] ###Output 10000/10000 [==============================] - 14s 1ms/step ###Markdown At this point, you might want to save your trained model (since you've spent so long waiting for it to train). The model will be saved in a file format called HDF5 (with the extension .h5). We save our model with this line of code: ###Code model.save('my_cifar10_model.h5') ###Output _____no_output_____ ###Markdown Testing out with your own images Now that we have a model, let's try it on our own images. To do so, place your image in the same directory as your notebook. For the purposes of this post, I'm going to use an image of a cat (which you can download here(link)). Now, we read in our JPEG file as an array of pixel values: ###Code my_image = plt.imread("cat.jpg") ###Output _____no_output_____ ###Markdown The first thing we have to do is to resize the image of our cat so that we can fit it into our model (input size of 32 * 32 * 3). ###Code from skimage.transform import resize my_image_resized = resize(my_image, (32,32,3)) img = plt.imshow(my_image_resized) ###Output _____no_output_____ ###Markdown And now, we see what our trained model will output when given an image of our cat, using this code: ###Code import numpy as np probabilities = model.predict(np.array( [my_image_resized,] )) probabilities number_to_class = ['airplane', 'automobile', 'bird', 'cat', 'deer', 'dog', 'frog', 'horse', 'ship', 'truck'] index = np.argsort(probabilities[0,:]) print("Most likely class:", number_to_class[index[9]], "-- Probability:", probabilities[0,index[9]]) print("Second most likely class:", number_to_class[index[8]], "-- Probability:", probabilities[0,index[8]]) print("Third most likely class:", number_to_class[index[7]], "-- Probability:", probabilities[0,index[7]]) print("Fourth most likely class:", number_to_class[index[6]], "-- Probability:", probabilities[0,index[6]]) print("Fifth most likely class:", number_to_class[index[5]], "-- Probability:", probabilities[0,index[5]]) ###Output Most likely class: cat -- Probability: 0.31140402 Second most likely class: horse -- Probability: 0.296455 Third most likely class: dog -- Probability: 0.1401798 Fourth most likely class: truck -- Probability: 0.12088975 Fifth most likely class: frog -- Probability: 0.078746535

jupyter_notebooks/Testing_dataset_unet.ipynb

###Markdown Importing and Installing libraries ###Code # Install required libs ### please update Albumentations to version>=0.3.0 for `Lambda` transform support !pip install -U albumentations>=0.3.0 --user !pip install -U --pre segmentation-models --user #This installation command is to resolve issues with respect to efficient not being found in the initila build of segmentation modle sm !pip install -U git+https://github.com/qubvel/segmentation_models #uPGRADE SCKITI IMAGE !pip install --upgrade scikit-image #RESTART THE KERNEL POST INSTALLATION #This is to resolve the dependency issues with skimage. !pip install numpy==1.17 !pip install ipdb !pip install pandas_ml !pip install nibabel pydicom medpy !pip install seaborn -U #RESTART THE KERNEL POST INSTALLATION of cell above import os #Confirmation that GPU is in working order. os.environ['CUDA_VISIBLE_DEVICES'] = '0' from medpy.io import load as load_segcaps import tensorflow as tf from sklearn.model_selection import train_test_split import glob import cv2 import keras import numpy as np import matplotlib.pyplot as plt import imageio import albumentations as A import random import segmentation_models as sm import datetime import itertools from sklearn.utils import class_weight import imageio import numpy as np import pickle import ipdb #os.environ['CUDA_VISIBLE_DEVICES'] = '0' from keras.models import load_model from scipy.spatial import distance from collections import OrderedDict from keras import backend as K_b import shutil import time from PIL import Image from pandas_ml import ConfusionMatrix from keras.preprocessing.image import ImageDataGenerator import pandas as pd import seaborn as sns import pathlib from medpy.io import load from sklearn.metrics import precision_recall_fscore_support print(tf.test.gpu_device_name()) with tf.device('/gpu:0'): a = tf.constant([1.0, 2.0, 3.0, 4.0, 5.0, 6.0], shape=[2, 3], name='a') b = tf.constant([1.0, 2.0, 3.0, 4.0, 5.0, 6.0], shape=[3, 2], name='b') c = tf.matmul(a, b) with tf.Session() as sess: print (sess.run(c)) ###Output /device:GPU:0 [[22. 28.] [49. 64.]] ###Markdown Loading data for analysis ###Code test_data_dir='/home/ec2-user/SageMaker/data/50_imgs/test/NIFTI_MR_256x256_png_256grey_lvl/t1dual_inphase' train_data_dir='/home/ec2-user/SageMaker/data/50_imgs/train/NIFTI_MR_256x256_png_256grey_lvl/t1dual_inphase' valid_data_dir='/home/ec2-user/SageMaker/data/50_imgs/valid/NIFTI_MR_256x256_png_256grey_lvl/t1dual_inphase' #Destination directory dst_dir='/home/ec2-user/SageMaker/data/250_imgs/merge/NIFTI_MR_256x256_png_256grey_lvl/t1dual_inphase' x_dst_dir = os.path.join(dst_dir, 'images') y_dst_dir = os.path.join(dst_dir, 'masks') paths_merge=list(zip(glob.glob(x_dst_dir+'/*.png'), glob.glob(y_dst_dir+'/*.png'))) x_test_dir = os.path.join(test_data_dir, 'images') y_test_dir = os.path.join(test_data_dir, 'masks') x_train_dir = os.path.join(train_data_dir, 'images') y_train_dir = os.path.join(train_data_dir, 'masks') x_valid_dir = os.path.join(valid_data_dir, 'images') y_valid_dir = os.path.join(valid_data_dir, 'masks') ###Output _____no_output_____ ###Markdown Merging of test/train and validation data for running per image prediction using keras prediction generator ###Code x_merge=[x_train_dir,x_test_dir,x_valid_dir] y_merge=[y_train_dir,y_test_dir,y_valid_dir] for x_dir,y_dir in list(zip(x_merge,y_merge)): x_file_list=glob.glob(x_dir+'/*.png') y_file_list=glob.glob(os.path.join(y_dir,'*.png')) [shutil.copy(x_tmp,os.path.join(x_dst_dir,os.path.basename(x_tmp))) for x_tmp in x_file_list] [shutil.copy(y_tmp,os.path.join(y_dst_dir,os.path.basename(y_tmp))) for y_tmp in y_file_list] ###Output _____no_output_____ ###Markdown Resizing of all images to match 256,256 size resolution ###Code for vals in paths_merge: trl_img=imageio.imread(vals[0]) trl_mask=imageio.imread(vals[1]) #trl_imgs_set={vals[0]:resize_img_PIL(trl_img),vals[1]:resize_img_PIL(trl_mask)} #ipdb.set_trace() #[imageio.imwrite(k,v) for k,v in trl_imgs_set.items() if type(v) is not str] if trl_mask.shape!=(256,256): print(vals[0]) ###Output _____no_output_____ ###Markdown Trouble shooting area of test dataset and model loads to ensure generators are working correctly ###Code test_dataset=gen_test_dataset(dst_dir,model_gnrl_params,preprocess_input,pred_gen_var=False) CLASSES = ['l_kidney','liver','r_kidney','spleen'] n_classes = 1 if len(CLASSES) == 1 else (len(CLASSES) + 1) test_dataset = Dataset( x_dst_dir, y_dst_dir, classes=CLASSES, preprocessing=get_preprocessing(preprocess_input), augmentation=get_validation_augmentation(),ret_img_path=True) #Local parameters for analysis lcl_wghts_dir='/home/ec2-user/SageMaker/Masters-Thesis-UNet-repository/jupyter_notebooks/weights_history_full/cat_focal_loss/btch_sz_7/lr_0.0003/weights/t1dual_inphase_all_orgs_grey_lvl_256_optm_Adam_loss_cat_focal_loss_trn_samp_sz_250_btch_sz_7_lr_0.0003_time_2019-11-18_00000096.h5' lcl_wghts_dir_2='/home/ec2-user/SageMaker/Masters-Thesis-UNet-repository/jupyter_notebooks/weights_history_full/cat_focal_loss/btch_sz_7/lr_0.0003/weights/t1dual_inphase_all_orgs_grey_lvl_256_optm_Adam_loss_cat_focal_loss_trn_samp_sz_250_btch_sz_7_lr_0.0003_time_2019-11-18_00000093.h5' optimiser_tmp=keras.optimizers.Adam(0.0003) total_loss_tmp=sm.losses.CategoricalFocalLoss() start_time=time.time() model_tmp=gen_test_model(model_gnrl_params,optimiser_tmp,total_loss_tmp,lcl_wghts_dir_2) end_time=time.time()-start_time print('processsing time:',end_time) import time start_time=time.time() output=model_tmp.predict_generator(test_dataset,steps=len(test_dataset)) end_time=time.time()-start_time print('processsing time:',end_time) trl_path=os.path.join(x_dst_dir, 'pat_id_38_t1dual_inphase_slice_no_21_256grey_lvl_256x256.png') trl_img=imageio.imread(trl_path) trl_img.shape img,mask,img_nm=test_dataset[1] test_dataloader = Dataloder(test_dataset, batch_size=1, shuffle=False) ###Output _____no_output_____ ###Markdown Loading function calls for analysis Data loader and dataset functions ###Code def resize_img_PIL(img:np.ndarray,shp_sp=(256,256)): if img.shape!=shp_sp: PIL_img=Image.fromarray(img) np_img_reshp=np.array(PIL_img.resize(shp_sp)) return np_img_reshp else: return img # helper function for data visualization def visualize(fig_nm=None,figdim=(33,3.1),**images): """PLot images in one row.""" n = len(images) print(fig_nm) plt.figure(figsize=figdim) for i, (name, image) in enumerate(images.items()): plt.subplot(1, n, i + 1) plt.xticks([]) plt.yticks([]) plt.title(' '.join(name.split('_')).title()) plt.imshow(image) if fig_nm is not None: plt.savefig(fig_nm,dpi=150) plt.clf() else: plt.show() # helper function for data visualization def denormalize(x): """Scale image to range 0..1 for correct plot""" x_max = np.percentile(x, 98) x_min = np.percentile(x, 2) x = (x - x_min) / (x_max - x_min) x = x.clip(0, 1) return x # classes for data loading and preprocessing class Dataset: """CamVid Dataset. Read images, apply augmentation and preprocessing transformations. Args: images_dir (str): path to images folder masks_dir (str): path to segmentation masks folder class_values (list): values of classes to extract from segmentation mask augmentation (albumentations.Compose): data transfromation pipeline (e.g. flip, scale, etc.) preprocessing (albumentations.Compose): data preprocessing (e.g. noralization, shape manipulation, etc.) """ CLASSES = {'background':0,'liver':63,'r_kidney':126,'l_kidney':189,'spleen':252} def __init__( self, images_dir, masks_dir, classes=None, augmentation=None, preprocessing=None, ret_img_path=False ): self.ids = os.listdir(images_dir) self.images_fps = [os.path.join(images_dir, image_id) for image_id in self.ids] self.masks_fps = [os.path.join(masks_dir, image_id) for image_id in self.ids] # convert str names to class values on masks self.class_values = [self.CLASSES[cls.lower()] for cls in classes] self.ret_img_path=ret_img_path self.augmentation = augmentation self.preprocessing = preprocessing def __getitem__(self, i): # read data image = imageio.imread(self.images_fps[i])#cv2.imread(self.images_fps[i]) image_nm=os.path.basename(self.images_fps[i]) #image = cv2.cvtColor(image, cv2.COLOR_BGR2RGB) image=np.expand_dims(image,axis=2) mask = cv2.imread(self.masks_fps[i], 0) # extract certain classes from mask (e.g. cars) masks = [(mask == v) for v in self.class_values] mask = np.stack(masks, axis=-1).astype('float') # add background if mask is not binary if mask.shape[-1] != 1: background = 1 - mask.sum(axis=-1, keepdims=True) mask = np.concatenate((mask, background), axis=-1) # apply augmentations if self.augmentation: sample = self.augmentation(image=image, mask=mask) image, mask = sample['image'], sample['mask'] # apply preprocessing if self.preprocessing: sample = self.preprocessing(image=image, mask=mask) image, mask = sample['image'], sample['mask'] if self.ret_img_path==True: return image, mask,image_nm else: return image, mask def __len__(self): return len(self.ids) class CustomDataloder(keras.utils.Sequence): """Load data from dataset and form batches Args: dataset: instance of Dataset class for image loading and preprocessing. batch_size: Integet number of images in batch. shuffle: Boolean, if `True` shuffle image indexes each epoch. """ def __init__(self, dataset, batch_size=1, shuffle=False): self.dataset = dataset self.batch_size = batch_size self.shuffle = shuffle self.indexes = np.arange(len(dataset)) self.on_epoch_end() def __getitem__(self, i): # collect batch data start = i * self.batch_size stop = (i + 1) * self.batch_size data = [] for j in range(start, stop): data.append(self.dataset[j]) # transpose list of lists batch = [np.stack(samples, axis=0) for samples in zip(*data)] return batch def __len__(self): """Denotes the number of batches per epoch""" return len(self.indexes) // self.batch_size def on_epoch_end(self): """Callback function to shuffle indexes each epoch""" if self.shuffle: self.indexes = np.random.permutation(self.indexes) def round_clip_0_1(x, **kwargs): return x.round().clip(0, 1) # define heavy augmentations def get_training_augmentation(dim_sp=256): rand_int_alpha=random.uniform(0,3) if rand_int_alpha<=0.5: rand_int_sigma=random.uniform(0.1,rand_int_alpha) elif rand_int_alpha>=2: rand_int_sigma=random.uniform(rand_int_alpha/1.8,rand_int_alpha) else: rand_int_sigma=random.uniform(rand_int_alpha/1.8,rand_int_alpha) train_transform = [ #A.RandomGridShuffle(p=0.4,grid=(8, 8)), A.ElasticTransform(p=0.9,alpha=rand_int_alpha,sigma=rand_int_sigma,border_mode=cv2.BORDER_REPLICATE), #,alpha_affine=20 A.HorizontalFlip(p=0.5), A.VerticalFlip(p=0.5), #A.RandomSizedCrop(p=0.5), A.ShiftScaleRotate(scale_limit=0.5, rotate_limit=90, shift_limit=0.1, p=0.5, border_mode=cv2.BORDER_REPLICATE), #A.PadIfNeeded(min_height=dim_sp, min_width=dim_sp, always_apply=True, border_mode=cv2.BORDER_REPLICATE), #A.RandomCrop(height=dim_sp, width=dim_sp, always_apply=True), A.OneOf( [ A.IAASharpen(p=0.5), A.Blur(blur_limit=3, p=0.5) ], p=0.2, ), A.Lambda(mask=round_clip_0_1) ] return A.Compose(train_transform) def get_validation_augmentation(): """Add paddings to make image shape divisible by 32""" test_transform = [ A.PadIfNeeded(256, 256) ] return A.Compose(test_transform) def get_preprocessing(preprocessing_fn): """Construct preprocessing transform Args: preprocessing_fn (callbale): data normalization function (can be specific for each pretrained neural network) Return: transform: albumentations.Compose """ _transform = [ A.Lambda(image=preprocessing_fn), ] return A.Compose(_transform) def keras_flow_from_dir(dst_dir,preprocess_input, target_size_var=(256, 256),batch_size_var=7): """Creation of template based keras image generator for batch scale prediction for efficient processing.""" gen_test_2 =ImageDataGenerator(preprocessing_function = preprocess_input) dst_dir=dst_dir+'_keras_dataloader' if dst_dir.find('_keras_dataloader')==-1 else dst_dir dataloader=gen_test_2.flow_from_directory(dst_dir,target_size=target_size_var, batch_size=batch_size_var, class_mode=None,color_mode='grayscale',shuffle=False) return dataloader #tmp_v=test_dataset.next() def gen_subdir_file_lst(dir_nm:str,file_sub_str:str): """The purpose of this method is to generate a file list of all h5 weights sorted for completing batch prediction""" #ipdb.set_trace() final_list=[] for root,subdir,files in os.walk(dir_nm): if len(files)>0: file_list=glob.glob(root+file_sub_str) final_list=final_list+file_list #Sorted to ensure history part 2,3 etc are synced together return sorted(final_list) def get_file_info(file,add_info): """The purpose of this method is to pull file information from the file name presnet in the string""" #ipdb.set_trace() split_vals=file[:-14].split('_') split_vals.sort() file_dict={} #Iterate through additional information of set of tuples on file strings for analysis for param_k,param_v in add_info: file_dict[param_k]=[x for x in param_v if x in split_vals][0] file_dict['epoch_no']=99#int(split_vals[-1][:-3]) return file_dict,split_vals def gen_test_dataset(test_data_dir,model_gnrl_params,preprocess_input,ret_img_path_var): x_test_dir=os.path.join(test_data_dir,'images') y_test_dir=os.path.join(test_data_dir,'masks') return Dataset(x_test_dir, y_test_dir, classes=model_gnrl_params['classes'], augmentation=get_validation_augmentation(), preprocessing=get_preprocessing(preprocess_input), ret_img_path=ret_img_path_var) ###Output _____no_output_____ ###Markdown Generate model and test model functions ###Code def gen_test_model(model_gnrl_param:dict,lrn_rate,total_loss,wghts_dir:str,cls_wghts_perc=None): """The purpose of this method is to generate a test model from the directory for analysis""" loss_func={'cat':sm.losses.CategoricalCELoss(class_weights=cls_wghts_perc), 'wce':sm.losses.CategoricalCELoss(class_weights=cls_wghts_perc), 'focal':sm.losses.CategoricalFocalLoss(), 'dice':sm.losses.DiceLoss(class_weights=cls_wghts_perc)} optim=keras.optimizers.Adam(lrn_rate) reload_model = sm.Unet(model_gnrl_param['backbone'], classes=model_gnrl_param['n_classes'], activation=model_gnrl_param['activation_type'], encoder_weights=None, input_shape=(None, None,model_gnrl_param['input_shape_N'])) reload_model.compile(optim,loss_func[total_loss],model_gnrl_param['metrics']) reload_model.load_weights(wghts_dir) return reload_model ###Output _____no_output_____ ###Markdown Metrics for analysis ###Code def gen_test_scores(model,test_dataloader,metrics)->dict: """The purpose of this method is to generate a summary dictionary of a model test set metrics for analysis""" metric_dict={} scores = model.evaluate_generator(test_dataloader) metric_dict["loss"]=scores[0] for metric, value in zip(metrics, scores[1:]): metric_dict[metric.__name__]=value return metric_dict def gen_per_class_dice_loss(y_true:np.ndarray,y_pred:np.ndarray, channel='channel_last', dice_dict=OrderedDict(left_kidney=0,liver=0,right_kidney=0,spleen=0,background=0))->dict: """The purpose of this method is to generate a dice loss for each organ within the logits present""" assert y_true.shape==y_pred.shape,'Error predicted and ground tensors incorrect shape' #ipdb.set_trace() if channel=='channel_last': channel_idx=2 assert y_true.shape[2]==len(dice_dict.keys()),'dictionary and prediction labels do not match' tmp_dict={tup_st[0]:dice_score(y_true[:,:,i],y_pred[:,:,i]) for i,tup_st in enumerate(dice_dict.items())} else: channel_idx=0 assert y_true.shape[0]==len(dice_dict.keys()),'dictionary and prediction labels do not match' tmp_dict={tup_st[0]:dice_score(y_true[i,:,:],y_pred[i,:,:]) for i,tup_st in enumerate(dice_dict.items())} return tmp_dict def dice_score(y_true_arr,y_pred_arr): """Return single f1 score for mask image for specific class. """ from sklearn.metrics import f1_score zero_sum_chk=np.count_nonzero(y_true_arr)+np.count_nonzero(y_pred_arr) if len(np.unique(y_true_arr))>2 or len(np.unique(y_pred_arr))>2: print('non binary masks') print(np.unique(y_true_arr)) print(np.unique(y_pred_arr)) if zero_sum_chk==0: return 'NaN no classes in image' else: #ipdb.set_trace() return f1_score(y_true_arr.astype(np.int64).flatten(), y_pred_arr.astype(np.int64).flatten(),average='binary') def cond_gen_dir(dst_dir_val): if os.path.isdir(dst_dir_val)==True: pass else: try: os.mkdir(dst_dir_val) except FileNotFoundError as e: print('creating a nested directory',dst_dir_val) os.makedirs(dst_dir_val) def gen_test_images(tmp_model,test_dataset,file_dict:dict,model_dir,mode,test_dataloder=None): """Generate testing images for analysis""" loss_func=file_dict['loss_type'] lrn_rate=file_dict['learn_rate'] epoch_no=str(file_dict['epoch_no']) btch_sz=str(file_dict['btch_sz']) dst_dir=os.path.join(model_dir,'predict_imgs',loss_func+'_btch_sz_'+btch_sz+'_lr_'+lrn_rate+'_epoch_no_'+epoch_no) #Generating new paths based on conditional path function for nested paths #ipdb.set_trace() dst_dir_logits=os.path.join(dst_dir,'prob_logits') dst_dir_imgs=os.path.join(dst_dir,'images') [cond_gen_dir(x) for x in [dst_dir_logits,dst_dir_imgs]] #Making a directory based on initial analysis if mode=='per_img_visualise': dice_score_lst=per_img_prediction_keras(test_dataset,tmp_model,dst_dir_imgs,dst_dir_logits,file_dict) else: dice_score_lst=per_batch_img_prediction_keras(test_dataset,test_dataloder, tmp_model,dst_dir_imgs,dst_dir_logits,file_dict) #Summary path and dataframe summary_path=os.path.join(dst_dir,'summary.csv') tmp_df=pd.DataFrame(dice_score_lst) tmp_df.to_csv(summary_path) return dice_score_lst def per_batch_img_prediction_keras(test_dataset,test_dataloder,tmp_model,dst_dir_imgs,dst_dir_logits,file_dict): dice_score_lst=[] #Squeezing predicted images down to pass testing. num_files=len(test_dataset) no_of_batches=len(test_dataloder) #Reseting test dataloader for each prediction to ensure consistent indexing test_dataloder.reset() img_nms_lst=test_dataloder.filenames pr_masks = tmp_model.predict_generator(test_dataloder,steps=no_of_batches) no_imgs=pr_masks.shape[0] #Creating logit binary mask for prediction writing logit file as well to file test_dataset_ids=test_dataset.ids for i in range(0,no_imgs): #Generating image dataset and mask #ipdb.set_trace() img_nm=os.path.basename(img_nms_lst[i]) dst_img_path=os.path.join(dst_dir_imgs,'predict_binary_'+img_nm) #Getting image mask from test dataset based on mask gt_mask_idx=[i for i in range(0,num_files) if test_dataset_ids[i]==img_nm][0] image,gt_mask,_=test_dataset[gt_mask_idx] #Converting softmax logit to binary logit pr_mask_sqz=write_logit_to_file(pr_masks[i,:,:,:],dst_dir_logits,img_nm) #Writing final output to file write_prediction_output(pr_masks[i,:,:,:],dst_dir_logits, img_nm,gt_mask,dst_img_path,image,file_dict) dice_loss_per_class=gen_full_dice_row(gt_mask,pr_mask_sqz,file_dict,img_nm) dice_score_lst.append(dice_loss_per_class) return dice_score_lst def per_img_prediction_keras(test_dataset,tmp_model,dst_dir_imgs,dst_dir_logits,file_dict): """Per image prediction script to write all images to file prediciting on a per image basis""" num_files=len(test_dataset) dice_score_lst=[] for i in range(0,num_files): #Generating image dataset and mask image,gt_mask,img_nm=test_dataset[i] dst_img_path=os.path.join(dst_dir_imgs,'predict_binary_'+img_nm) #Getting images setup for testing image = np.expand_dims(image, axis=0) #Squeezing predicted images down to pass testing. pr_mask = tmp_model.predict(image) pr_mask_sqz_logit=pr_mask.squeeze() #Creating logit binary mask for prediction writing logit file as well to file write_prediction_output(pr_mask_sqz_logit,dst_dir_logits, img_nm,gt_mask,dst_img_path,image,file_dict) dice_loss_per_class=gen_full_dice_row(gt_mask,pr_mask_sqz,file_dict,img_nm,file_dict) dice_score_lst.append(dice_loss_per_class) return dice_score_lst def write_prediction_output(pr_mask_sqz_logit,dst_dir_logits,img_nm, gt_mask,dst_img_path,image,file_dict): pr_mask_sqz=write_logit_to_file(pr_mask_sqz_logit,dst_dir_logits,img_nm) if file_dict['epoch_no']>96: #Writing line of predicted images to file for analysis and verification. visualize(dst_img_path, image=denormalize(image.squeeze()), gt_mask_l_kidney=gt_mask[:,:,0], pr_mask_l_kidney=pr_mask_sqz[:,:,0], gt_mask_liver=gt_mask[:,:,1], pr_mask_liver=pr_mask_sqz[:,:,1], gt_mask_r_kidney=gt_mask[:,:,2], pr_mask_r_kidney=pr_mask_sqz[:,:,2], gt_mask_spleen=gt_mask[:,:,3], pr_mask_spleen=pr_mask_sqz[:,:,3], gt_mask_background=gt_mask[:,:,4], pr_mask_background=pr_mask_sqz[:,:,4], ) def gen_full_dice_row(gt_mask:np.ndarray,pr_mask_sqz:np.ndarray,file_dict,img_nm)->dict: #Generate dice loss per image dice_loss_per_class=gen_per_class_dice_loss(gt_mask,pr_mask_sqz) dice_loss_per_class['file_nm']=img_nm dice_loss_per_class['loss_func']=file_dict['loss_type'] dice_loss_per_class['btch_sz']=float(file_dict['btch_sz']) dice_loss_per_class['learn_rate']=float(file_dict['learn_rate']) dice_loss_per_class['epoch_no']=float(file_dict['epoch_no']) return dice_loss_per_class def logit_binarize(logit_arr): """The purpose of this method is to perform softmax binarisation of logit array """ return np.where(logit_arr.max(axis=2,keepdims=True) == logit_arr,1,0).astype(np.float64) def write_logit_to_file(pr_mask_sqz_logit,dst_dir_logits,img_nm): pr_mask_sqz=logit_binarize(pr_mask_sqz_logit) dst_logit_path=os.path.join(dst_dir_logits,'predict_logit_'+os.path.splitext(img_nm)[0]) np.save(dst_logit_path,pr_mask_sqz_logit) return pr_mask_sqz def get_test_set_df(model_dir,test_data_dir, model_gnrl_param_dict,add_info,mode='Test', cls_wghts_perc_var=np.array([0.03987201, 0.36867433, 0.35872208, 0.2314718 , 0.00125978])): """The purpose of this method is to generate a """ #Generating assertion assert mode.lower() in ['test','batch_visualise','per_img_visualise'],'incorrect mode selection' #ipdb.set_trace() #Generating list of paths to models weights for analysis model_weights_dir=gen_subdir_file_lst(model_dir,'/*.h5') #Model weights directory #model_weights_dir=[x for x in model_weights_dir if x.find('focal')==-1] model_weights_dir=[x for x in model_weights_dir if x.find('wce')==-1] model_weights_dir=[x for x in model_weights_dir if x.find('cat_ce')==-1] tmp_dice_lst_2=['dice','0.1','0.0003'] model_weights_dir=[x for x in model_weights_dir if len([y for y in tmp_dice_lst_2 if x.find(y)!=-1])<2] #ipdb.set_trace() #Generating dataset for analysis preprocess_input = sm.get_preprocessing(model_gnrl_param_dict['backbone']) test_dataset=gen_test_dataset(test_data_dir,model_gnrl_params,preprocess_input,ret_img_path_var=True) if mode.lower()=='batch_visualise': test_dataloader = keras_flow_from_dir(test_data_dir,preprocess_input) elif mode.lower()=='test': test_dataset=gen_test_dataset(test_data_dir,model_gnrl_params,preprocess_input,ret_img_path_var=False) test_dataloader = CustomDataloder(test_dataset, batch_size=1, shuffle=False) #ipdb.set_trace() #Final json list to return for analysis final_lst=[] for fl_path in model_weights_dir: print(fl_path) #ipdb.set_trace() #File path dictionayr information for analysis file_dict,split_vals=get_file_info(fl_path,add_info) #ipdb.set_trace() #Generating specific parameters for laoding the model based on file nam start_model=time.time() #Load temporary model for analysis tmp_model=gen_test_model(model_gnrl_param_dict, float(file_dict['learn_rate']), file_dict['loss_type'],fl_path,cls_wghts_perc_var) finish_model=time.time() #Test model based on dataset and analysis if mode.lower()=='test': tmp_score_dict=gen_test_scores(tmp_model,test_dataloader,model_gnrl_params['metrics']) file_dict.update(tmp_score_dict) final_lst.append(file_dict) else: #ipdb.set_trace() start=time.time() tmp_lst=gen_test_images(tmp_model,test_dataset,file_dict,model_dir,mode,test_dataloader) finish=time.time() print('total time loading model:',finish_model-start_model) print('total time predicting images:',finish-start) #Merging list of dictionaries for analysis final_lst=final_lst+tmp_lst #print(pd.DataFrame.from_dict(tmp_lst[:10])) K_b.clear_session() return final_lst ###Output _____no_output_____ ###Markdown Load initial parameters for analysis ###Code #Loading arguments for analysis #'efficientnetb3'densenet121 #BATCH_SIZE = 3 CLASSES = ['l_kidney','liver','r_kidney','spleen'] activation = 'sigmoid' if len(CLASSES) == 1 else 'softmax' metrics = [sm.metrics.IOUScore(threshold=0.5), sm.metrics.FScore(threshold=0.5)] cls_wghts_perc=np.array([0.03987201, 0.36867433, 0.35872208, 0.2314718 , 0.00125978]) #Getting keys for different analysis types add_info=[('learn_rate',['0.0003','0.001','0.01','0.1']), ('samp_sz',['500','250','50']),('btch_sz',['3','7']), ('loss_type',['dice','focal','wce'])] model_gnrl_params={'backbone':'resnet101','n_classes':len(CLASSES)+1, 'metrics':metrics,'input_shape_N':1, 'activation_type':activation,'classes':['l_kidney','liver','r_kidney','spleen']} #Generating weights directory for iterating for analysis #Directory lists model_dir='/home/ec2-user/SageMaker/data/unet_data_aug_modified_results/data_aug_all_param_reducd_50perc/cat_focal_loss/btch_sz_3/lr_0.001/final_epch_wghts' test_data_dir='/home/ec2-user/SageMaker/data/250_imgs/merge/NIFTI_MR_256x256_png_256grey_lvl/t1dual_inphase' preprocess_input = sm.get_preprocessing(model_gnrl_params['backbone']) trl_ls=[] for vals in model_weights_dir: tmp_dict={} val_split=vals.split('/') tmp_dict['lrn_rate']=val_split[-3] tmp_dict['btch_sz']=val_split[-4] tmp_dict['loss']=val_split[-5] trl_ls.append(tmp_dict) trl_df=pd.DataFrame(trl_ls) #trl_df.drop_duplicates(inplace=True) trl_df.shape model_results=get_test_set_df(model_dir,test_data_dir, model_gnrl_params,add_info) model_df=pd.DataFrame.from_dict(model_results) model_df.to_csv('unet_model_test_data_summary_results_05_11_2019.csv') model_df.sort_values('f1-score',ascending=False) ###Output _____no_output_____ ###Markdown Visualisation of results Testing on single set of parameters ###Code fl_path='/home/ec2-user/SageMaker/Masters-Thesis-UNet-repository/jupyter_notebooks/weights_history_full/wce_loss/btch_sz_3/lr_0.001/weights/t1dual_inphase_all_orgs_grey_lvl_256_optm_Adam_loss_wce_loss_trn_samp_sz_250_btch_sz_3_lr_0.001_time_2019-11-17_00000006.h5' loss='focal' #gen_test_model(model_gnrl_param:dict,lrn_rate,total_loss,wghts_dir:str,cls_wghts_perc=None) tmp_model=gen_test_model(model_gnrl_params, 0.003, loss,fl_path) #test_dataset_visualise=gen_test_dataset(test_data_dir,model_gnrl_params,preprocess_input,) tmp_model.count_params() ###Output _____no_output_____ ###Markdown Testing across all parameters please check gen_test_set_df for list filters however! ###Code model_dir='/home/ec2-user/SageMaker/data/unet_data_aug_modified_results/data_aug_all_param_reducd_25perc/cat_focal_loss/btch_sz_3/final_epch_wghts' tmp_subdir_lst=['50','250','500'] for file_sz in tmp_subdir_lst: model_dir_gnrl=os.path.join(model_dir,file_sz+'_imgs') model_results=get_test_set_df(model_dir_gnrl,test_data_dir, model_gnrl_params,add_info,mode='batch_visualise') ###Output _____no_output_____ ###Markdown Comparing plots of predicted images to masks to determine if kidneys predict more kidneys and vice versa Generating initial dataset for analysis ###Code src_logit_dir='/home/ec2-user/SageMaker/data/unet_predict_logits/500_imgs/500_img/predict_imgs/focal_btch_sz_3_lr_0.0003_epoch_no_99/prob_logits' src_mask_dir='/home/ec2-user/SageMaker/data/500_imgs/' #Getting the logit files for analysis logit_dir_fl=list(pathlib.Path(src_logit_dir).rglob('*.npy')) #Substirng to filter for masks sub_str_chk=['/masks/','/t1dual_inphase/'] lr_rates=['lr_0.001','lr_0.0003','lr_0.01','lr_0.1'] loss_type=['focal','dice'] from sklearn.metrics import precision_recall_fscore_support #Class dictionaries for anlysis org_idx={'l_kidney':0,'liver':1,'r_kidney':2,'spleen':3,'background':-1} cls_dict = {'background':0,'liver':63,'r_kidney':126,'l_kidney':189,'spleen':252} cls_int_inv_dict={org_idx[k]:v for k,v in cls_dict.items()} classes=['l_kidney','liver','r_kidney','spleen'] class_values = [cls_dict[cls.lower()] for cls in classes] #Getting mask files for analysis mask_raw_fl=list(pathlib.Path(src_mask_dir).rglob('*.png')) #Creating basename dictionary for file list logit_dir_dict={os.path.splitext(os.path.basename(x))[0]:x for x in logit_dir_fl if str(x).find(loss_type[0])!=-1} #Finding only t1dual images with masks for analysis mask_dir_fl=[x for x in mask_raw_fl if all(str(x).find(y)!=-1 for y in sub_str_chk)] #Creating basename file name dictionary for string matching. bs_nm_msk_dict_pth={os.path.splitext(os.path.basename(x))[0]:x for x in mask_dir_fl} cd /home/ec2-user/SageMaker/Masters-Thesis-UNet-repository/jupyter_notebooks final_src_dst_dict={} for k,v in logit_dir_dict.items(): k_mask_str=k.replace('predict_logit_','') #Getting final mask directory and logit directory together to run analysis against one another try: final_src_dst_dict[v]=bs_nm_msk_dict_pth[k_mask_str] except KeyError as e: print('key not found for:',k_mask_str) final_src_dst_dict ###Output _____no_output_____ ###Markdown Generating F1 score for analysis ###Code final_lst=[] for logit_pth,mask_file_pth in final_src_dst_dict.items(): #Get arrays loaded up logit_arr=np.load(logit_pth) logit_arr=logit_binarize(logit_arr) # read data mask = imageio.imread(mask_file_pth) mask=resize_img_PIL(mask) mask=gen_binary_mask(mask,class_values) for org_nm,idx in org_idx.items(): if np.sum((mask[:,:,idx],logit_arr[:,:,idx]))!=0: #print('mask_value',np.sum(mask[:,:,idx])) #print('logit_value',np.sum(logit_arr[:,:,idx])) tmp_prec,tmp_recall,tmp_f1,tmp_support=precision_recall_fscore_support(mask[:,:,idx].flatten(), logit_arr[:,:,idx].flatten(), average='binary') tmp_tp,tmp_fp,tmp_tn,tmp_fn=gen_tp_fp_fp_fn(mask[:,:,idx].flatten(),logit_arr[:,:,idx].flatten()) else: tmp_prec,tmp_recall,tmp_f1,tmp_support=('NaN','NaN','NaN','NaN') tmp_tp,tmp_fp,tmp_tn,tmp_fn=('NaN','NaN','NaN','NaN') #Get temporary statical dictionary tmp_stat_dict=gen_pred_row(mask_file_pth,logit_pth,org_nm, tmp_prec,tmp_recall,tmp_f1,tmp_support, tmp_tp,tmp_fp,tmp_tn,tmp_fn,loss_type='focal',lr_rate=0.001,samp_sz=500) final_lst.append(tmp_stat_dict) final_df=pd.DataFrame(final_lst) final_df.to_excel('unet_focal_loss_f1_score_per_class_500_imgs_data.xlsx') import pickle with open('/home/ec2-user/SageMaker/data/per_pat_gnrl_info/per_pat_slc_no.pickle','rb') as fb: per_pat_per_slc_dict=pickle.load(fb) per_pat_per_slc_dict={int(k):int(v) for k,v in per_pat_per_slc_dict.items()} def gen_perc_slc_grad(pat_no,slc_no,slc_dict): try: total_no_slcs=slc_dict[pat_no] except KeyError as e: ipdb.set_trace() return slc_no/total_no_slcs final_df['slice_no']=final_df.patient.str.split('_',expand=True)[7] final_df['pat_id']=final_df.patient.str.extract('(\d+)')[0] cols_num_conv=['pat_id','false_positive','false_negative','true_positive','true_negative','pat_id','slice_no', 'precision', 'recall','F1_score'] final_df[cols_num_conv] = final_df[cols_num_conv].apply(pd.to_numeric, errors='coerce') final_df['perc_slice_no'] = final_df.apply(lambda x: gen_perc_slc_grad(x.pat_id, x.slice_no, per_pat_per_slc_dict), axis=1) #slice_test df results final_df['perc_slice_no'] = final_df['perc_slice_no'].apply(pd.to_numeric, errors='coerce') final_df_test=final_df[final_df.pat_id.isin([2,3,8,32,39])] final_df[final_df.F1_score==0].groupby(['organ_type'])['false_negative'].sum() final_df_test.organ_type.unique() pwd final_df[final_df.F1_score==0].groupby(['organ_type'])['false_negative'].sum() #fig,axs=plt.subplots(figsize=(20,20)) #sns.set(font_scale=1.1) org_str='spleen' g=sns.jointplot(data=final_df_test[(final_df_test.organ_type==org_str)], x='perc_slice_no',y='F1_score',kind='kde',ylim=(0,1),xlim=(0,1)) g.savefig('u_net_focal_loss_lr_0.001_samp_sz_50_'+org_str+'_f1score_wrt_per_slice_no_t1dual.jpeg') ###Output _____no_output_____ ###Markdown Kidney specific scripting for dice scores ###Code kidney_mask_concat=merge_arrs(mask[:,:,0],mask[:,:,2]) kidney_logit_concat=merge_arrs(logit_arr[:,:,0],logit_arr[:,:,2]) tmp_prec,tmp_recall,tmp_f1,tmp_support=precision_recall_fscore_support(kidney_mask_concat.flatten(), kidney_logit_concat.flatten(), average='binary') tmp_stat_dict=gen_pred_row(mask_file_pth,logit_pth,'both_kidneys', tmp_prec,tmp_recall,tmp_f1,tmp_support) final_lst.append(tmp_stat_dict) #Right kidney predicting left kidney tmp_prec,tmp_recall,tmp_f1,tmp_support=precision_recall_fscore_support(mask[:,:,0].flatten(), logit_arr[:,:,2].flatten(), average='binary') tmp_stat_dict=gen_pred_row(mask_file_pth,logit_pth,'right_kidney_pred_left', tmp_prec,tmp_recall,tmp_f1,tmp_support) final_lst.append(tmp_stat_dict) #Left kidney predicting right kidney tmp_prec,tmp_recall,tmp_f1,tmp_support=precision_recall_fscore_support(mask[:,:,2].flatten(), logit_arr[:,:,0].flatten(), average='binary') final_df.to_csv('unet_dice_lr_0.0003_epch_69_per_organ_prec_recall_f1score.csv') final_df[['F1_score','precision','recall']]=final_df[['F1_score','precision','recall']].apply(pd.to_numeric, errors='coerce') final_df_agg=final_df.groupby('organ_type')[['F1_score','precision','recall']].mean() final_df_agg.columns=['Dice_score','Precision','Recall'] final_df_agg.to_csv('aggregate_unet_dice_lr_0.0003_epch_69__dice_prec_recall_table.csv') final_df_agg ###Output _____no_output_____ ###Markdown Generating logit to actual image predictions side by side. ###Code #'SegCaps_multilabels_2019-11-28_11-24-37 file_name='SegCaps_multilabels_2019-11-09_01-25-53' src_logit_dir=os.path.join('/home/ec2-user/SageMaker/data/seg_caps_predict_logits',file_name) src_mask_dir='/home/ec2-user/SageMaker/data/500_imgs/' dst_path=os.path.join('/home/ec2-user/SageMaker/results_segcaps_predict_imgs',file_name) #Getting the logit files for analysis logit_dir_fl=list(pathlib.Path(src_logit_dir).rglob('*.mha')) #Substirng to filter for masks sub_str_chk_mask=['/masks/','/t1dual_inphase/'] #Substirng to filter for images sub_str_chk_img=['/images/','/t1dual_inphase/'] #learning rate and model names to filter logits lr_rates=['lr_0.001','lr_0.0003','lr_0.01','lr_0.1'] segcap_model=['SegCaps_multilabels_2019-11-09_01-25-53','SegCaps_multilabels_2019-11-27_20-02-58', 'SegCaps_multilabels_2019-11-28_11-24-37'] #Class dictionaries for anlysis org_idx_unet={'l_kidney':0,'liver':1,'r_kidney':2,'spleen':3,'background':4} org_idx_segcaps={'l_kidney':2,'liver':1,'r_kidney':3,'spleen':4,'background':0} cls_dict = {'background':0,'liver':63,'r_kidney':126,'l_kidney':189,'spleen':252} #cls int dict defined for fdining maximum arrays cls_int_inv_dict_unet={org_idx_unet[k]:v for k,v in cls_dict.items()} cls_int_inv_dict_segcaps={org_idx_segcaps[k]:v for k,v in cls_dict.items()} classes=['l_kidney','liver','r_kidney','spleen'] class_values = [cls_dict[cls.lower()] for cls in classes] #Getting mask files for analysis mask_raw_fl=list(pathlib.Path(src_mask_dir).rglob('*.png')) #Creating basename dictionary for file list logit_dir_dict={os.path.splitext(os.path.basename(x))[0]:x for x in logit_dir_fl if str(x).find(file_name)!=-1} #Finding only t1dual images with masks for analysis mask_dir_fl=[x for x in mask_raw_fl if all(str(x).find(y)!=-1 for y in sub_str_chk_mask)] #Finding image substring match img_dir_fl=[x for x in mask_raw_fl if all(str(x).find(y)!=-1 for y in sub_str_chk_img)] #Creating basename file name dictionary for string matching. bs_nm_msk_dict_pth={os.path.splitext(os.path.basename(x))[0]:x for x in mask_dir_fl} bs_nm_img_dict_pth={os.path.basename(x):x for x in img_dir_fl} final_src_dst_dict={} for k,v in logit_dir_dict.items(): k_mask_str=k.replace('_prediction','') #Getting final mask directory and logit directory together to run analysis against one another try: final_src_dst_dict[v]=bs_nm_msk_dict_pth[k_mask_str] except KeyError as e: print('key not found for:',k_mask_str) plt.imshow(logit_arr[:,:,0]) plt.hist(logit_arr[:,:,0].flatten()) plt.xlabel('probability map value') plt.ylabel('occurences') concat_arr_logit_background=None for logit_pth,mask_file_pth in final_src_dst_dict.items(): #Get arrays loaded up logit_arr,_=load(str(logit_pth)) back_arr=logit_arr[:,:,0].flatten() if concat_arr_logit_background is None: concat_arr_logit_background=back_arr else: concat_arr_logit_background=np.concatenate((concat_arr_logit_background,back_arr)) plt.hist(concat_arr_logit_background,density=True,bins=20) plt.xticks(np.arange(0, 1, step=0.05),rotation=45) plt.xlabel('probability map value') plt.ylabel('occurences') final_src_dst_dict #Index slicing dictionary for visualisation. first index in tuple is logit 2ns index is mask. mask_logit_idx_slc_segcaps={'background':(0,4),'l_kidney':(3,0),'r_kidney':(2,2),'liver':(1,1),'spleen':(4,3)} mask_logit_idx_slc_unet={'background':(4,4),'l_kidney':(0,0),'r_kidney':(2,2),'liver':(1,1),'spleen':(3,3)} final_lst=[] for logit_pth,mask_file_pth in final_src_dst_dict.items(): #Get arrays loaded up logit_arr,_=load(str(logit_pth)) break logit_arr=logit_binarize(logit_arr) #logit_arr=reset_logit_int(logit_arr,cls_int_inv_dict_segcaps) pr_mask=np.rot90(logit_arr,3) #pr_mask_arr=logit_binarize(np.array(rot_img)) #tmp_img_path img_nm=os.path.basename(mask_file_pth) tmp_img=imageio.imread(bs_nm_img_dict_pth[img_nm]) dst_img_path=os.path.join(dst_path,'binary_predict_'+img_nm) # read data mask = imageio.imread(mask_file_pth) mask=resize_img_PIL(mask) gt_mask=gen_binary_mask(mask,class_values) visualize(dst_img_path, image=tmp_img, gt_mask_l_kidney=gt_mask[:,:,mask_logit_idx_slc_segcaps['l_kidney'][1]], pr_mask_l_kidney=pr_mask[:,:,mask_logit_idx_slc_segcaps['l_kidney'][0]], gt_mask_liver=gt_mask[:,:,mask_logit_idx_slc_segcaps['liver'][1]], pr_mask_liver=pr_mask[:,:,mask_logit_idx_slc_segcaps['liver'][0]], gt_mask_r_kidney=gt_mask[:,:,mask_logit_idx_slc_segcaps['r_kidney'][1]], pr_mask_r_kidney=pr_mask[:,:,mask_logit_idx_slc_segcaps['r_kidney'][0]], gt_mask_spleen=gt_mask[:,:,mask_logit_idx_slc_segcaps['spleen'][1]], pr_mask_spleen=pr_mask[:,:,mask_logit_idx_slc_segcaps['spleen'][0]], gt_mask_background=gt_mask[:,:,mask_logit_idx_slc_segcaps['background'][1]], pr_mask_background=pr_mask[:,:,mask_logit_idx_slc_segcaps['background'][0]], ) for org_nm,idx in org_idx_segcaps.items(): if np.sum((gt_mask[:,:,idx],pr_mask[:,:,idx]))!=0: #print('mask_value',np.sum(mask[:,:,idx])) #print('logit_value',np.sum(logit_arr[:,:,idx])) tmp_prec,tmp_recall,tmp_f1,tmp_support=precision_recall_fscore_support(gt_mask[:,:,idx].flatten(), pr_mask[:,:,idx].flatten(), average='binary') tmp_tp,tmp_fp,tmp_tn,tmp_fn=gen_tp_fp_fp_fn(gt_mask[:,:,idx].flatten(),pr_mask[:,:,idx].flatten()) else: tmp_prec,tmp_recall,tmp_f1,tmp_support=('NaN','NaN','NaN','NaN') tmp_tp,tmp_fp,tmp_tn,tmp_fn=('NaN','NaN','NaN','NaN') #Get temporary statical dictionary tmp_stat_dict=gen_pred_row(mask_file_pth,logit_pth,org_nm, tmp_prec,tmp_recall,tmp_f1,tmp_support, tmp_tp,tmp_fp,tmp_tn,tmp_fn,loss_type='WCE',lr_rate=0.1,samp_sz=250) final_lst.append(tmp_stat_dict) final_df_segcaps=pd.DataFrame(final_lst) final_df_segcaps.to_csv(os.path.join(dst_path,file_name+'df_f1score_re_prec_df.csv')) ###Output _____no_output_____ ###Markdown Confusion matrix generation ###Code from sklearn.metrics import precision_recall_fscore_support y_true_arr=None y_pred_arr=None for logit_pth,mask_file_pth in final_src_dst_dict.items(): #Get arrays loaded up logit_arr=np.load(logit_pth) logit_arr=logit_binarize(logit_arr) logit_arr=reset_logit_int(logit_arr,cls_int_inv_dict) logit_arr=comp_logit(logit_arr) y_pred_arr=concat_flat_arr(logit_arr.flatten(),y_pred_arr) # read data mask = imageio.imread(mask_file_pth) mask=resize_img_PIL(mask) y_true_arr=concat_flat_arr(mask.flatten(),y_true_arr) #Generating temporary confusion matrix tmp_conf_mat=ConfusionMatrix(y_true_arr,y_pred_arr) tmp_conf_mat_df=tmp_conf_mat.to_dataframe() #rename analysis tmp_conf_mat_df=tmp_conf_mat.to_dataframe() tmp_conf_mat_df.rename({0.0:'Background', 63:'liver', 126:'r_kidney', 189:'l_kidney', 252:'spleen'},axis=0,inplace=True) tmp_conf_mat_df.rename({0.0:'Background', 63:'liver', 126:'r_kidney', 189:'l_kidney', 252:'spleen'},axis=1,inplace=True) tmp_conf_mat_df.to_csv('unet_focal_loss_lr_0.001_epch_no99_samp_sz_500_conf_mat.csv') tmp_conf_mat_df pwd def concat_flat_arr(arr:np.ndarray,concat_arr)->np.ndarray: """The purpose of this method is to concat an array together with an arra yor none type primarily this function is used as an aggregatoin function at the end of a for loop. """ if concat_arr is None: return arr else: #ipdb.set_trace() concat_arr=np.concatenate((concat_arr,arr)) return concat_arr def reset_logit_int(logit:np.ndarray,cls_lbl_dict)->np.ndarray: """The purpose of this method is to compress a logit down into a single layer array for analysis """ for k,v in cls_lbl_dict.items(): logit[:,:,k]=np.where(logit[:,:,k]==1,v,0) return logit def comp_logit(logit:np.ndarray)->np.ndarray: return np.amax(logit,axis=2) def gen_pred_row(mask_file_pth:str,logit_pth:str, org_nm:str,tmp_prec,tmp_recall,tmp_f1, tmp_support,tmp_tp,tmp_fp,tmp_tn,tmp_fn, loss_type=None,lr_rate=None,samp_sz=None)->dict: final_dict={'patient':os.path.splitext(os.path.basename(mask_file_pth))[0],'samp_sz':samp_sz, 'loss':loss_type, 'learn_rate':lr_rate, 'organ_type':org_nm, 'precision':tmp_prec,'recall':tmp_recall,'F1_score':tmp_f1, 'support_no':tmp_support,'true_positive':tmp_tp,'false_positive':tmp_fp, 'true_negative':tmp_tn,'false_negative':tmp_fn} if loss_type is None: final_dict['loss']=[x for x in loss_type if str(logit_pth).find(x)!=-1][0] if lr_rate is None: final_dict['learn_rate']=[x for x in lr_rates if str(logit_pth).find(x)!=-1][0] return final_dict def gen_tp_fp_fp_fn(y_true,y_pred): #Y true y predict true positive and negatives pos_y_true=(y_true==1) pos_y_pred=(y_pred==1) neg_y_true=(y_true==0) neg_y_pred=(y_pred==0) #Generating false positive values true_pos=len(np.where(pos_y_true&pos_y_pred)[0]) false_pos=len(np.where(pos_y_pred&neg_y_true)[0]) #Generating true negatives and false negatives true_neg=len(np.where(neg_y_true&neg_y_pred)[0]) false_neg=len(np.where(neg_y_pred&pos_y_true)[0]) return true_pos,false_pos,true_neg,false_neg def gen_binary_mask(mask:np.ndarray,class_values:list,reord_stack=None)->np.ndarray: # extract certain classes from mask (e.g. cars) masks = [(mask == v) for v in class_values] mask = np.stack(masks, axis=-1).astype('float') # add background if mask is not binary if mask.shape[-1] != 1: background = 1 - mask.sum(axis=-1, keepdims=True) mask = np.concatenate((mask, background), axis=-1) if reord_stack is None: return mask else: mask=np.transpose(mask,reord_stack) def merge_arrs(arr1,arr2): return np.where(arr2>0,1,arr1) ###Output _____no_output_____

Lectures/Lecture10_AdvancedTopics/notebook.ipynb

###Markdown Introduction to CNN (Convolutional Neural Network) May 1 2021 Hosted by and maintained by the [Student Association for Applied Statistics (SAAS)](https://saas.berkeley.edu).Created by Chinmay Gharpure, Zoe Liu, Ritvik Iyer, Jessica Wang, Harry Dong, Derek Cai, Matt Moon Table of Contents1. [What is a Convolutional Neural Net?](cnn_intro) 1. [Why use CNNs over MLPs?](cnn_mlp)2. [CNN Layers](layers) 1. [Convolutional layers](cnn_layers) 2. [Pooling layers](pooling_layers)3. [Key terms](key_terms)4. [Convolution Demo](demo)5. [Example of CNN Architecture](cnn_arch)6. [Classifying MNIST with CNN](mnist)7. [Summary](summary) What is a Convolutional Neural Net? One important class of neural net architectures is convolution neural networks. Convolutional neural networks, or CNNs, are a type of neural network that can take in an input image, recognize particular patterns in the image like edge locations, and use the differences in patterns to differentiate images from each other. This architecture is very popular in problems involving images, such as object recognition and image classification, although there are many other applications too. We will primarily use image inputs as the running example. Why use CNNs over MLPs?If we consider each pixel to be a feature, we can consider an image to be a matrix of numeric values. In that case, **why can't we flatten the matrix and pass it into a multi-layer perceptron to perform tasks involving images?**The answer is that **regular neural networks like MLPs don't scale well with image tasks**. Let's consider the example of a 32x32x3 image (32 pixels wide, 32 pixels high, and 3 color channels). In this case, we would need to find 32 x 32 x 3 = 3072 weights. However, if we would like to use high quality images, the number of weights we would need to find quickly balloons in value. This makes normal neural networks extremely weighty and computationally expensive. In addition, patterns in images are usually not recognizable at a pixel level of granuarity. When you look at a a picture of a dog, you likely recognize it as a dog not by looking at each individual hair, but by looking at the placement and shape of its eyes, nose, and mouth. Similarly, CNNs help us capture more general patterns in images like edges, textures, and visual patterns. CNN Layers Just like multi-layer perceptrons, convolutional neural networks are made up of layers that do specialized processing on the input. Today, we'll focus on two of the most important layer types found in CNNs: **convolutional layers** and **pooling layers**. ChannelsAn important concept we need to understand before we talk about the different layers is channels. Channels refer to the color channels present in the image. In a normal color image, there are three color channels present: red, green, and blue. However, images don't have to be constrained to RBG. For example, CMYK images that have four color channels: cyan, magenta, yellow, and black. A color image can be represented as a matrix of dimensions $width×height×\channels$, and we convolve over each channel separately. As we go deeper into the network and the number of channels increase, the channels become more abstract and are hard to place a color on each. As such, it may be helpful to think of images as 3-D matrices, also known as tensors, and as we go through each layer of the network, we are operating on this tensor to create new tensors of possibly different shapes and sizes. Basically, try not to think about colors when dealing with CNNs. Convolutions, Filters, and Convolutional LayersA **convolution** operation is an element wise matrix multiplication operation, where one of the matrices is the image, and the other is the **filter** (also called kernel or feature detector) that turns the image into something else. A filter is a learnable matrix that we "slide", or convolve, across the image. As we do so, perform the dot product between the image and the filter. The output of this is the final convoluted image.+ input (\[input height] x \[input width] x \[input channels])+ filters (\[filter height] x \[filter width] x \[input channels] x \[output channels])+ output (\[output height] x \[output width] x \[output channels])In the example below, the filter is the yellow sliding window and its value is $$\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}$$.**Convolutional layers**, which consist of convolution operations performed on the entire image, make up one. ofthe most important parts of a CNN architecture  Pooling LayersFor fully connected networks discussed in the previous lecture, we had nonlinearities between each fully connected layer. Similarly, convolutional layers are linear operations, so we should also have nonlinearities between them as well. These nonlinearity layers for CNNs are known as pooling layers. It operates similarly to a convolutional layer in that we slide a window like in the previous example and we apply a function to that window to output a scalar. A couple popular choices are max pooling (where we output the max value in that window) and average pooling (where we output the average of all values in the window). We do this for each channel, so the number of channels is preserved.+ input (\[input height] x \[input width] x \[input channels])+ pooling window (\[window height] x \[window width])+ output (\[output height] x \[output width] x \[input channels])Here is an example of max pooling: More Key Terms for CNN In order to comprehend convolutional neural nets, we also need to understand some common terms. PaddingYou may want to add borders to your inputs, typically some constant such as 0. The purpose of this is to prevent our outputs from shrinking too much after each layer. For instance you could 0-pad a 5x5x3 image by width 2, which would result in the same image but bordered by 2 layers of 0's (a 9x9x3 image). Another example is shown below.  StrideInstead of sliding the window in convolutional and pooling layers one pixel at a time, we can choose to apply the filter or pooling function after each stride of length $k$. This applies to both columns and rows. With strides, you can greatly reduce the amount of computation at this layer, but taking too big of a stride will irrecoverably lose a lot of crucial information. As an example of strides, applying a 3x3x1x1 filter to a 5x5x1 image would typically get us a 3x3x1 output, but with a stride of 2, the output would be a 2x2x1 since we take two steps each time we apply a convolution/pooling. Another example is shown below. DilationWe can add spaces between each element in the filter. This allows the filter to have a more global view of the picture. CNN Convolution DemoLet's take a closer look at how convolutions are performed on a simple 7x7x3 image with two filters and padding: https://cs231n.github.io/convolutional-networks/ Example of CNN Architecture  Here, we start with an 36x36 RGB image. Next, we apply filters of dimensions 11x11x3x9 (recall \[filter height] x \[filter width] x \[input channels] x \[output channels]). The result output is 26x26x9 (recall \[output height] x \[output width] x \[output channels]). Notice how the height and width of the output is smaller than the input. Can you reason why? **Hint**: Look at the simple single channel example from before and see how we go from a 5x5 to a 3x3.From a 26x26x9, we get a 12x12x9 after taking a max pool of stride 2. Can you find the stride lengths of convolutional layer 2 and max pooling layer 2, assuming no padding and dilations?**Hint**: It may be helpful to draw it out.Once we have a small enough dimensions (in this case it's a 2x2x3), we can flatten it into a vector (in this case it's a 12x1 vector) which we can feed into a fully connected network. Example of a More Complex CNNBelow, we have the architecture of the VGG model. It takes in a 224x244 RGB input image and returns the predicted image class among 1000 classes. VGG and similarly complex models are exceptionally expensive to train, so do not try to build this and run it unprepared--your computer will be very sad. See if you can understand what this model does.  Interactive VisualizationLet's look at an interactive visualization of a CNN classifying numbers for a handwritten digit. Visualization: https://www.cs.ryerson.ca/~aharley/vis/conv/ MNIST example in PytorchHere, we will implement a CNN to classify handwritten digits from the [MNIST dataset](https://keras.io/api/datasets/mnist/) of grayscale images. ###Code !wget www.di.ens.fr/~lelarge/MNIST.tar.gz !tar -zxvf MNIST.tar.gz import torch import torchvision from torchvision import datasets, transforms from torchvision.datasets import MNIST # Set some parameters n_epochs = 3 batch_size_train = 64 batch_size_test = 1000 learning_rate = 0.01 momentum = 0.5 log_interval = 10 random_seed = 1 torch.backends.cudnn.enabled = False torch.manual_seed(random_seed) # Define some preprocessing steps transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.1307,), (0.3081,))]) train_loader = torch.utils.data.DataLoader(MNIST(root = './', train=True, download=True, transform=transform),batch_size=batch_size_train) test_loader = torch.utils.data.DataLoader(MNIST(root = './', train=False, download=True, transform=transform),batch_size=batch_size_test) ###Output --2021-04-28 02:17:43-- http://www.di.ens.fr/~lelarge/MNIST.tar.gz Resolving www.di.ens.fr (www.di.ens.fr)... 129.199.99.14 Connecting to www.di.ens.fr (www.di.ens.fr)|129.199.99.14|:80... connected. HTTP request sent, awaiting response... 302 Found Location: https://www.di.ens.fr/~lelarge/MNIST.tar.gz [following] --2021-04-28 02:17:43-- https://www.di.ens.fr/~lelarge/MNIST.tar.gz Connecting to www.di.ens.fr (www.di.ens.fr)|129.199.99.14|:443... connected. HTTP request sent, awaiting response... 200 OK Length: unspecified [application/x-gzip] Saving to: ‘MNIST.tar.gz.8’ MNIST.tar.gz.8 [ <=> ] 33.20M 13.3MB/s in 2.5s 2021-04-28 02:17:46 (13.3 MB/s) - ‘MNIST.tar.gz.8’ saved [34813078] MNIST/ MNIST/raw/ MNIST/raw/train-labels-idx1-ubyte MNIST/raw/t10k-labels-idx1-ubyte.gz MNIST/raw/t10k-labels-idx1-ubyte MNIST/raw/t10k-images-idx3-ubyte.gz MNIST/raw/train-images-idx3-ubyte MNIST/raw/train-labels-idx1-ubyte.gz MNIST/raw/t10k-images-idx3-ubyte MNIST/raw/train-images-idx3-ubyte.gz MNIST/processed/ MNIST/processed/training.pt MNIST/processed/test.pt ###Markdown Let's take a look at the MNIST dataset ###Code examples = enumerate(test_loader) batch_idx, (example_data, example_targets) = next(examples) example_data.shape ###Output _____no_output_____ ###Markdown **Question: Looking at the cell above, can you interpret those tensor dimensions?****Answer: ** ###Code import matplotlib.pyplot as plt fig = plt.figure() for i in range(6): plt.subplot(2,3,i+1) plt.tight_layout() plt.imshow(example_data[i][0], cmap='gray', interpolation='none') plt.title("Ground Truth: {}".format(example_targets[i])) plt.xticks([]) plt.yticks([]) import torch.nn as nn import torch.nn.functional as F import torch.optim as optim # Set the network architecture class Net(nn.Module): def __init__(self): super(Net, self).__init__() self.conv1 = nn.Conv2d(1, 10, kernel_size=5) self.conv2 = nn.Conv2d(10, 20, kernel_size=5) self.conv2_drop = nn.Dropout2d() self.fc1 = nn.Linear(320, 50) self.fc2 = nn.Linear(50, 10) def forward(self, x): x = F.relu(F.max_pool2d(self.conv1(x), 2)) x = F.relu(F.max_pool2d(self.conv2_drop(self.conv2(x)), 2)) x = x.view(-1, 320) x = F.relu(self.fc1(x)) x = F.dropout(x, training=self.training) x = self.fc2(x) return F.log_softmax(x) network = Net() optimizer = optim.SGD(network.parameters(), lr=learning_rate, momentum=momentum) train_losses = [] train_counter = [] test_losses = [] test_counter = [i*len(train_loader.dataset) for i in range(n_epochs + 1)] def train(epoch): network.train() for batch_idx, (data, target) in enumerate(train_loader): optimizer.zero_grad() output = network(data) loss = F.nll_loss(output, target) loss.backward() optimizer.step() if batch_idx % log_interval == 0: print('Train Epoch: {} [{}/{} ({:.0f}%)]\tLoss: {:.6f}'.format( epoch, batch_idx * len(data), len(train_loader.dataset), 100. * batch_idx / len(train_loader), loss.item())) train_losses.append(loss.item()) train_counter.append( (batch_idx*64) + ((epoch-1)*len(train_loader.dataset))) def test(): network.eval() test_loss = 0 correct = 0 with torch.no_grad(): for data, target in test_loader: output = network(data) test_loss += F.nll_loss(output, target, size_average=False).item() pred = output.data.max(1, keepdim=True)[1] correct += pred.eq(target.data.view_as(pred)).sum() test_loss /= len(test_loader.dataset) test_losses.append(test_loss) print('\nTest set: Avg. loss: {:.4f}, Accuracy: {}/{} ({:.0f}%)\n'.format( test_loss, correct, len(test_loader.dataset), 100. * correct / len(test_loader.dataset))) test() for epoch in range(1, n_epochs + 1): train(epoch) test() fig = plt.figure() plt.plot(train_counter, train_losses, color='blue') plt.scatter(test_counter, test_losses, color='red') plt.legend(['Train Loss', 'Test Loss'], loc='upper right') plt.xlabel('Number of Training Examples') plt.ylabel('Negative Log Likelihood') with torch.no_grad(): output = network(example_data) fig = plt.figure() for i in range(6): plt.subplot(2,3,i+1) plt.tight_layout() plt.imshow(example_data[i][0], cmap='gray', interpolation='none') plt.title("Prediction: {}".format( output.data.max(1, keepdim=True)[1][i].item())) plt.xticks([]) plt.yticks([]) ###Output _____no_output_____

10. Old Project/Projects/Market Regimes/Функция ChangeFinder.ipynb

###Markdown Метод 2 ###Code import numpy as np import matplotlib.pyplot as plt import seaborn def generate_normal_time_series(num, minl=50, maxl=1000): data = np.array([], dtype=np.float64) partition = np.random.randint(minl, maxl, num) for p in partition: mean = np.random.randn()*10 var = np.random.randn()*1 if var < 0: var = var * -1 tdata = np.random.normal(mean, var, p) data = np.concatenate((data, tdata)) return data data = generate_normal_time_series(7, 50, 200) fig, ax = plt.subplots(figsize=[16, 12]) ax.plot(data) import cProfile import bayesian_changepoint_detection.online_changepoint_detection as oncd from functools import partial R, maxes = oncd.online_changepoint_detection(df_data['close'][0:100].values, partial(oncd.constant_hazard, 250), oncd.StudentT(0.1, .01, 1, 0)) import matplotlib.cm as cm fig, ax = plt.subplots(figsize=[18, 16]) ax = fig.add_subplot(3, 1, 1) ax.plot(df_data['close'][0:100].values) ax = fig.add_subplot(3, 1, 2, sharex=ax) sparsity = 10 # only plot every fifth data for faster display ax.pcolor(np.array(range(0, len(R[:,0]), sparsity)), np.array(range(0, len(R[:,0]), sparsity)), -np.log(R[0:-1:sparsity, 0:-1:sparsity]), cmap=cm.Greys, vmin=0, vmax=30) ax = fig.add_subplot(3, 1, 3, sharex=ax) Nw=10; ax.plot(R[Nw,Nw:-1]) ###Output /home/brainiac/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: RuntimeWarning: divide by zero encountered in log # Remove the CWD from sys.path while we load stuff.

LAB/Feature selection/7_Discriminative Feature Selection.ipynb

###Markdown **Discriminative Feature Selection** FEATURE SELECTIONFeature Selection is the process where you automatically or manually select those features which contribute most to your prediction variable or output in which you are interested in. Having irrelevant features in your data can decrease the accuracy of the models and make your model learn based on irrelevant features.We are going to understand it with a practice example. Steps are as follows :>1) Import important libraries>2) Importing data>3) Data Preprocessing>>i) Price>>ii) Size>>iii) Installs>4) Discriminative Feature Check>>i) Reviews>>ii) Price **1. Import Important Libraries** ###Code import pandas as pd import matplotlib.pyplot as plt import numpy as np #from google.colab import drive #drive.mount('/content/drive') ###Output _____no_output_____ ###Markdown **2. Importing Data**Today we will be working on a playstore apps dataset with ratings. Link to the dataset --> https://www.kaggle.com/lava18/google-play-store-apps/data ###Code df = pd.read_csv('googleplaystore.csv',encoding='unicode_escape') df.head() ###Output _____no_output_____ ###Markdown **3. Data Preprocessing**Let us have a look at all the datatypes first : ###Code df.dtypes ###Output _____no_output_____ ###Markdown We see that all the columns except 'Rating' are object datatype. We want those columns also as numeric as they dont make sense when they are in object form.Let us start with the 'Price' column.**i) Price** When we saw the head of the dataset, we only see the 0 values in 'Price' column. Let us have a look at the rows with non zero data. As the 'Price column is object type, we compare the column with '0' instead of 0. ###Code df[df['Price']!='0'].head() ###Output _____no_output_____ ###Markdown We see that the 'Price' column has dollar sign in the beginning for the apps which are not free. Hence we cannot directly convert it to numeric type. We will first have to remove the $ sign so that all datas are uniform and can be converted.We use the replace function over here to replace the dollar sign by blank. Notice that we had to convert the column to string type from object type as the replace function is only applicable on string functions. ###Code df['Price'] = df['Price'].str.replace('$','') df[df['Price']!='0'].head() ###Output <ipython-input-6-a2a650a36113>:1: FutureWarning: The default value of regex will change from True to False in a future version. In addition, single character regular expressions will*not* be treated as literal strings when regex=True. df['Price'] = df['Price'].str.replace('$','') ###Markdown **ii) Size**As we see the 'Size' column, we see that the value ends with the letter 'M' for mega. We want to convert the size to numeric value to use in the dataset. Hence we will need to remove the letter 'M'.For this, we convert the column to string and omit the last letter of the string and save the data in 'Size' column.Notice from the previous head that we saw, that the 'Size' for row 427 is given as varies with device. We obviously cannot convert such data to numeric. We will see how to deal with it later. ###Code df['Size'] = df['Size'].str[:-1] df.head() ###Output _____no_output_____ ###Markdown **iii) Installs**If we see the 'Installs' column, there are 2 major changes that we need to make to convert it to numeric. We have to remove the '+' sign from the end of the data as well as remove the commas before converting to numeric.To remove the last letter, we apply the same procedure as for the 'Size' column : ###Code df['Installs'] = df['Installs'].str[:-1] df.head() ###Output _____no_output_____ ###Markdown For the removal of commas, we will use the replace function to replace commas with blank.Replace function only works on string, hence we access the values of the series as string before applying the replace function : ###Code df['Installs'] = df['Installs'].str.replace(',','') df.head() ###Output _____no_output_____ ###Markdown Now, we will finally convert all the data to numeric type using the to_numeric function. Notice that we have used the errors='coerce' parameter. This parameter converts all the data which cannot be converted to numeric into NaN. For example the 'Size' in row 427 cannot be converted to int. Hence it will be converted to NaN. After that we take a look at the datatypes of the columns again. ###Code df['Reviews'] = pd.to_numeric(df['Reviews'],errors='coerce') df['Size'] = pd.to_numeric(df['Size'],errors='coerce') df['Installs'] = pd.to_numeric(df['Installs'],errors='coerce') df['Price'] = pd.to_numeric(df['Price'],errors='coerce') df.dtypes ###Output _____no_output_____ ###Markdown Now we will see and work with all the NaN values. Let us first have a look at all the NaN values in the dataset : ###Code df.isna().sum() ###Output _____no_output_____ ###Markdown As rating is the output of our dataset, we cannot have that to be NaN. Hence we will remove all the rows with 'Rating' as NaN : ###Code df = df[df['Rating'].isna()==False] df.isna().sum() ###Output _____no_output_____ ###Markdown This is the final preprocessed dataset that we obtained : ###Code df.head() ###Output _____no_output_____ ###Markdown **4. Discriminative Feature Check**Now we will move on to checking the discriminative feature checking, to see which feature is good and which is not. We will start with the 'Reviews' column. For our case, we will take rating > 4.3 as a good rating. We take that value because as we see in the following stats, the rating is divided 50:50 at that value.Before we do that, let us have a look at the statistics of the whole table : ###Code df.describe() ###Output _____no_output_____ ###Markdown **i) Reviews**We will have to check for multiple values that which of them has the best rating distinction. We will start by comparing with the mean of the 'Reviews' column which is 514098.We will use a new function over here known as crosstab. Crosstab allows us to have a frequency count across 2 columns or conditions.We could also normalize the column results to obtain the conditional probability of P(Rating = HIGH | condition)We have also turned on the margins to see the total frequency under that condition. ###Code pd.crosstab(df['Rating']>4.3,df['Reviews']>514098,rownames=['Ratings>4.3'],colnames=['Reviews>514098'],margins= True) ###Output _____no_output_____ ###Markdown We see that the number of ratings in the case of Reviews > 514098 is very less (close to 10%).Hence it is preferred to take the 50 percentile point rather than the mean to be the pivot point. Let us now take the 50 percentile point which is 5930 reviews in this case. So let us take a look at that : ###Code pd.crosstab(df['Rating']>4.3,df['Reviews']>5930,rownames=['Ratings>4.3'],colnames=['Reviews>5930'],margins= True) ###Output _____no_output_____ ###Markdown Now we see that the number of ratings is equal for both high and low reviews. So we will take the 50 percentile point to start from now on. Let us now look at the conditional probability : ###Code pd.crosstab(df['Rating']>4.3,df['Reviews']>5930,rownames=['Ratings>4.3'],colnames=['Reviews>5930'],margins= True,normalize='columns') ###Output _____no_output_____ ###Markdown There is not much difference between P(Ratings=HIGH|Reviews5930) so this is a bad feature.Let us increase the value of the pivot for ratings to 80000 and check again. We dont need to check for the percentage being too low as we are almost at 75 percentile mark. ###Code pd.crosstab(df['Rating']>4.3,df['Reviews']>80000,rownames=['Ratings>4.3'],colnames=['Reviews>80000'],margins= True,normalize='columns') ###Output _____no_output_____ ###Markdown Now we see that there is a good difference in the probabilities and hence Rating>80000 is a good feature. **ii) Price**We will do the same for 'Price' column to find out the best distinctive feature. We see that in this case, even the 75 percentile mark also points to 0. Hence in this case, we will classify the data as Free or not : ###Code pd.crosstab(df['Rating']>4.3,df['Price']==0,rownames=['Ratings>4.3'],colnames=['Price=$0'],margins= True) ###Output _____no_output_____ ###Markdown This shows us that it is very difficult to use the Price as a feature. Hence it is a doubtful feature. If then also we want to force this as a feature, let us see the conditional probability : ###Code pd.crosstab(df['Rating']>4.3,df['Price']==0,rownames=['Ratings>4.3'],colnames=['Price=$0'],margins= True,normalize='columns') ###Output _____no_output_____

notebooks/180807 - Oahu Qualification Residual Analysis.ipynb

###Markdown Load Data ###Code persistence_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_persistence.csv") #sarima_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_sarima.csv") var_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_var.csv") hofts_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_hofts.csv") cvfts_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_cvfts.csv") cmvfts_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_cmvfts.csv") lstm_multi_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_lstm_multi.csv") lstm_uni_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_lstm_uni.csv") mlp_multi_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_mlp_multi.csv") mlp_uni_ssa_results = pd.read_csv(results_path + "rolling_cv_oahu_residual_mlp_uni.csv") RMSE_real = [] for i in cvfts_ssa_results.RMSE: comp = complex(i) RMSE_real.append(comp.real) cvfts_ssa_results['RMSE'] = RMSE_real U_real = [] for i in cvfts_ssa_results.U: comp = complex(i) U_real.append(comp.real) cvfts_ssa_results['U'] = U_real ##TODO: confirmar porque 5 splits dao erros maiores em SARIMA e CMVFTS sarima_ssa_results = sarima_ssa_results[sarima_ssa_results.RMSE < 500] cmvfts_ssa_results = cmvfts_ssa_results[cmvfts_ssa_results.RMSE < 500] def createBoxplot(filename, data, xticklabels, ylabel): # Create a figure instance fig = plt.figure(1, figsize=(9, 6)) # Create an axes instance ax = fig.add_subplot(111) # Create the boxplot bp = ax.boxplot(data, patch_artist=True) ## change outline color, fill color and linewidth of the boxes for box in bp['boxes']: # change outline color box.set( color='#7570b3', linewidth=2) # change fill color box.set( facecolor = '#1b9e77' ) ## change color and linewidth of the whiskers for whisker in bp['whiskers']: whisker.set(color='#7570b3', linewidth=2) ## change color and linewidth of the caps for cap in bp['caps']: cap.set(color='#7570b3', linewidth=2) ## change color and linewidth of the medians for median in bp['medians']: median.set(color='#b2df8a', linewidth=2) ## change the style of fliers and their fill for flier in bp['fliers']: flier.set(marker='o', color='#e7298a', alpha=0.5) ## Custom x-axis labels ax.set_xticklabels(xticklabels) ax.set_ylabel(ylabel) plt.show() fig.savefig(filename, bbox_inches='tight') ###Output _____no_output_____ ###Markdown Boxplot OAHU Residual Multivariate ###Code metric = 'RMSE' multi_data = [persistence_ssa_results[metric], var_ssa_results[metric], cmvfts_ssa_results[metric], lstm_multi_ssa_results[metric], mlp_multi_ssa_results[metric]] xticks = ['Persistence','VAR','CMVFTS','LSTM_MULTI','MLP_MULTI'] ylab = 'RMSE' createBoxplot("boxplot_rmse_oahu_residual_multi", multi_data, xticks, ylab) metric = 'SMAPE' multi_data = [persistence_ssa_results[metric], var_ssa_results[metric], cmvfts_ssa_results[metric], lstm_multi_ssa_results[metric], mlp_multi_ssa_results[metric]] xticks = ['Persistence','VAR','CMVFTS','LSTM_MULTI','MLP_MULTI'] ylab = 'SMAPE' createBoxplot("boxplot_smape_oahu_residual_multi", multi_data, xticks, ylab) metric = 'U' multi_data = [persistence_ssa_results[metric], var_ssa_results[metric], cmvfts_ssa_results[metric], lstm_multi_ssa_results[metric], mlp_multi_ssa_results[metric]] xticks = ['Persistence','VAR','CMVFTS','LSTM_MULTI','MLP_MULTI'] ylab = 'U Statistic' createBoxplot("boxplot_u_oahu_residual_multi", multi_data, xticks, ylab) ###Output _____no_output_____ ###Markdown Improvement table Multivariate ###Code def improvement(metric_model, metric_persistence): return (1 - (np.mean(metric_model) / np.mean(metric_persistence))) index = ['Persistence','VAR','CMVFTS','LSTM_MULTI','MLP_MULTI'] columns = ['imp(RMSE)', 'imp(SMAPE)', 'imp(U)'] imp_df = pd.DataFrame(columns=columns, index=index) metric = 'RMSE' imp_prst = improvement(persistence_ssa_results[metric], persistence_ssa_results[metric]) imp_var = improvement(var_ssa_results[metric], persistence_ssa_results[metric]) imp_cmvfts = improvement(cmvfts_ssa_results[metric], persistence_ssa_results[metric]) imp_lstm_multi = improvement(lstm_multi_ssa_results[metric], persistence_ssa_results[metric]) imp_mlp_multi = improvement(mlp_multi_ssa_results[metric], persistence_ssa_results[metric]) imp_df['imp('+metric+')'] = [imp_prst, imp_var, imp_cmvfts, imp_lstm_multi, imp_mlp_multi] metric = 'SMAPE' imp_prst = improvement(persistence_ssa_results[metric], persistence_ssa_results[metric]) imp_var = improvement(var_ssa_results[metric], persistence_ssa_results[metric]) imp_cmvfts = improvement(cmvfts_ssa_results[metric], persistence_ssa_results[metric]) imp_lstm_multi = improvement(lstm_multi_ssa_results[metric], persistence_ssa_results[metric]) imp_mlp_multi = improvement(mlp_multi_ssa_results[metric], persistence_ssa_results[metric]) imp_df['imp('+metric+')'] = [imp_prst, imp_var, imp_cmvfts, imp_lstm_multi, imp_mlp_multi] metric = 'U' imp_prst = improvement(persistence_ssa_results[metric], persistence_ssa_results[metric]) imp_var = improvement(var_ssa_results[metric], persistence_ssa_results[metric]) imp_cmvfts = improvement(cmvfts_ssa_results[metric], persistence_ssa_results[metric]) imp_lstm_multi = improvement(lstm_multi_ssa_results[metric], persistence_ssa_results[metric]) imp_mlp_multi = improvement(mlp_multi_ssa_results[metric], persistence_ssa_results[metric]) imp_df['imp('+metric+')'] = [imp_prst, imp_var, imp_cmvfts, imp_lstm_multi, imp_mlp_multi] print(imp_df.to_latex()) ###Output _____no_output_____ ###Markdown Boxplot OAHU Residual Univariate ###Code metric = 'RMSE' #uni_data = [persistence_ssa_results[metric], sarima_ssa_results[metric], hofts_ssa_results[metric], cvfts_ssa_results[metric], lstm_uni_ssa_results[metric], mlp_uni_ssa_results[metric]] #xticks = ['Persistence', 'SARIMA', 'HOFTS','CVFTS','LSTM_UNI','MLP_UNI'] uni_data = [persistence_ssa_results[metric], hofts_ssa_results[metric], cvfts_ssa_results[metric], lstm_uni_ssa_results[metric], mlp_uni_ssa_results[metric]] xticks = ['Persistence', 'HOFTS','CVFTS','LSTM_UNI','MLP_UNI'] ylab = 'RMSE' createBoxplot("boxplot_rmse_oahu_residual_uni", uni_data, xticks, ylab) metric = 'SMAPE' #uni_data = [persistence_ssa_results[metric], sarima_ssa_results[metric], hofts_ssa_results[metric], cvfts_ssa_results[metric], lstm_uni_ssa_results[metric], mlp_uni_ssa_results[metric]] #xticks = ['Persistence', 'SARIMA', 'HOFTS','CVFTS','LSTM_UNI','MLP_UNI'] uni_data = [persistence_ssa_results[metric], hofts_ssa_results[metric], cvfts_ssa_results[metric], lstm_uni_ssa_results[metric], mlp_uni_ssa_results[metric]] xticks = ['Persistence', 'HOFTS','CVFTS','LSTM_UNI','MLP_UNI'] ylab = 'SMAPE' createBoxplot("boxplot_smape_oahu_residual_uni", uni_data, xticks, ylab) metric = 'U' #uni_data = [persistence_ssa_results[metric], sarima_ssa_results[metric], hofts_ssa_results[metric], cvfts_ssa_results[metric], lstm_uni_ssa_results[metric], mlp_uni_ssa_results[metric]] #xticks = ['Persistence', 'SARIMA', 'HOFTS','CVFTS','LSTM_UNI','MLP_UNI'] uni_data = [persistence_ssa_results[metric], hofts_ssa_results[metric], cvfts_ssa_results[metric], lstm_uni_ssa_results[metric], mlp_uni_ssa_results[metric]] xticks = ['Persistence', 'HOFTS','CVFTS','LSTM_UNI','MLP_UNI'] ylab = 'U Statistic' createBoxplot("boxplot_u_oahu_residual_uni", uni_data, xticks, ylab) ###Output _____no_output_____ ###Markdown Improvement Table Univariate ###Code index = ['Persistence', 'SARIMA', 'HOFTS','CVFTS','LSTM_UNI','MLP_UNI'] columns = ['imp(RMSE)', 'imp(SMAPE)', 'imp(U)'] metrics = ['RMSE', 'SMAPE', 'U'] imp_df = pd.DataFrame(columns=columns, index=index) for metric in metrics: imp_prst = improvement(persistence_ssa_results[metric], persistence_ssa_results[metric]) imp_sarima = improvement(sarima_ssa_results[metric], persistence_ssa_results[metric]) imp_hofts = improvement(hofts_ssa_results[metric], persistence_ssa_results[metric]) imp_cvfts = improvement(cvfts_ssa_results[metric], persistence_ssa_results[metric]) imp_lstm_uni = improvement(lstm_uni_ssa_results[metric], persistence_ssa_results[metric]) imp_mlp_uni = improvement(mlp_uni_ssa_results[metric], persistence_ssa_results[metric]) imp_df['imp('+metric+')'] = [imp_prst, imp_sarima, imp_hofts, imp_cvfts, imp_lstm_uni, imp_mlp_uni] print(imp_df.to_latex()) ###Output _____no_output_____

docs/beta/notebooks/Grammars2.ipynb

###Markdown Fuzzing with GrammarsIn the chapter on ["Mutation-Based Fuzzing"](MutationFuzzer.ipynb), we have seen how to use extra hints – such as sample input files – to speed up test generation. In this chapter, we take this idea one step further, by providing a _specification_ of the legal inputs to a program. These _grammars_ allow for very effective and efficient testing, as we will see in this chapter. **Prerequisites*** You should know how basic fuzzing works, e.g. from the [Chapter introducing fuzzing](Fuzzer.ipynb).* Knowledge on [mutation-based fuzzing](MutationFuzzer.ipynb) and [coverage](Coverage.ipynb) is _not_ required yet, but still recommended. Input LanguagesAll possible behaviors of a program can be triggered by its input. "Input" here can be a wide range of possible sources: We are talking about data read from files, from the environment, or over the network, data input by the user, or data acquired from interaction with other resources. The set of all these inputs determines how the program will behave – including its failures. When testing, it is thus very helpful to think about possible input sources, how to get them under control, and _how to systematically test them_.For the sake of simplicity, we will assume for now that the program has only one source of inputs; this is the same assumption we have been using in the previous chapters, too. The set of valid inputs to a program is called a _language_. Languages range from the simple to the complex: the CSV language denotes the set of valid comma-separated inputs, whereas the Python language denotes the set of valid Python programs. We commonly separate data languages and programming languages, although any program can also be treated as input data (say, to a compiler). The [Wikipedia page on file formats](https://en.wikipedia.org/wiki/List_of_file_formats) lists more than 1,000 different file formats, each of which is its own language. Grammars Rules and ExpansionsTo formally specify input languages, _grammars_ are among the most popular (and best understood) formalisms. A grammar consists of a _start symbol_ and a set of _rules_ which indicate how the start symbol (and other symbols) can be expanded. As an example, consider the following grammar, denoting a sequence of two digits:``` ::= ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9```To read such a grammar, start with the starting symbol (``). A rule ` ::= ` means that the symbol on the left side (``) can be replaced by the string on the right side (``). In the above grammar, `` would be replaced by ``.In this string again, `` would be replaced by the string on the right side of the `` rule. The special operator `|` denotes _alternatives_, meaning that any of the digits can be chosen for an expansion. Each `` thus would be expanded into one of the given digits, eventually yielding a string between `00` and `99`. There are no further expansions for `0` to `9`, so we are all set.The interesting thing about grammars is that they can be _recursive_. That is, expansions can make use of symbols expanded earlier – which would then be expanded again. As an example, consider a grammar that describes integers:``` ::= ::= | ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9```Here, a `` is either a single digit, or a digit followed by another integer. The number `1234` thus would be represented as a single digit `1`, followed by the integer `234`, which in turn is a digit `2`, followed by the integer `34`.If we wanted to express that an integer can be preceded by a sign (`+` or `-`), we would write the grammar as``` ::= ::= | + | - ::= | ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9```These rules formally define the language: Anything that can be derived from the start symbol is part of the language; anything that cannot is not. Arithmetic ExpressionsLet us expand our grammar to cover full _arithmetic expressions_ – a poster child example for a grammar. We see that an expression (``) is either a sum, or a difference, or a term; a term is either a product or a division, or a factor; and a factor is either a number or a parenthesized expression. Amost all rules can have recursion, and thus allow arbitrary complex expressions such as `(1 + 2) * (3.4 / 5.6 - 789)`.``` ::= ::= + | - | ::= * | / | ::= + | - | () | | . ::= | ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9```In such a grammar, if we start with `` and then expand one symbol after another, randomly choosing alternatives, we can quickly produce one valid arithmetic expression after another. Such _grammar fuzzing_ is highly effective as it comes to produce complex inputs, and this is what we will implement in this chapter. Representing Grammars in PythonOur first step in building a grammar fuzzer is to find an appropriate format for grammars. To make the writing of grammars as simple as possible, we use a mostly format that is mostly based on strings. Our grammars in Python takes the format of a _mapping_ between symbol names and expansions, where expansions are _lists_ of alternatives. A one-rule grammar for digits thus takes the form ###Code import fuzzingbook_utils DIGIT_GRAMMAR = { "<start>": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"] } ###Output _____no_output_____ ###Markdown whereas the full grammar for arithmetic expressions looks like this: ###Code EXPR_GRAMMAR = { "<start>": ["<expr>"], "<expr>": ["<term> + <expr>", "<term> - <expr>", "<term>"], "<term>": ["<factor> * <term>", "<factor> / <term>", "<factor>"], "<factor>": ["+<factor>", "-<factor>", "(<expr>)", "<integer>", "<integer>.<integer>"], "<integer>": ["<digit><integer>", "<digit>"], "<digit>": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"] } ###Output _____no_output_____ ###Markdown In the grammar, we can access any rule by its symbol... ###Code EXPR_GRAMMAR["<digit>"] ###Output _____no_output_____ ###Markdown ....and we can check whether a symbol is in the grammar: ###Code "<identifier>" in EXPR_GRAMMAR ###Output _____no_output_____ ###Markdown Some Definitions We assume that the canonical start symbol is ``: ###Code START_SYMBOL = "<start>" ###Output _____no_output_____ ###Markdown The handy `nonterminals()` function extracts the list of nonterminal symbols (i.e., anything between ``) from an expansion. ###Code import re # As a symbol, we can have anything between <...> except spaces. RE_NONTERMINAL = re.compile(r'(<[^<> ]*>)') def nonterminals(expansion): # In later chapters, we allow expansions to be tuples, # with the expansion being the first element if isinstance(expansion, tuple): expansion = expansion[0] return re.findall(RE_NONTERMINAL, expansion) assert nonterminals("<term> * <factor>") == ["<term>", "<factor>"] assert nonterminals("<digit><integer>") == ["<digit>", "<integer>"] assert nonterminals("1 < 3 > 2") == [] assert nonterminals("1 <3> 2") == ["<3>"] assert nonterminals("1 + 2") == [] assert nonterminals(("<1>", {'option': 'value'})) == ["<1>"] ###Output _____no_output_____ ###Markdown Likewise, `is_nonterminal()` checks whether some symbol is a nonterminal: ###Code def is_nonterminal(s): return re.match(RE_NONTERMINAL, s) assert is_nonterminal("<abc>") assert not is_nonterminal("+") ###Output _____no_output_____ ###Markdown A Simple Grammar FuzzerLet us now put the above grammars to use. We will build a very simple grammar fuzzer that starts with a start symbol (`""`) and then keeps on expanding it. To avoid expansion to infinite inputs, we place a limit (`max_symbols`) on the number of symbols. Furthermore, to avoid being stuck in a situation where we cannot reduce the number of symbols any further, we also limit the total number of expansion steps. ###Code import random class ExpansionError(Exception): pass def simple_grammar_fuzzer(grammar, start_symbol=START_SYMBOL, max_nonterminals=10, max_expansion_trials=100, log=False): term = start_symbol expansion_trials = 0 while len(nonterminals(term)) > 0: symbol_to_expand = random.choice(nonterminals(term)) expansion = random.choice(grammar[symbol_to_expand]) new_term = term.replace(symbol_to_expand, expansion, 1) if len(nonterminals(new_term)) < max_nonterminals: term = new_term if log: print("%-40s" % (symbol_to_expand + " -> " + expansion), term) expansion_trials = 0 else: expansion_trials += 1 if expansion_trials >= max_expansion_trials: raise ExpansionError("Cannot expand " + repr(term)) return term ###Output _____no_output_____ ###Markdown Let us see how this simple grammar fuzzer obtains an arithmetic expression from the start symbol: ###Code simple_grammar_fuzzer(grammar=EXPR_GRAMMAR, max_nonterminals=3, log=True) for i in range(10): print(simple_grammar_fuzzer(grammar=EXPR_GRAMMAR, max_nonterminals=5)) ###Output +9 / 7 / -(+4) - (+(8)) + -++((-+1 - 5) / 1) / +2 * (+9 + (+(+(+1 + +3420 / -33) * +-6 / 2))) (8) * (+3 * (19) - ++--+-+-(4 * +93) + 69.28024) - 1.0 - 8 74.5 * (((-+(-0 * +(----+-(+((+-930 / 1))))))) / (+-(-+++-(+(-1 + 4)))) * 8 * -(--5.52) * 5) 0 / (+0) / 3 - --(+((+(((0)))))) - +--5 / (--+-+(2) / +7) + +((5.6 + (+8.7 + 7.6 / ((((-(+-0))) + +-9) * ------((-++7.5)) * +--+-((47 / 34 * ((1) / 4 + +-+(-+9) + 9.1))) - +67))) * 8) (+9) + +-6 / +(--3 * +(20)) + ++---(+((+--+(8) - (-6) + ((((9) + 35 - -+5.7) * (-(961.4 - -4 * +5.994))))) - ((-+8 * +8)))) / -7 +++--((-((++0)) + (0 * 9 + (63) / 9))) * +(-6) / 9 - -(+-81.7) 9 * --70 - 1 - 56 2 / 5 * +8 / --+--+--+--+-((-+((-2 / (-+4)) / 4 * 9692.2) / -9 + 5 * 62)) - +9 - -8 - 7 8.7 - 25.3 + -20.8 +-+(+(8)) * (1.4) + --(+---1.4 * -+5.901 * -+(++7 + -+5 - --7.0 - (6 + 6 * +24) * -3)) - +8 ###Markdown \todo{Discuss.} Note that this fuzzer is rather inefficient due to the large number of search and replace operations. On the other hand, the implementation is straightforward and does the job. For this chapter, we'll stick to it; in the [next chapter](GrammarFuzzer.ipynb), we'll show how to build a more efficient one. Some Grammars With grammars, we can easily specify the format for several of the examples we discussed earlier. The above arithmetic expressions, for instance, can be directly sent into `bc` (or any other program that takes arithmetic expressions. Let us create some more grammars. Here's one for `cgi_decode()`: ###Code CGI_GRAMMAR = { "<start>": ["<string>"], "<string>": ["<letter>", "<letter><string>"], "<letter>": ["<plus>", "<percent>", "<other>"], "<plus>": ["+"], "<percent>": ["%<hexdigit><hexdigit>"], "<hexdigit>": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a", "b", "c", "d", "e", "f"], "<other>": # Actually, could be _all_ letters ["0", "1", "2", "3", "4", "5", "a", "b", "c", "d", "e", "-", "_"], } for i in range(10): print(simple_grammar_fuzzer(grammar=CGI_GRAMMAR, max_nonterminals=10)) ###Output %0e_++++ae + %bf 2 5 1 + +%98 ++ +%5b%51 ###Markdown Or a URL grammar: ###Code URL_GRAMMAR = { "<start>": ["<call>"], "<call>": ["<url>"], "<url>": ["<scheme>://<authority><path><query>"], "<scheme>": ["http", "https", "ftp", "ftps"], "<authority>": ["<host>", "<host>:<port>", "<userinfo>@<host>", "<userinfo>@<host>:<port>"], "<host>": # Just a few ["cispa.saarland", "www.google.com", "fuzzingbook.com"], "<port>": ["80", "8080", "<nat>"], "<nat>": ["<digit>", "<digit><digit>"], "<digit>": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9"], "<userinfo>": # Just one ["user:password"], "<path>": # Just a few ["", "/", "/<id>"], "<id>": # Just a few ["abc", "def", "x<digit><digit>"], "<query>": ["", "?<params>"], "<params>": ["<param>", "<param>&<params>"], "<param>": # Just a few ["<id>=<id>", "<id>=<nat>"], } for i in range(10): print(simple_grammar_fuzzer(grammar=URL_GRAMMAR, max_nonterminals=10)) ###Output ftp://www.google.com/?def=39 ftps://user:[email protected]:8080/abc ftp://fuzzingbook.com:8080/abc?x25=abc https://user:[email protected]/abc https://fuzzingbook.com:78/ https://user:[email protected]/?abc=x45&x91=37&def=92&x78=def&abc=16&x43=x47 http://user:[email protected]:80 ftps://fuzzingbook.com:8?abc=50 ftps://cispa.saarland/abc https://user:[email protected]:80/ ###Markdown Hatching GrammarsSince grammars are represented as strings, it is fairly easy to introduce errors. So let us introduce a helper function that checks a grammar for consistency.First, this handy `nonterminals()` function gets us the list of nonterminals in an expansion. The helper function `is_valid_grammar()` iterates over a grammar to check whether all used symbols are defined, and vice versa, which is very useful for debugging. You don't have to delve into details here, but as always, it is important to get the input data straight before we make use of it. ###Code import sys def is_valid_grammar(grammar, start_symbol=START_SYMBOL): used_nonterminals = set([start_symbol]) defined_nonterminals = set() for defined_nonterminal in grammar: defined_nonterminals.add(defined_nonterminal) expansions = grammar[defined_nonterminal] if not isinstance(expansions, list): print(repr(defined_nonterminal) + ": expansion is not a list", file=sys.stderr) return False if len(expansions) == 0: print(repr(defined_nonterminal) + ": expansion list empty", file=sys.stderr) return False for expansion in expansions: if isinstance(expansion, tuple): expansion = expansion[0] if not isinstance(expansion, str): print(repr(defined_nonterminal) + ": " + repr(expansion) + ": not a string", file=sys.stderr) return False for used_nonterminal in nonterminals(expansion): used_nonterminals.add(used_nonterminal) for unused_nonterminal in defined_nonterminals - used_nonterminals: print(repr(unused_nonterminal) + ": defined, but not used", file=sys.stderr) for undefined_nonterminal in used_nonterminals - defined_nonterminals: print(repr(undefined_nonterminal) + ": used, but not defined", file=sys.stderr) return used_nonterminals == defined_nonterminals ###Output _____no_output_____ ###Markdown Our grammars defined above pass the test: ###Code assert is_valid_grammar(EXPR_GRAMMAR) assert is_valid_grammar(CGI_GRAMMAR) assert is_valid_grammar(URL_GRAMMAR) ###Output _____no_output_____ ###Markdown But these ones don't: ###Code assert not is_valid_grammar({"<start>": ["<x>"], "<y>": ["1"]}) assert not is_valid_grammar({"<start>": "123"}) assert not is_valid_grammar({"<start>": []}) assert not is_valid_grammar({"<start>": [1, 2, 3]}) ###Output '<start>': 1: not a string

notebooks/xgboost/train-iris.ipynb

###Markdown Train with xgboostdescription: train xgboost model on iris data ###Code from azureml.core import Workspace ws = Workspace.from_config() ws import git from pathlib import Path # get root of git repo prefix = Path(git.Repo(".", search_parent_directories=True).working_tree_dir) # training script script_dir = prefix.joinpath("code", "models", "xgboost", "iris") script_name = "train.py" # environment file environment_file = prefix.joinpath("environments", "xgboost-example.txt") # azure ml settings environment_name = "xgboost-iris-example" experiment_name = "xgboost-iris-example" compute_target = "cpu-cluster" print(open(script_dir.joinpath(script_name)).read()) from azureml.core import ScriptRunConfig, Experiment, Environment env = Environment.from_pip_requirements(environment_name, environment_file) src = ScriptRunConfig( source_directory=script_dir, script=script_name, environment=env, compute_target=compute_target, ) run = Experiment(ws, experiment_name).submit(src) run from azureml.widgets import RunDetails RunDetails(run).show() run.wait_for_completion(show_output=True) ###Output _____no_output_____ ###Markdown Train with xgboostdescription: train xgboost model on iris data ###Code from azureml.core import Workspace ws = Workspace.from_config() ws import git from pathlib import Path # get root of git repo prefix = Path(git.Repo(".", search_parent_directories=True).working_tree_dir) # training script script_dir = prefix.joinpath("code", "models", "xgboost", "iris") script_name = "train.py" # environment file environment_file = prefix.joinpath("environments", "xgboost-example.txt") # azure ml settings environment_name = "xgboost-iris-example" experiment_name = "xgboost-iris-example" compute_target = "cpu-cluster" print(open(script_dir.joinpath(script_name)).read()) from azureml.core import ScriptRunConfig, Experiment, Environment env = Environment.from_pip_requirements(environment_name, environment_file) src = ScriptRunConfig( source_directory=script_dir, script=script_name, environment=env, compute_target=compute_target, ) run = Experiment(ws, experiment_name).submit(src) run from azureml.widgets import RunDetails RunDetails(run).show() run.wait_for_completion(show_output=True) ###Output _____no_output_____

docs/python/seaborn/KDEplot.ipynb

###Markdown ---title: "KDEplot"author: "Aavinash"date: 2020-09-04description: "-"type: technical_notedraft: false--- ###Code import seaborn as sns rng = np.random.RandomState(0) x = np.linspace(0, 10, 500) y = np.cumsum(rng.randn(500, 6), 0) plt.plot(x, y) plt.legend('ABCDEF', ncol=2, loc='upper left'); for col in 'xy': sns.kdeplot(data[col], shade=True) ###Output _____no_output_____

Archieve/4.DBScan Clusters with Doc2Word_v2.0.ipynb

###Markdown 1.1 Word Embedding ###Code ## Word Embeddings Functions ## Generate the tagged documents (tagging based on the category column) def create_tagged_document(list_of_list_of_words): for i, list_of_words in enumerate(list_of_list_of_words): yield gensim.models.doc2vec.TaggedDocument(list_of_words, [i]) ## Generate the tagged documents (each record in single tag ) def create_tagged_document_based_on_tags(list_of_list_of_words, tags): for i in range(len(list_of_list_of_words)): yield gensim.models.doc2vec.TaggedDocument(list_of_list_of_words[i], [tags[i]]) ## Generate output using the word embedding model prediction - takes long time to regenerate def vec_for_learning(model, tagged_docs): sents = tagged_docs#.values targets, regressors = zip(*[(doc.tags[0], model.infer_vector(doc.words, steps=20)) for doc in sents]) return targets, regressors ## creating a tagged document DescDict=[[x for x in str(i).split()] for i in df.PreProcessedDescription] tagged_value_tags = list(create_tagged_document_based_on_tags(DescDict, df.Category.tolist())) tagged_value = list(create_tagged_document(DescDict)) print(str(datetime.datetime.now()),'Started') # Init the Doc2Vec model model = gensim.models.doc2vec.Doc2Vec(vector_size=50, min_count=5, epochs=40, alpha = 0.02, dm=1, workers=multiprocessing.cpu_count()) #### Hyper parameter #### ## vector_size – Dimensionality of the feature vectors. ## If dm=1, ‘distributed memory’ (PV-DM) (CBOW - similar to continuous bag-of-words) ## alpha - The initial learning rate. ## min_count – Ignores all words with total frequency lower than this. # Build the Volabulary model.build_vocab(tagged_value) model.train(tagged_value, total_examples=len(tagged_value), epochs=40) print(str(datetime.datetime.now()),'Completed') ## Validating the model response for random words modelchecked=model target_word='environment' print('target_word: %r model: %s similar words:' % (target_word, modelchecked)) for i, (word, sim) in enumerate(modelchecked.wv.most_similar(target_word, topn=20), 1): print(' %d. %.2f %r' % (i, sim, word)) ###Output target_word: 'environment' model: Doc2Vec(dm/m,d50,n5,w5,mc5,s0.001,t4) similar words: 1. 0.65 'situation' 2. 0.65 'system' 3. 0.63 'constantly' 4. 0.62 'kind' 5. 0.61 'way' 6. 0.60 'habitat' 7. 0.59 'reservoir' 8. 0.58 'contexts' 9. 0.58 'resource' 10. 0.58 'climatically' 11. 0.57 'scenario' 12. 0.57 'continuously' 13. 0.57 'setting' 14. 0.57 'potentially' 15. 0.55 'environments' 16. 0.55 'object' 17. 0.55 'community' 18. 0.55 'circumstance' 19. 0.55 'obviously' 20. 0.55 'area' ###Markdown 1.2. PCA ###Code ## PCA - reducing the dimenstion ps=10 pcamodel = PCA(n_components=ps) pca=pcamodel.fit_transform(model.docvecs.vectors_docs) print('PCA components :',ps,'Variance coveragence' ,np.max(pcamodel.explained_variance_ratio_.cumsum())*100) dummies=pd.get_dummies(df['Category']) merged_data=pd.concat([df,dummies], axis=1,ignore_index=False) merged_data=pd.concat([merged_data,pd.DataFrame(pca)], axis=1,ignore_index=False) merged_data=merged_data[pd.isnull(merged_data["Category"])==False] merged_data['DBScanCluster']=0 ###Output _____no_output_____ ###Markdown 2. DBScan ###Code ### DBSCAN - Density-Based Spatial Clustering of Applications with Noise. # Finds core samples of high density and expands clusters from them. FeatureCols=list(range(ps)) for cat in merged_data.Category.unique(): print(str(datetime.datetime.now()),'Started') CategoricalDS= merged_data[FeatureCols][merged_data.Category==cat] clusterer = DBSCAN(eps=2.6, min_samples=5, n_jobs=4) #### Hyper parameter #### # eps - The maximum distance between two samples for one to be considered as in the neighborhood of the other. # min_samples -The number of samples (or total weight) in a neighborhood for a point to be considered as a core point preds = clusterer.fit_predict(CategoricalDS) merged_data.loc[merged_data.Category==cat,'DBScanCluster']=preds print('******'+cat+'******') print(pd.Series(preds).value_counts()) score = silhouette_score(CategoricalDS, preds, metric='euclidean') print('silhouette score:',score) print(str(datetime.datetime.now()),'Completed') print('') merged_data['DBScanCluster'].value_counts() ## Reseting the index, converting category to int for supervised learning def CattoID(input_cat): if(input_cat=='Engineering Sciences'): return 0 elif(input_cat=='Humanities and Social Sciences'): return 1 elif(input_cat=='Natural Sciences'): return 2 elif(input_cat=='Life Sciences'): return 3 else : return -1 merged_data=merged_data.reset_index()[merged_data.columns[0:]] merged_data['CategoryConv']=merged_data.Category.apply(CattoID) merged_data['CategoryConv']=merged_data['CategoryConv'].astype('int') ###Output _____no_output_____ ###Markdown 3. Supervised learning ###Code Features=merged_data.columns[16:len(merged_data.columns)-2] #list(range(500)) merged_data[Features]=MinMaxScaler().fit_transform(merged_data[Features]) OP_Feature='CategoryConv' ## Training & Test data are splitted based on the DBScanCluster result. outlier data are considering as test data to reevaluate. X_Training_DS=merged_data[Features][merged_data.DBScanCluster==0] y_Training_DS=merged_data[OP_Feature][merged_data.DBScanCluster==0] X_Test_DS=merged_data[Features][merged_data.DBScanCluster!=0] y_Test_DS=merged_data[OP_Feature][merged_data.DBScanCluster!=0] X_train, X_test, y_train, y_test = train_test_split(X_Training_DS,y_Training_DS, test_size=0.2, random_state=0) ###Output _____no_output_____ ###Markdown 3.1 NaiveBayes ###Code modelNB = MultinomialNB(alpha=1) #### Hyper parameter #### # alpha - Additive (Laplace/Lidstone) smoothing parameter (0 for no smoothing). modelNB.fit(X_train, y_train) nfolds=5 scores=cross_val_score(modelNB, X_Training_DS,y_Training_DS, cv=nfolds, scoring="accuracy") pd.Series(scores).plot(kind="box", label="Accuracy"); plt.title('Accuracy_score from '+str(nfolds)+' Folds (Accuracy) for '+str(round(pd.Series(scores).mean(), 2))) y_pred = modelNB.predict(X_test) print('Accuracy Score : '+str(accuracy_score(y_test,y_pred )*100)) ###Output Accuracy Score : 34.91118288251918 ###Markdown 3.1 k-nearest neighbors ###Code for k in [4,8,16,25,30]: modelKBC = KNeighborsClassifier(n_neighbors=k, weights='distance') #### Hyper parameter #### # n_neighbors - Number of neighbors to use by default for kneighbors queries # weights - weight function used in prediction (‘distance’ : weight points by the inverse of their distance. #in this case, closer neighbors of a query point will have a greater influence than neighbors which are further away.) modelKBC.fit(X_train, y_train) y_pred = modelKBC.predict(X_test) print('neighbors:',k,'Accuracy Score : '+str(accuracy_score(y_test,y_pred ))) #nfolds=3 #scores=cross_val_score(modelKBC, X_train,y_train, cv=nfolds, scoring="accuracy") #pd.Series(scores).plot(kind="box", label="Accuracy"); #plt.title('Accuracy_score from '+str(nfolds)+' Folds (Accuracy) for '+str(round(pd.Series(scores).mean(), 2))) k=25 modelKBC = KNeighborsClassifier(n_neighbors=k, weights='distance') modelKBC.fit(X_train, y_train) y_pred = modelKBC.predict(X_test) print('neighbors:',k,'Accuracy Score : '+str(accuracy_score(y_test,y_pred ))) nfolds=3 scores=cross_val_score(modelKBC, X_train,y_train, cv=nfolds, scoring="accuracy") pd.Series(scores).plot(kind="box", label="Accuracy"); plt.title('Accuracy_score from '+str(nfolds)+' Folds (Accuracy) for '+str(round(pd.Series(scores).mean(), 2))) print(str(datetime.datetime.now()),'Started') modelSVC = svm.LinearSVC(C=0.01) #### Hyper parameter #### # C - The strength of the regularization is inversely proportional to C. modelSVC.fit(X_train, y_train) print(str(datetime.datetime.now()),'Fit Completed') nfolds=3 scores=cross_val_score(modelSVC, X_train, y_train, cv=nfolds, scoring="accuracy") pd.Series(scores).plot(kind="box", label="Accuracy"); plt.title('Accuracy_score from '+str(nfolds)+' Folds (Accuracy) for '+str(round(pd.Series(scores).mean(), 2))) y_pred = modelSVC.predict(X_test) print('Accuracy Score : '+str(accuracy_score(y_test,y_pred )*100)) print(str(datetime.datetime.now()),'Completed') ###Output 2020-01-24 10:53:11.357936 Started 2020-01-24 10:53:11.732016 Fit Completed Accuracy Score : 83.44771901493743 2020-01-24 10:53:12.725544 Completed ###Markdown 4. Formatting the output categories based on the predict_proba ###Code ## Based on predict_proba result. reorder to values and categories based on high probablity. def name_max_value(DF): colname='Category_1_Values' if (DF['Engineering Sciences']==DF[colname]): return 'Engineering Sciences' elif (DF['Humanities and Social Sciences']==DF[colname]): return 'Humanities and Social Sciences' elif (DF['Natural Sciences']==DF[colname]): return 'Natural Sciences' elif (DF['Life Sciences']==DF[colname]): return 'Life Sciences' else: return '' def name_sec_max_value(DF): colname='Category_2_Values' if(DF[colname]==0): return '' elif ((DF['Engineering Sciences']==DF[colname]) & (DF['Category_1']!='Engineering Sciences')): return 'Engineering Sciences' elif ((DF['Humanities and Social Sciences']==DF[colname]) & (DF['Category_1']!='Humanities and Social Sciences')): return 'Humanities and Social Sciences' elif ((DF['Natural Sciences']==DF[colname]) & (DF['Category_1']!='Natural Sciences')): return 'Natural Sciences' elif ((DF['Life Sciences']==DF[colname]) & (DF['Category_1']!='Life Sciences')): return 'Life Sciences' else: return '' def name_3rd_max_value(DF): colname='Category_3_Values' if(DF[colname]==0): return '' elif ((DF['Engineering Sciences']==DF[colname]) & (DF['Category_2']!='Engineering Sciences')): return 'Engineering Sciences' elif ((DF['Humanities and Social Sciences']==DF[colname]) & (DF['Category_2']!='Humanities and Social Sciences')): return 'Humanities and Social Sciences' elif ((DF['Natural Sciences']==DF[colname]) & (DF['Category_2']!='Natural Sciences')): return 'Natural Sciences' elif ((DF['Life Sciences']==DF[colname]) & (DF['Category_2']!='Life Sciences')): return 'Life Sciences' else: return '' cols=['Engineering Sciences','Humanities and Social Sciences','Natural Sciences','Life Sciences'] PredictedValues=pd.DataFrame(modelKBC.predict_proba(merged_data[Features]), columns=cols) PredictedValues['Category_1_Values']=PredictedValues[cols].apply(np.max,axis=1) PredictedValues['Category_2_Values']=PredictedValues[cols].apply(np.sort,axis=1).apply(lambda x:x[2]) PredictedValues['Category_3_Values']=PredictedValues[cols].apply(np.sort,axis=1).apply(lambda x:x[1]) PredictedValues['Category_1']=PredictedValues.apply(name_max_value,axis=1) PredictedValues['Category_2']=PredictedValues.apply(name_sec_max_value,axis=1) PredictedValues['Category_3']=PredictedValues.apply(name_3rd_max_value,axis=1) PredictedValues['Category_12_Variance']=PredictedValues.apply(lambda x :x['Category_1_Values']-x['Category_2_Values'], axis=1) PredictedValues['Category_23_Variance']=PredictedValues.apply(lambda x :x['Category_2_Values']-x['Category_3_Values'], axis=1) ###Output _____no_output_____ ###Markdown 5.1. Random manual result evaluvation ###Code PredictedValues.head(16694).tail(5) ## regenerating dataset NewMergedDSAligned=pd.concat([merged_data[merged_data.columns.tolist()[:12]+['DBScanCluster']],PredictedValues[PredictedValues.columns[4:]]], axis=1, ignore_index=False) #(NewMergedDSAligned.DBScanCluster!=0) & NewMergedDSAligned['DBScanCluster'][ (NewMergedDSAligned['Category']!=NewMergedDSAligned['Category_1'])].value_counts() NewMergedDSAligned['Category'][(NewMergedDSAligned.DBScanCluster!=0) & (NewMergedDSAligned['Category']!=NewMergedDSAligned['Category_1'])].value_counts() cats='Natural Sciences' lim=200 NewMergedDSAligned[['Translates','Category']+NewMergedDSAligned.columns[13:].tolist()][(NewMergedDSAligned['Category_1']!=cats) & (NewMergedDSAligned['Category']==cats) & (NewMergedDSAligned.DBScanCluster==0) & (NewMergedDSAligned['Category']!=NewMergedDSAligned['Category_1'])].sort_values('Category_1_Values', ascending=False).head(lim).tail(5) #cats='Humanities and Social Sciences' NewMergedDSAligned[['Translates','Category_1_Values']][(NewMergedDSAligned['Category_1']!=cats) & (NewMergedDSAligned['Category']==cats) & (NewMergedDSAligned.DBScanCluster==0) & (NewMergedDSAligned['Category']!=NewMergedDSAligned['Category_1'])].sort_values('Category_1_Values', ascending=False).Translates.head(lim).tail(5).tolist()#.tail(). #NewMergedDSAligned.to_csv(Path+'WEPCADBScanFindingsKMeans.csv', index=False) ###Output _____no_output_____ ###Markdown 5.2. Each category TF/IDF based result evaluvation ###Code #&(NewMergedDSAligned['Category']==cats) &(NewMergedDSAligned['Category_1']==check_cat) input_data=NewMergedDSAligned[(NewMergedDSAligned['Category']!=NewMergedDSAligned['Category_1']) & (NewMergedDSAligned.DBScanCluster!=0) ] input_data.loc[:,'CategoryCollc']=input_data[['Category','Category_1','Category_2','Category_3']].apply(lambda x:x[0]+','+x[1]+','+x[2]+','+x[3], axis=1) #input_data.loc[:,'CategoryCollc']=input_data[['Category','Category_1']].apply(lambda x:x[0]+','+x[1], axis=1) input_data.loc[:,'CategoryCollc']=input_data['CategoryCollc'].str.strip(",") varcluster_info.cluster_id=varcluster_info.cluster_id.astype('int32') varclusterall=varcluster.merge(varcluster_info, how='left',left_on='Cluster', right_on='cluster_id') varclusterall=varclusterall[varclusterall.RS_Ratio<.98] def find_category(target_word): try : sim_word=list(map(lambda x:x[0] ,modelchecked.wv.most_similar(target_word, topn=5))) finalcategory=varclusterall[varclusterall.Variable.isin(sim_word)].category.value_counts().sort_values(ascending=False).head(1).index if(len(finalcategory)>0): return finalcategory[0] else: return np.NaN except : return np.NaN input_data.head() sizes=len(input_data.CategoryCollc.unique()) #plt.subplots(figsize=(8,150)) j=1 for i,bucket in input_data.groupby(['CategoryCollc']): print(i.split(',')[0],'-',i.split(',')[1:],': Number of Documents -',len(bucket)) if(len(bucket)>1): vectorizer = TfidfVectorizer(max_features=20, ngram_range=(1, 1)) review_vectors = vectorizer.fit_transform(bucket["PreProcessedDescription"]) features_df = pd.DataFrame(review_vectors.toarray(), columns = vectorizer.get_feature_names()) varcat=pd.DataFrame(features_df.sum().sort_values(ascending=False)).merge(varclusterall, how='left', left_index=True, right_on='Variable')[['Variable','category']] varcat.category=varcat[['Variable', 'category']].apply(lambda x: find_category(x.Variable) if(pd.isnull(x['category'])) else x['category'], axis=1) #print(varcat.category.value_counts()) #print(varcat.apply(lambda x: x.Variable +' - NA' if(pd.isnull(x.category)) else x.Variable +' - '+x.category , axis=1)) print('Rare words',list(varcat[varcat.category!='General'].Variable)) else: print(bucket.Translates.tolist()) print('----------------------------------------------------------') #print(features_df.sum().sort_values(ascending=False),'\n') #vectorizer.get_feature_names() #plt.subplot(1,sizes,j) #features_df.sum().sort_values(ascending=False).plot(kind='bar',color='green') #plt.title(i.split(',')[0]+' -'+','.join(i.split(',')[1:])) #plt.xticks(rotation=60) #j=j+1 #plt.tight_layout() ###Output Engineering Sciences - ['Humanities and Social Sciences'] : Number of Documents - 6 Rare words ['metal', 'landscape', 'design', 'jewish', 'medium', 'research', 'study', 'political', 'conflict', 'architecture', 'building', 'architectural', 'public', 'mass', 'east', 'process', 'history'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Engineering Sciences'] : Number of Documents - 14 Rare words ['building', 'system', 'architecture', 'design', 'architectural', 'new', 'research', 'concept', 'learning', 'urban', 'model', 'development', 'study', 'develop', 'different', 'peer'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Engineering Sciences', 'Life Sciences'] : Number of Documents - 7 Rare words ['method', 'perception', 'privacy', 'research', 'vr', 'ess', 'site', 'user', 'development', 'energy', 'model', 'approach', 'exist', 'location', 'regional', 'develop'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Engineering Sciences', 'Natural Sciences'] : Number of Documents - 7 Rare words ['urban', 'design', 'good', 'newspaper', 'new', 'development', 'research', 'study', 'function', 'method', 'barter', 'practice', 'party', 'historic', 'develop', 'historical', 'national'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Life Sciences'] : Number of Documents - 2 Rare words ['sound', 'shift', 'melatonin', 'night', 'noise', 'light', 'judgement', 'process', 'test', 'suppression', 'effect', 'health', 'low', 'profile', 'high', 'synthesis', 'experiment', 'hourly'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Life Sciences', 'Engineering Sciences'] : Number of Documents - 9 Rare words ['different', 'planning', 'model', 'noise', 'impact', 'system', 'video', 'self', 'pain', 'state', 'brain', 'approach', 'carshare', 'training', 'study', 'control'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Natural Sciences'] : Number of Documents - 3 Rare words ['housing', 'jewish', 'facility', 'naumburg', 'schultze', 'local', 'community', 'architecture', 'building', 'network', 'national', 'art', 'process', 'research', 'architectural', 'berlin', 'new', 'center'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Natural Sciences', 'Engineering Sciences'] : Number of Documents - 6 Rare words ['urban', 'city', 'environmental', 'new', 'research', 'infrastructure', 'form', 'west', 'bengal', 'historical', 'ideal', 'area', 'planning', 'landscape', 'cultural', 'development', 'element'] ---------------------------------------------------------- Engineering Sciences - ['Humanities and Social Sciences', 'Natural Sciences', 'Life Sciences'] : Number of Documents - 1 ["'Ecosystem services' (ESS) has become a key term of the international, the European and increasingly also the German debates on nature conservation and landscape management. It may be regarded as an indicator of a programmatic reorientation of biodiversity policies in an economic vein. It has hardly been studied hitherto how governing in the policy area 'nature conservation and landscape management' is changing in Germany with the increased use of the term 'ecosystem services'. For instance, does an economisation or neoliberalisation of nature and landscape occur, that is, an expansion of the application of economic and market-based principles, as is often described at the international level? Or do counteracting forces prevail that end up reinforcing the well-established relationship of governmental regulation, civil society involvement and market forces? Or is a specific novel understanding of nature and landscape policies developing in the course of the ESS discourses currently being produced in Germany? - These fundamental questions lie at the heart of the proposed project. The aim is to study ESS discourses in Germany from the perspective of governmentality research. It is to be analysed how nature conservation and landscape management are debated in connection with the economically influenced ESS concept. The focus is on the problematisations and rationalities of governing in the policy area 'nature conservation and landscape management', in particular on the dynamics of changes in these problematisations and rationalities in Germany. Closely related is the question which changes are to be observed in how the objects of these policies (that is, nature, landscape, biological diversity, planning etc.) are constituted as a part of problematisations and whether even entirely new objects arise in the course of the ES discourses. The project is conceived as a discourse analysis, relying on quantitative lexicometric methods as well as on qualitative empirical methods such as document analyses, semi-structured interviews and participant observation. Among others, the initiatives 'Nature capital Germany - TEEB DE' and 'Implementation of Action 5 of the EU Biodiversity Strategy in Germany' (MAES DE) are to be studied in depth. "] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences'] : Number of Documents - 5 Rare words ['cell', 'brain', 'nirs', 'olg', 'tissue', 'lung', 'model', 'shall', 'experiment', 'perfusion', 'crs', 'eit', 'regional', 'signal', 'develop'] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences', 'Engineering Sciences'] : Number of Documents - 8 Rare words ['cell', 'blood', 'process', 'system', 'surfactin', 'cementum', 'bladder', 'model', 'culture', 'method', 'development', 'contact', 'study', 'co', 'analysis', 'synaptic', 'neural', 'image'] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences', 'Engineering Sciences', 'Humanities and Social Sciences'] : Number of Documents - 4 Rare words ['bci', 'motion', 'system', 'model', 'mutation', 'sickness', 'glucose', 'patient', 'test', 'mutant', 'detect', 'suite', 'insulin', 'diabetes', 'control', 'approach', 'influence', 'study'] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences', 'Engineering Sciences', 'Natural Sciences'] : Number of Documents - 14 Rare words ['cell', 'system', 'control', 'production', 'microfluidic', 'method', 'surface', 'process', 'high', 'protein', 'nanoparticle', 'sample', 'detection', 'biomarker', 'develop', 'electrode', 'wood', 'low'] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences', 'Humanities and Social Sciences'] : Number of Documents - 2 Rare words ['leg', 'network', 'oscillator', 'neuronal', 'cpg', 'coupling', 'mechanism', 'know', 'signal', 'different', 'understand', 'system', 'neuron', 'type', 'inter', 'insect', 'model', 'stick', 'joint', 'influence'] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences', 'Humanities and Social Sciences', 'Engineering Sciences'] : Number of Documents - 5 Rare words ['algorithm', 'water', 'eye', 'speech', 'assessment', 'test', 'impact', 'method', 'processing', 'methodological', 'develop', 'eeg', 'signal', 'use', 'consumption', 'footprint', 'intelligibility', 'manufacturing'] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences', 'Humanities and Social Sciences', 'Natural Sciences'] : Number of Documents - 1 ["The BULB project aims at supporting the documentation of unwritten languages with the help of automatic speech and language processing, in particular automatic speech recognition (ASR) and machine translation (MT). We will address the documentation of three mostly unwritten African languages of the Bantu family (Basaa, Myene and Embosi). The main steps of the project are:1. To collect the corpora at a reasonable cost, using a three step methodology, following the work of S. Bird and M. Liberman:collecting a large corpus of speech (100 hours) in a community, including elicited material, stories, dialogs and broadcasts;re-speaking. As the sound quality of the recordings will be very spontaneous, with possibly overlapping speech in noisy environments, carefully articulated re-speaking by a reference speaker will give rise to more accurate automatic phonetic transcriptions and to improved material for phonetic/phonological studies.oral translation. Translation is the natural way to document a new language; oral translations will accelerate the documentation process. Our Bantu data will be translated to French, a major language and a second language in the regions of our studied communities.2. The collected oral data (Bantu originals and French translations) contain the necessary information to document the studied languages. ASR is expected to automatically produce accurate transcriptions in source and target languages and MT to provide meaningful alignments between both, to speed up the major tasks of documentation, description and analysis. The major automatic processing steps are:phonetic transcription of the studied languages. This step requires first a set of language-independent phone models which must be tuned to the language under study via unsupervised adaptation techniques;word transcription of the oral French translations. Language and acoustic models need to be adapted to obtain high transcription accuracy;alignments between the phonetic transcriptions (originals, respeaking) of the studied language. Alignments are highly valuable for large scale acoustic-phonetic studies, phonological and prosodic data mining and dialectal variations studies;cross-language alignments that aim at linking phone sequences in the studied language with French words. Such alignments may prove very useful for morphological studies, vocabulary and pronunciation elaboration.The success of the project relies on a strong German-French cooperation between linguists and computer scientists. Cooperations will be fostered and strengthened by a series of courses benefiting the scientific community beyond the present consortium. During these courses, linguists will present to computer scientists the major steps to document an unknown language, and computer scientists will introduce their methods to process a 'new' language thus generating phonetic transcriptions and pseudo-word alignments to be returned to linguists. "] ---------------------------------------------------------- Engineering Sciences - ['Life Sciences', 'Natural Sciences'] : Number of Documents - 5 ###Markdown Visualization ###Code def CattoID(input_cat): if(input_cat=='Engineering Sciences'): return 0 elif(input_cat=='Humanities and Social Sciences'): return 1 elif(input_cat=='Natural Sciences'): return 2 elif(input_cat=='Life Sciences'): return 3 else : return -1 NewMergedDSAligned2=pd.concat([merged_data,PredictedValues[PredictedValues.columns[4:]]], axis=1, ignore_index=False) NewMergedDSAligned2.loc[:,'Category_1_ID']=NewMergedDSAligned2.Category_1.apply(CattoID) NewMergedDSAligned2.loc[:,'Category_2_ID']=NewMergedDSAligned2.Category_2.apply(CattoID) NewMergedDSAligned2.loc[:,'Category_3_ID']=NewMergedDSAligned2.Category_3.apply(CattoID) NewMergedDSAligned2=pd.DataFrame(enumerate(NewMergedDSAligned2.SubjectArea.unique()), columns=['Subjectid','SubjectAreaMatching']).merge(NewMergedDSAligned2,left_on='SubjectAreaMatching', right_on='SubjectArea') cats=['Engineering Sciences','Humanities and Social Sciences', 'Life Sciences','Natural Sciences'] cats_dist=[] ## Finiding the overall similiarity for c, w in NewMergedDSAligned2[(NewMergedDSAligned2['Category']!=NewMergedDSAligned2['Category_1']) & (NewMergedDSAligned2['DBScanCluster']!=0)].groupby('Category'): #print('') #print(c, len(w)) #other_cat=list(filter(lambda x:x!=c, cats)) cat_dist=[] for oc in cats: if oc==c: oc_sim=0 else: oc_sum=sum(w[w['Category_1']==oc].Category_1_Values.tolist()+w[w['Category_2']==oc].Category_2_Values.tolist()+w[w['Category_3']==oc].Category_3_Values.tolist()) oc_sim=oc_sum/len(w) cat_dist.append(oc_sim) #print(c,':',oc,'-', round(oc_sim,2)) #oc_sum=w[w['Category_1']==oc].Category_1_Values.tolist()+w[w['Category_2']==oc].Category_2_Values.tolist()+w[w['Category_3']==oc].Category_3_Values.tolist() #oc_sim=sum(oc_sum)/len(oc_sum) #print(c,':',oc,'-', round(oc_sim,2)) cats_dist.append(np.array(cat_dist)) cats_dist=np.array(cats_dist) ## Making symmetric matrix sym_dist=np.zeros(cats_dist.shape) for i in range(cats_dist.shape[0]): for j in range(cats_dist.shape[0]): sym_dist[i][j]=cats_dist[i][j]+ cats_dist[j][i] if(i==j): sym_dist[i][j]=1 # 1-x : convert similiarity to distance sym_dist=1-pd.DataFrame(sym_dist, columns=cats, index=cats) ## Generating coordinates from distance #, angle=0.8 #coords = TSNE(n_components=2,perplexity=.1, random_state=12, metric='precomputed').fit_transform(sym_dist) #coords = TSNE(n_components=2,perplexity=.1, random_state=23, metric='precomputed').fit_transform(sym_dist) coords = PCA(n_components=2, svd_solver = 'full').fit_transform(sym_dist) coords=MinMaxScaler([0,1000]).fit_transform(coords) coords=pd.DataFrame(coords, index=cats).reset_index() p1=sns.scatterplot( x=0, y=1, hue="index", # palette=sns.color_palette("hls", 4), data=coords, # legend="full", alpha=1, size = 8, legend=False ); for line in range(0,coords.shape[0]): p1.text(coords[0][line]+0.01, coords[1][line], cats[line], horizontalalignment='left', size='medium', color='black') sym_dist newrange=pd.DataFrame(NewMergedDSAligned2.Category.value_counts()/80).reset_index().merge(coords,left_on='index',right_on='index') newrange.loc[:,'Min_X']=newrange[0]-newrange['Category'] newrange.loc[:,'Max_X']=newrange[0]+newrange['Category'] newrange.loc[:,'Min_Y']=newrange[1]-(newrange['Category']*.60) newrange.loc[:,'Max_Y']=newrange[1]+(newrange['Category']*.60) newrange.columns=['Category','size', 0, 1, 'Min_X', 'Max_X', 'Min_Y', 'Max_Y'] newrange pca.shape catsperplexity={'Engineering Sciences':5,'Humanities and Social Sciences':5, 'Life Sciences':10,'Natural Sciences':8} ## T-SNE separately for each categories outerclusterfeatures=['Category_1_Values','Category_1_ID','Category_2_ID','Category_2_Values','Category_3_ID','Category_3_Values','Subjectid'] #Doc2VecModelData=pd.concat([pd.DataFrame(model.docvecs.vectors_docs),NewMergedDSAligned2[outerclusterfeatures]], axis=1) Doc2VecModelData=pd.concat([pd.DataFrame(pca),NewMergedDSAligned2[outerclusterfeatures]], axis=1) Doc2VecModelData['tsne-2d-one']=0 Doc2VecModelData['tsne-2d-two']=0 for cat in cats:#['Life Sciences']:# print(str(datetime.datetime.now()),'Started for', cat) tsne = TSNE(n_components=2, perplexity=catsperplexity[cat], n_iter=300, random_state=0, learning_rate=100) ## The perplexity is related to the number of nearest neighbors that is used in other manifold learning algorithms. ## Larger datasets usually require a larger perplexity. Consider selecting a value between 5 and 50. tsne_results = tsne.fit_transform(Doc2VecModelData[NewMergedDSAligned2.Category==cat]) Doc2VecModelData.loc[NewMergedDSAligned2.Category==cat,'tsne-2d-one'] = tsne_results[:,0] Doc2VecModelData.loc[NewMergedDSAligned2.Category==cat,'tsne-2d-two'] = tsne_results[:,1] print(str(datetime.datetime.now()),'Completed for', cat) Doc2VecModelData.loc[:,'Category'] = NewMergedDSAligned2.Category Doc2VecModelData.loc[:,'Category_1'] = NewMergedDSAligned2.Category_1 # Reshaping for cat in cats: model_x=MinMaxScaler([newrange[newrange['Category']==cat].Min_X.values[0],newrange[newrange['Category']==cat].Max_X.values[0]]) Doc2VecModelData.loc[Doc2VecModelData['Category']==cat,'tsne-2d-one']=model_x.fit_transform(Doc2VecModelData[Doc2VecModelData['Category']==cat][['tsne-2d-one']]) model_y=MinMaxScaler([newrange[newrange['Category']==cat].Min_Y.values[0],newrange[newrange['Category']==cat].Max_Y.values[0]]) Doc2VecModelData.loc[Doc2VecModelData['Category']==cat,'tsne-2d-two']=model_y.fit_transform(Doc2VecModelData[Doc2VecModelData['Category']==cat][['tsne-2d-two']]) cat='Life Sciences'#'Engineering Sciences'#'Life Sciences'#'Humanities and Social Sciences'#'Life Sciences'#' plt.figure(figsize=(13,8)) sns.scatterplot( x="tsne-2d-one", y="tsne-2d-two", hue="Category_1", data=Doc2VecModelData[Doc2VecModelData.Category==cat], legend="full", # style='Category_1', alpha=0.8 ); plt.figure(figsize=(13,8)) sns.scatterplot( x="tsne-2d-one", y="tsne-2d-two", hue="Category_1", data=Doc2VecModelData, legend="full", style='Category', alpha=0.8 ); def label_genarator(input): if((input.Category==input.Category_1) or (input.DBScanCluster==0)): return ''#'Category : '+input.Category else: if((input.Category_3_Values==0) and (input.Category_2_Values==0)): return '('+input.Category_1+' '+str(round(input.Category_1_Values*100))+'%'+')' elif((input.Category_3_Values==0) and (input.Category_2_Values!=0)): return '('+input.Category_1+' '+str(round(input.Category_1_Values*100))+'%, '+input.Category_2+' '+str(round(input.Category_2_Values*100))+'%)' else: return '('+input.Category_1+' '+str(round(input.Category_1_Values*100))+'%, '+input.Category_2+' '+str(round(input.Category_2_Values*100))+'%, '+input.Category_3+' '+str(round(input.Category_3_Values*100))+'%)' Report_extrat=pd.concat([NewMergedDSAligned2[['Name','Institution','FundingFrom','FundingEnd', 'Category','Category_1_Values','Category_2_Values','Category_3_Values','Category_1','Category_2','Category_3','DBScanCluster']],Doc2VecModelData[['tsne-2d-one', 'tsne-2d-two']]], axis=1) Report_extrat['ProjectURL']=NewMergedDSAligned2.SubUrl.apply(lambda x:'https://gepris.dfg.de'+x) Report_extrat['label']=Report_extrat.apply(label_genarator, axis=1) Report_extrat['interdiscipilinary']=False Report_extrat.loc[(Report_extrat.label!='') & (NewMergedDSAligned2['DBScanCluster']!=0),'interdiscipilinary']=True Report_extrat['color']=Report_extrat['Category'] Report_extrat.loc[Report_extrat['interdiscipilinary'],'color']=Report_extrat.loc[Report_extrat['interdiscipilinary'],'Category_1'] Report_extrat.to_csv(Path+'Report_WEPCADBScanFindingsKMeansV2.csv', index=False) newrange.to_csv(Path+'CATRANGE_WEPCADBScanFindingsKMeansV2.csv', index=False) ###Output _____no_output_____

doc/source/ray-air/examples/rl_online_example.ipynb

###Markdown Online reinforcement learning with Ray AIRIn this example, we'll train a reinforcement learning agent using online training.Online trainig means that the data from the environment is sampled while we are running the algorithm. In contrast, offline training uses data that has been stored on disk before. Let's start with installing our dependencies: ###Code !pip install -qU "ray[rllib]" gym ###Output _____no_output_____ ###Markdown Now we can run some imports: ###Code import argparse import gym import os import numpy as np import ray from ray.ml import Checkpoint from ray.ml.config import RunConfig from ray.ml.predictors.integrations.rl.rl_predictor import RLPredictor from ray.ml.train.integrations.rl.rl_trainer import RLTrainer from ray.ml.result import Result from ray.rllib.agents.marwil import BCTrainer from ray.tune.tuner import Tuner ###Output 2022-05-19 13:54:16,520 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:54:16,531 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.marwil` has been deprecated. Use `ray.rllib.algorithms.marwil` instead. This will raise an error in the future! ###Markdown Here we define the training function. It will create an `RLTrainer` using the `PPO` algorithm and kick off training on the `CartPole-v0` environment: ###Code def train_rl_ppo_online(num_workers: int, use_gpu: bool = False) -> Result: print("Starting online training") trainer = RLTrainer( run_config=RunConfig(stop={"training_iteration": 5}), scaling_config={ "num_workers": num_workers, "use_gpu": use_gpu, }, algorithm="PPO", config={ "env": "CartPole-v0", "framework": "tf", }, ) # Todo (krfricke/xwjiang): Enable checkpoint config in RunConfig # result = trainer.fit() tuner = Tuner( trainer, _tuner_kwargs={"checkpoint_at_end": True}, ) result = tuner.fit()[0] return result ###Output _____no_output_____ ###Markdown Once we trained our RL policy, we want to evaluate it on a fresh environment. For this, we will also define a utility function: ###Code def evaluate_using_checkpoint(checkpoint: Checkpoint, num_episodes) -> list: predictor = RLPredictor.from_checkpoint(checkpoint) env = gym.make("CartPole-v0") rewards = [] for i in range(num_episodes): obs = env.reset() reward = 0.0 done = False while not done: action = predictor.predict([obs]) obs, r, done, _ = env.step(action[0]) reward += r rewards.append(reward) return rewards ###Output _____no_output_____ ###Markdown Let's put it all together. First, we run training: ###Code result = train_rl_ppo_online(num_workers=2, use_gpu=False) ###Output 2022-05-19 13:54:16,582 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.dqn.dqn.DEFAULT_CONFIG` has been deprecated. Use `ray.rllib.agents.dqn.dqn.DQNConfig(...)` instead. This will raise an error in the future! ###Markdown And then, using the obtained checkpoint, we evaluate the policy on a fresh environment: ###Code num_eval_episodes = 3 rewards = evaluate_using_checkpoint(result.checkpoint, num_episodes=num_eval_episodes) print(f"Average reward over {num_eval_episodes} episodes: " f"{np.mean(rewards)}") ###Output 2022-05-19 13:54:58,589 INFO trainer.py:1728 -- Your framework setting is 'tf', meaning you are using static-graph mode. Set framework='tf2' to enable eager execution with tf2.x. You may also then want to set eager_tracing=True in order to reach similar execution speed as with static-graph mode. 2022-05-19 13:54:58,590 WARNING deprecation.py:47 -- DeprecationWarning: `simple_optimizer` has been deprecated. This will raise an error in the future! 2022-05-19 13:54:58,591 INFO ppo.py:361 -- In multi-agent mode, policies will be optimized sequentially by the multi-GPU optimizer. Consider setting simple_optimizer=True if this doesn't work for you. 2022-05-19 13:54:58,591 INFO trainer.py:328 -- Current log_level is WARN. For more information, set 'log_level': 'INFO' / 'DEBUG' or use the -v and -vv flags. (RolloutWorker pid=14191) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! (RolloutWorker pid=14192) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:55:07,968 WARNING util.py:65 -- Install gputil for GPU system monitoring. 2022-05-19 13:55:08,021 INFO trainable.py:589 -- Restored on 127.0.0.1 from checkpoint: /Users/kai/ray_results/AIRPPOTrainer_2022-05-19_13-54-16/AIRPPOTrainer_cd8d6_00000_0_2022-05-19_13-54-22/checkpoint_000005/checkpoint-5 2022-05-19 13:55:08,021 INFO trainable.py:597 -- Current state after restoring: {'_iteration': 5, '_timesteps_total': None, '_time_total': 16.702913284301758, '_episodes_total': 354} ###Markdown Online reinforcement learning with Ray AIRIn this example, we'll train a reinforcement learning agent using online training.Online trainig means that the data from the environment is sampled while we are running the algorithm. In contrast, offline training uses data that has been stored on disk before. Let's start with installing our dependencies: ###Code !pip install -qU "ray[rllib]" gym ###Output _____no_output_____ ###Markdown Now we can run some imports: ###Code import argparse import gym import os import numpy as np import ray from ray.air import Checkpoint from ray.air.config import RunConfig from ray.air.predictors.integrations.rl.rl_predictor import RLPredictor from ray.air.train.integrations.rl.rl_trainer import RLTrainer from ray.air.result import Result from ray.rllib.agents.marwil import BCTrainer from ray.tune.tuner import Tuner ###Output 2022-05-19 13:54:16,520 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:54:16,531 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.marwil` has been deprecated. Use `ray.rllib.algorithms.marwil` instead. This will raise an error in the future! ###Markdown Here we define the training function. It will create an `RLTrainer` using the `PPO` algorithm and kick off training on the `CartPole-v0` environment: ###Code def train_rl_ppo_online(num_workers: int, use_gpu: bool = False) -> Result: print("Starting online training") trainer = RLTrainer( run_config=RunConfig(stop={"training_iteration": 5}), scaling_config={ "num_workers": num_workers, "use_gpu": use_gpu, }, algorithm="PPO", config={ "env": "CartPole-v0", "framework": "tf", }, ) # Todo (krfricke/xwjiang): Enable checkpoint config in RunConfig # result = trainer.fit() tuner = Tuner( trainer, _tuner_kwargs={"checkpoint_at_end": True}, ) result = tuner.fit()[0] return result ###Output _____no_output_____ ###Markdown Once we trained our RL policy, we want to evaluate it on a fresh environment. For this, we will also define a utility function: ###Code def evaluate_using_checkpoint(checkpoint: Checkpoint, num_episodes) -> list: predictor = RLPredictor.from_checkpoint(checkpoint) env = gym.make("CartPole-v0") rewards = [] for i in range(num_episodes): obs = env.reset() reward = 0.0 done = False while not done: action = predictor.predict([obs]) obs, r, done, _ = env.step(action[0]) reward += r rewards.append(reward) return rewards ###Output _____no_output_____ ###Markdown Let's put it all together. First, we run training: ###Code result = train_rl_ppo_online(num_workers=2, use_gpu=False) ###Output 2022-05-19 13:54:16,582 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.dqn.dqn.DEFAULT_CONFIG` has been deprecated. Use `ray.rllib.agents.dqn.dqn.DQNConfig(...)` instead. This will raise an error in the future! ###Markdown And then, using the obtained checkpoint, we evaluate the policy on a fresh environment: ###Code num_eval_episodes = 3 rewards = evaluate_using_checkpoint(result.checkpoint, num_episodes=num_eval_episodes) print(f"Average reward over {num_eval_episodes} episodes: " f"{np.mean(rewards)}") ###Output 2022-05-19 13:54:58,589 INFO trainer.py:1728 -- Your framework setting is 'tf', meaning you are using static-graph mode. Set framework='tf2' to enable eager execution with tf2.x. You may also then want to set eager_tracing=True in order to reach similar execution speed as with static-graph mode. 2022-05-19 13:54:58,590 WARNING deprecation.py:47 -- DeprecationWarning: `simple_optimizer` has been deprecated. This will raise an error in the future! 2022-05-19 13:54:58,591 INFO ppo.py:361 -- In multi-agent mode, policies will be optimized sequentially by the multi-GPU optimizer. Consider setting simple_optimizer=True if this doesn't work for you. 2022-05-19 13:54:58,591 INFO trainer.py:328 -- Current log_level is WARN. For more information, set 'log_level': 'INFO' / 'DEBUG' or use the -v and -vv flags. (RolloutWorker pid=14191) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! (RolloutWorker pid=14192) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:55:07,968 WARNING util.py:65 -- Install gputil for GPU system monitoring. 2022-05-19 13:55:08,021 INFO trainable.py:589 -- Restored on 127.0.0.1 from checkpoint: /Users/kai/ray_results/AIRPPOTrainer_2022-05-19_13-54-16/AIRPPOTrainer_cd8d6_00000_0_2022-05-19_13-54-22/checkpoint_000005/checkpoint-5 2022-05-19 13:55:08,021 INFO trainable.py:597 -- Current state after restoring: {'_iteration': 5, '_timesteps_total': None, '_time_total': 16.702913284301758, '_episodes_total': 354} ###Markdown Online reinforcement learning with Ray AIRIn this example, we'll train a reinforcement learning agent using online training.Online training means that the data from the environment is sampled while we are running the algorithm. In contrast, offline training uses data that has been stored on disk before. Let's start with installing our dependencies: ###Code !pip install -qU "ray[rllib]" gym ###Output _____no_output_____ ###Markdown Now we can run some imports: ###Code import argparse import gym import os import numpy as np import ray from ray.air import Checkpoint from ray.air.config import RunConfig from ray.air.predictors.integrations.rl.rl_predictor import RLPredictor from ray.train.rl.rl_trainer import RLTrainer from ray.air.result import Result from ray.rllib.agents.marwil import BCTrainer from ray.tune.tuner import Tuner ###Output 2022-05-19 13:54:16,520 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:54:16,531 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.marwil` has been deprecated. Use `ray.rllib.algorithms.marwil` instead. This will raise an error in the future! ###Markdown Here we define the training function. It will create an `RLTrainer` using the `PPO` algorithm and kick off training on the `CartPole-v0` environment: ###Code def train_rl_ppo_online(num_workers: int, use_gpu: bool = False) -> Result: print("Starting online training") trainer = RLTrainer( run_config=RunConfig(stop={"training_iteration": 5}), scaling_config={ "num_workers": num_workers, "use_gpu": use_gpu, }, algorithm="PPO", config={ "env": "CartPole-v0", "framework": "tf", }, ) # Todo (krfricke/xwjiang): Enable checkpoint config in RunConfig # result = trainer.fit() tuner = Tuner( trainer, _tuner_kwargs={"checkpoint_at_end": True}, ) result = tuner.fit()[0] return result ###Output _____no_output_____ ###Markdown Once we trained our RL policy, we want to evaluate it on a fresh environment. For this, we will also define a utility function: ###Code def evaluate_using_checkpoint(checkpoint: Checkpoint, num_episodes) -> list: predictor = RLPredictor.from_checkpoint(checkpoint) env = gym.make("CartPole-v0") rewards = [] for i in range(num_episodes): obs = env.reset() reward = 0.0 done = False while not done: action = predictor.predict([obs]) obs, r, done, _ = env.step(action[0]) reward += r rewards.append(reward) return rewards ###Output _____no_output_____ ###Markdown Let's put it all together. First, we run training: ###Code result = train_rl_ppo_online(num_workers=2, use_gpu=False) ###Output 2022-05-19 13:54:16,582 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.dqn.dqn.DEFAULT_CONFIG` has been deprecated. Use `ray.rllib.agents.dqn.dqn.DQNConfig(...)` instead. This will raise an error in the future! ###Markdown And then, using the obtained checkpoint, we evaluate the policy on a fresh environment: ###Code num_eval_episodes = 3 rewards = evaluate_using_checkpoint(result.checkpoint, num_episodes=num_eval_episodes) print(f"Average reward over {num_eval_episodes} episodes: " f"{np.mean(rewards)}") ###Output 2022-05-19 13:54:58,589 INFO trainer.py:1728 -- Your framework setting is 'tf', meaning you are using static-graph mode. Set framework='tf2' to enable eager execution with tf2.x. You may also then want to set eager_tracing=True in order to reach similar execution speed as with static-graph mode. 2022-05-19 13:54:58,590 WARNING deprecation.py:47 -- DeprecationWarning: `simple_optimizer` has been deprecated. This will raise an error in the future! 2022-05-19 13:54:58,591 INFO ppo.py:361 -- In multi-agent mode, policies will be optimized sequentially by the multi-GPU optimizer. Consider setting simple_optimizer=True if this doesn't work for you. 2022-05-19 13:54:58,591 INFO trainer.py:328 -- Current log_level is WARN. For more information, set 'log_level': 'INFO' / 'DEBUG' or use the -v and -vv flags. (RolloutWorker pid=14191) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! (RolloutWorker pid=14192) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:55:07,968 WARNING util.py:65 -- Install gputil for GPU system monitoring. 2022-05-19 13:55:08,021 INFO trainable.py:589 -- Restored on 127.0.0.1 from checkpoint: /Users/kai/ray_results/AIRPPOTrainer_2022-05-19_13-54-16/AIRPPOTrainer_cd8d6_00000_0_2022-05-19_13-54-22/checkpoint_000005/checkpoint-5 2022-05-19 13:55:08,021 INFO trainable.py:597 -- Current state after restoring: {'_iteration': 5, '_timesteps_total': None, '_time_total': 16.702913284301758, '_episodes_total': 354} ###Markdown Online reinforcement learning with Ray AIRIn this example, we'll train a reinforcement learning agent using online training.Online training means that the data from the environment is sampled while we are running the algorithm. In contrast, offline training uses data that has been stored on disk before. Let's start with installing our dependencies: ###Code !pip install -qU "ray[rllib]" gym ###Output _____no_output_____ ###Markdown Now we can run some imports: ###Code import argparse import gym import os import numpy as np import ray from ray.air import Checkpoint from ray.air.config import RunConfig from ray.train.rl.rl_predictor import RLPredictor from ray.train.rl.rl_trainer import RLTrainer from ray.air.result import Result from ray.rllib.agents.marwil import BCTrainer from ray.tune.tuner import Tuner ###Output 2022-05-19 13:54:16,520 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:54:16,531 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.marwil` has been deprecated. Use `ray.rllib.algorithms.marwil` instead. This will raise an error in the future! ###Markdown Here we define the training function. It will create an `RLTrainer` using the `PPO` algorithm and kick off training on the `CartPole-v0` environment: ###Code def train_rl_ppo_online(num_workers: int, use_gpu: bool = False) -> Result: print("Starting online training") trainer = RLTrainer( run_config=RunConfig(stop={"training_iteration": 5}), scaling_config={ "num_workers": num_workers, "use_gpu": use_gpu, }, algorithm="PPO", config={ "env": "CartPole-v0", "framework": "tf", }, ) # Todo (krfricke/xwjiang): Enable checkpoint config in RunConfig # result = trainer.fit() tuner = Tuner( trainer, _tuner_kwargs={"checkpoint_at_end": True}, ) result = tuner.fit()[0] return result ###Output _____no_output_____ ###Markdown Once we trained our RL policy, we want to evaluate it on a fresh environment. For this, we will also define a utility function: ###Code def evaluate_using_checkpoint(checkpoint: Checkpoint, num_episodes) -> list: predictor = RLPredictor.from_checkpoint(checkpoint) env = gym.make("CartPole-v0") rewards = [] for i in range(num_episodes): obs = env.reset() reward = 0.0 done = False while not done: action = predictor.predict([obs]) obs, r, done, _ = env.step(action[0]) reward += r rewards.append(reward) return rewards ###Output _____no_output_____ ###Markdown Let's put it all together. First, we run training: ###Code result = train_rl_ppo_online(num_workers=2, use_gpu=False) ###Output 2022-05-19 13:54:16,582 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.dqn.dqn.DEFAULT_CONFIG` has been deprecated. Use `ray.rllib.agents.dqn.dqn.DQNConfig(...)` instead. This will raise an error in the future! ###Markdown And then, using the obtained checkpoint, we evaluate the policy on a fresh environment: ###Code num_eval_episodes = 3 rewards = evaluate_using_checkpoint(result.checkpoint, num_episodes=num_eval_episodes) print(f"Average reward over {num_eval_episodes} episodes: " f"{np.mean(rewards)}") ###Output 2022-05-19 13:54:58,589 INFO trainer.py:1728 -- Your framework setting is 'tf', meaning you are using static-graph mode. Set framework='tf2' to enable eager execution with tf2.x. You may also then want to set eager_tracing=True in order to reach similar execution speed as with static-graph mode. 2022-05-19 13:54:58,590 WARNING deprecation.py:47 -- DeprecationWarning: `simple_optimizer` has been deprecated. This will raise an error in the future! 2022-05-19 13:54:58,591 INFO ppo.py:361 -- In multi-agent mode, policies will be optimized sequentially by the multi-GPU optimizer. Consider setting simple_optimizer=True if this doesn't work for you. 2022-05-19 13:54:58,591 INFO trainer.py:328 -- Current log_level is WARN. For more information, set 'log_level': 'INFO' / 'DEBUG' or use the -v and -vv flags. (RolloutWorker pid=14191) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! (RolloutWorker pid=14192) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:55:07,968 WARNING util.py:65 -- Install gputil for GPU system monitoring. 2022-05-19 13:55:08,021 INFO trainable.py:589 -- Restored on 127.0.0.1 from checkpoint: /Users/kai/ray_results/AIRPPOTrainer_2022-05-19_13-54-16/AIRPPOTrainer_cd8d6_00000_0_2022-05-19_13-54-22/checkpoint_000005/checkpoint-5 2022-05-19 13:55:08,021 INFO trainable.py:597 -- Current state after restoring: {'_iteration': 5, '_timesteps_total': None, '_time_total': 16.702913284301758, '_episodes_total': 354} ###Markdown Online reinforcement learning with Ray AIRIn this example, we'll train a reinforcement learning agent using online training.Online training means that the data from the environment is sampled while we are running the algorithm. In contrast, offline training uses data that has been stored on disk before. Let's start with installing our dependencies: ###Code !pip install -qU "ray[rllib]" gym ###Output _____no_output_____ ###Markdown Now we can run some imports: ###Code import argparse import gym import os import numpy as np import ray from ray.air import Checkpoint from ray.air.config import RunConfig from ray.air.predictors.integrations.rl.rl_predictor import RLPredictor from ray.air.train.integrations.rl.rl_trainer import RLTrainer from ray.air.result import Result from ray.rllib.agents.marwil import BCTrainer from ray.tune.tuner import Tuner ###Output 2022-05-19 13:54:16,520 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:54:16,531 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.marwil` has been deprecated. Use `ray.rllib.algorithms.marwil` instead. This will raise an error in the future! ###Markdown Here we define the training function. It will create an `RLTrainer` using the `PPO` algorithm and kick off training on the `CartPole-v0` environment: ###Code def train_rl_ppo_online(num_workers: int, use_gpu: bool = False) -> Result: print("Starting online training") trainer = RLTrainer( run_config=RunConfig(stop={"training_iteration": 5}), scaling_config={ "num_workers": num_workers, "use_gpu": use_gpu, }, algorithm="PPO", config={ "env": "CartPole-v0", "framework": "tf", }, ) # Todo (krfricke/xwjiang): Enable checkpoint config in RunConfig # result = trainer.fit() tuner = Tuner( trainer, _tuner_kwargs={"checkpoint_at_end": True}, ) result = tuner.fit()[0] return result ###Output _____no_output_____ ###Markdown Once we trained our RL policy, we want to evaluate it on a fresh environment. For this, we will also define a utility function: ###Code def evaluate_using_checkpoint(checkpoint: Checkpoint, num_episodes) -> list: predictor = RLPredictor.from_checkpoint(checkpoint) env = gym.make("CartPole-v0") rewards = [] for i in range(num_episodes): obs = env.reset() reward = 0.0 done = False while not done: action = predictor.predict([obs]) obs, r, done, _ = env.step(action[0]) reward += r rewards.append(reward) return rewards ###Output _____no_output_____ ###Markdown Let's put it all together. First, we run training: ###Code result = train_rl_ppo_online(num_workers=2, use_gpu=False) ###Output 2022-05-19 13:54:16,582 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.agents.dqn.dqn.DEFAULT_CONFIG` has been deprecated. Use `ray.rllib.agents.dqn.dqn.DQNConfig(...)` instead. This will raise an error in the future! ###Markdown And then, using the obtained checkpoint, we evaluate the policy on a fresh environment: ###Code num_eval_episodes = 3 rewards = evaluate_using_checkpoint(result.checkpoint, num_episodes=num_eval_episodes) print(f"Average reward over {num_eval_episodes} episodes: " f"{np.mean(rewards)}") ###Output 2022-05-19 13:54:58,589 INFO trainer.py:1728 -- Your framework setting is 'tf', meaning you are using static-graph mode. Set framework='tf2' to enable eager execution with tf2.x. You may also then want to set eager_tracing=True in order to reach similar execution speed as with static-graph mode. 2022-05-19 13:54:58,590 WARNING deprecation.py:47 -- DeprecationWarning: `simple_optimizer` has been deprecated. This will raise an error in the future! 2022-05-19 13:54:58,591 INFO ppo.py:361 -- In multi-agent mode, policies will be optimized sequentially by the multi-GPU optimizer. Consider setting simple_optimizer=True if this doesn't work for you. 2022-05-19 13:54:58,591 INFO trainer.py:328 -- Current log_level is WARN. For more information, set 'log_level': 'INFO' / 'DEBUG' or use the -v and -vv flags. (RolloutWorker pid=14191) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! (RolloutWorker pid=14192) 2022-05-19 13:55:06,622 WARNING deprecation.py:47 -- DeprecationWarning: `ray.rllib.execution.buffers` has been deprecated. Use `ray.rllib.utils.replay_buffers` instead. This will raise an error in the future! 2022-05-19 13:55:07,968 WARNING util.py:65 -- Install gputil for GPU system monitoring. 2022-05-19 13:55:08,021 INFO trainable.py:589 -- Restored on 127.0.0.1 from checkpoint: /Users/kai/ray_results/AIRPPOTrainer_2022-05-19_13-54-16/AIRPPOTrainer_cd8d6_00000_0_2022-05-19_13-54-22/checkpoint_000005/checkpoint-5 2022-05-19 13:55:08,021 INFO trainable.py:597 -- Current state after restoring: {'_iteration': 5, '_timesteps_total': None, '_time_total': 16.702913284301758, '_episodes_total': 354}

In-Db2-ML-Experiment-master/In-Db2-ML-Experiment-master/CreditCard-Notebook-Predict.ipynb

###Markdown Predicting Credit Card Fraud using Jupyter Notebook ###Code import ibm_db import ibm_db_dbi from time import time import pandas as pd from joblib import dump, load # Connect to Db2 t0=time() conn_str = "DATABASE=CRCARD;" + \ "HOSTNAME=entb06.canlab.ibm.com;"+ \ "PROTOCOL=TCPIP;" + \ "PORT=50000;" + \ "UID=PERFPOL2;" + \ "PWD=blu4speed;" ibm_db_conn = ibm_db.connect(conn_str,"","") conn = ibm_db_dbi.Connection(ibm_db_conn) print('Connection to Db2 Instance Created!') ## Load testing data from Db2 sql = 'SELECT * FROM CC_PREDICT_SCALED' #CREDIT_CARD_PREDICTION X_test = pd.read_sql(sql,conn) print('Successfully pulled test data from Db2!') # Load model + scaler saved_model = load('test/saved_model.joblib') #/data2/home/apu/saved_model.joblib print('Model loaded successfully!') # saved_scaler = load('test/saved_scaler.joblib') #/data2/home/apu/saved_scaler.joblib # print('Scaler loaded successfully!') # # Scale AMOUNT column # X_test['AMOUNT_SCALED'] = saved_scaler.transform(X_test['AMOUNT_SCALED'].values.reshape(-1,1)) ###Output _____no_output_____ ###Markdown Change `num_rows` variable to set prediction batch size ###Code # Use saved model to make a prediction on the test set num_rows=100000 y_pred_saved = saved_model.predict(X_test.sample(n=num_rows)) t1 = time() tot_time = t1-t0 print('It took', round(tot_time, 3),'s to make a prediction on', num_rows,'instances.') ###Output It took 6.246 s to make a prediction on 100000 instances.

samples/nucleus/inspect_nucleus_data.ipynb

###Markdown Inspect Nucleus Training DataInspect and visualize data loading and pre-processing code.https://www.kaggle.com/c/data-science-bowl-2018 ###Code import os import sys import itertools import math import logging import json import re import random import time import concurrent.futures import numpy as np import matplotlib import matplotlib.pyplot as plt import matplotlib.patches as patches import matplotlib.lines as lines from matplotlib.patches import Polygon import imgaug from imgaug import augmenters as iaa # Root directory of the project ROOT_DIR = os.getcwd() if ROOT_DIR.endswith("samples/nucleus"): # Go up two levels to the repo root ROOT_DIR = os.path.dirname(os.path.dirname(ROOT_DIR)) # Import Mask RCNN sys.path.append(ROOT_DIR) from mrcnn import utils from mrcnn import visualize from mrcnn.visualize import display_images from mrcnn import model as modellib from mrcnn.model import log import nucleus %matplotlib inline # Comment out to reload imported modules if they change # %load_ext autoreload # %autoreload 2 ###Output _____no_output_____ ###Markdown Configurations ###Code # Dataset directory DATASET_DIR = os.path.join(ROOT_DIR, "datasets/nucleus") # Use configuation from nucleus.py, but override # image resizing so we see the real sizes here class NoResizeConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "none" config = NoResizeConfig() ###Output _____no_output_____ ###Markdown Notebook Preferences ###Code def get_ax(rows=1, cols=1, size=16): """Return a Matplotlib Axes array to be used in all visualizations in the notebook. Provide a central point to control graph sizes. Adjust the size attribute to control how big to render images """ _, ax = plt.subplots(rows, cols, figsize=(size*cols, size*rows)) return ax ###Output _____no_output_____ ###Markdown DatasetDownload the dataset from the competition Website. Unzip it and save it in `mask_rcnn/datasets/nucleus`. If you prefer a different directory then change the `DATASET_DIR` variable above.https://www.kaggle.com/c/data-science-bowl-2018/data ###Code # Load dataset dataset = nucleus.NucleusDataset() # The subset is the name of the sub-directory, such as stage1_train, # stage1_test, ...etc. You can also use these special values: # train: loads stage1_train but excludes validation images # val: loads validation images from stage1_train. For a list # of validation images see nucleus.py dataset.load_nucleus(DATASET_DIR, subset="train") # Must call before using the dataset dataset.prepare() print("Image Count: {}".format(len(dataset.image_ids))) print("Class Count: {}".format(dataset.num_classes)) for i, info in enumerate(dataset.class_info): print("{:3}. {:50}".format(i, info['name'])) ###Output Image Count: 645 Class Count: 2 0. BG 1. nucleus ###Markdown Display Samples ###Code # Load and display random samples image_ids = np.random.choice(dataset.image_ids, 4) for image_id in image_ids: image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) visualize.display_top_masks(image, mask, class_ids, dataset.class_names, limit=1) # Example of loading a specific image by its source ID source_id = "ed5be4b63e9506ad64660dd92a098ffcc0325195298c13c815a73773f1efc279" # Map source ID to Dataset image_id # Notice the nucleus prefix: it's the name given to the dataset in NucleusDataset image_id = dataset.image_from_source_map["nucleus.{}".format(source_id)] # Load and display image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("molded_image", image) log("mask", mask) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, show_bbox=False) ###Output molded_image shape: (256, 320, 3) min: 28.00000 max: 232.00000 uint8 mask shape: (56, 56, 42) min: 0.00000 max: 1.00000 bool ###Markdown Dataset StatsLoop through all images in the dataset and collect aggregate stats. ###Code def image_stats(image_id): """Returns a dict of stats for one image.""" image = dataset.load_image(image_id) mask, _ = dataset.load_mask(image_id) bbox = utils.extract_bboxes(mask) # Sanity check assert mask.shape[:2] == image.shape[:2] # Return stats dict return { "id": image_id, "shape": list(image.shape), "bbox": [[b[2] - b[0], b[3] - b[1]] for b in bbox # Uncomment to exclude nuclei with 1 pixel width # or height (often on edges) # if b[2] - b[0] > 1 and b[3] - b[1] > 1 ], "color": np.mean(image, axis=(0, 1)), } # Loop through the dataset and compute stats over multiple threads # This might take a few minutes t_start = time.time() with concurrent.futures.ThreadPoolExecutor() as e: stats = list(e.map(image_stats, dataset.image_ids)) t_total = time.time() - t_start print("Total time: {:.1f} seconds".format(t_total)) ###Output _____no_output_____ ###Markdown Image Size Stats ###Code # Image stats image_shape = np.array([s['shape'] for s in stats]) image_color = np.array([s['color'] for s in stats]) print("Image Count: ", image_shape.shape[0]) print("Height mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 0]), np.median(image_shape[:, 0]), np.min(image_shape[:, 0]), np.max(image_shape[:, 0]))) print("Width mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 1]), np.median(image_shape[:, 1]), np.min(image_shape[:, 1]), np.max(image_shape[:, 1]))) print("Color mean (RGB): {:.2f} {:.2f} {:.2f}".format(*np.mean(image_color, axis=0))) # Histograms fig, ax = plt.subplots(1, 3, figsize=(16, 4)) ax[0].set_title("Height") _ = ax[0].hist(image_shape[:, 0], bins=20) ax[1].set_title("Width") _ = ax[1].hist(image_shape[:, 1], bins=20) ax[2].set_title("Height & Width") _ = ax[2].hist2d(image_shape[:, 1], image_shape[:, 0], bins=10, cmap="Blues") ###Output _____no_output_____ ###Markdown Nuclei per Image Stats ###Code # Segment by image area image_area_bins = [256**2, 600**2, 1300**2] print("Nuclei/Image") fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nuclei_per_image = np.array([len(s['bbox']) for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area]) area_threshold = image_area if len(nuclei_per_image) == 0: print("Image area <= {:4}**2: None".format(np.sqrt(image_area))) continue print("Image area <= {:4.0f}**2: mean: {:.1f} median: {:.1f} min: {:.1f} max: {:.1f}".format( np.sqrt(image_area), nuclei_per_image.mean(), np.median(nuclei_per_image), nuclei_per_image.min(), nuclei_per_image.max())) ax[i].set_title("Image Area <= {:4}**2".format(np.sqrt(image_area))) _ = ax[i].hist(nuclei_per_image, bins=10) ###Output _____no_output_____ ###Markdown Nuclei Size Stats ###Code # Nuclei size stats fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nucleus_shape = np.array([ b for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area for b in s['bbox']]) nucleus_area = nucleus_shape[:, 0] * nucleus_shape[:, 1] area_threshold = image_area print("\nImage Area <= {:.0f}**2".format(np.sqrt(image_area))) print(" Total Nuclei: ", nucleus_shape.shape[0]) print(" Nucleus Height. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 0]), np.median(nucleus_shape[:, 0]), np.min(nucleus_shape[:, 0]), np.max(nucleus_shape[:, 0]))) print(" Nucleus Width. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 1]), np.median(nucleus_shape[:, 1]), np.min(nucleus_shape[:, 1]), np.max(nucleus_shape[:, 1]))) print(" Nucleus Area. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_area), np.median(nucleus_area), np.min(nucleus_area), np.max(nucleus_area))) # Show 2D histogram _ = ax[i].hist2d(nucleus_shape[:, 1], nucleus_shape[:, 0], bins=20, cmap="Blues") # Nuclei height/width ratio nucleus_aspect_ratio = nucleus_shape[:, 0] / nucleus_shape[:, 1] print("Nucleus Aspect Ratio. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_aspect_ratio), np.median(nucleus_aspect_ratio), np.min(nucleus_aspect_ratio), np.max(nucleus_aspect_ratio))) plt.figure(figsize=(15, 5)) _ = plt.hist(nucleus_aspect_ratio, bins=100, range=[0, 5]) ###Output _____no_output_____ ###Markdown Image AugmentationTest out different augmentation methods ###Code # List of augmentations # http://imgaug.readthedocs.io/en/latest/source/augmenters.html augmentation = iaa.Sometimes(0.9, [ iaa.Fliplr(0.5), iaa.Flipud(0.5), iaa.Multiply((0.8, 1.2)), iaa.GaussianBlur(sigma=(0.0, 5.0)) ]) # Load the image multiple times to show augmentations limit = 4 ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False, augment=False, augmentation=augmentation) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Image CropsMicroscoy images tend to be large, but nuclei are small. So it's more efficient to train on random crops from large images. This is handled by `config.IMAGE_RESIZE_MODE = "crop"`. ###Code class RandomCropConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "crop" IMAGE_MIN_DIM = 256 IMAGE_MAX_DIM = 256 crop_config = RandomCropConfig() # Load the image multiple times to show augmentations limit = 4 image_id = np.random.choice(dataset.image_ids, 1)[0] ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, crop_config, image_id, use_mini_mask=False) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Mini MasksInstance binary masks can get large when training with high resolution images. For example, if training with 1024x1024 image then the mask of a single instance requires 1MB of memory (Numpy uses bytes for boolean values). If an image has 100 instances then that's 100MB for the masks alone. To improve training speed, we optimize masks:* We store mask pixels that are inside the object bounding box, rather than a mask of the full image. Most objects are small compared to the image size, so we save space by not storing a lot of zeros around the object.* We resize the mask to a smaller size (e.g. 56x56). For objects that are larger than the selected size we lose a bit of accuracy. But most object annotations are not very accuracy to begin with, so this loss is negligable for most practical purposes. Thie size of the mini_mask can be set in the config class.To visualize the effect of mask resizing, and to verify the code correctness, we visualize some examples. ###Code # Load random image and mask. image_id = np.random.choice(dataset.image_ids, 1)[0] image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) original_shape = image.shape # Resize image, window, scale, padding, _ = utils.resize_image( image, min_dim=config.IMAGE_MIN_DIM, max_dim=config.IMAGE_MAX_DIM, mode=config.IMAGE_RESIZE_MODE) mask = utils.resize_mask(mask, scale, padding) # Compute Bounding box bbox = utils.extract_bboxes(mask) # Display image and additional stats print("image_id: ", image_id, dataset.image_reference(image_id)) print("Original shape: ", original_shape) log("image", image) log("mask", mask) log("class_ids", class_ids) log("bbox", bbox) # Display image and instances visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("image", image) log("image_meta", image_meta) log("class_ids", class_ids) log("bbox", bbox) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) # Add augmentation and mask resizing. image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, augment=True, use_mini_mask=True) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) mask = utils.expand_mask(bbox, mask, image.shape) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) ###Output _____no_output_____ ###Markdown AnchorsFor an FPN network, the anchors must be ordered in a way that makes it easy to match anchors to the output of the convolution layers that predict anchor scores and shifts. * Sort by pyramid level first. All anchors of the first level, then all of the second and so on. This makes it easier to separate anchors by level.* Within each level, sort anchors by feature map processing sequence. Typically, a convolution layer processes a feature map starting from top-left and moving right row by row. * For each feature map cell, pick any sorting order for the anchors of different ratios. Here we match the order of ratios passed to the function. ###Code ## Visualize anchors of one cell at the center of the feature map # Load and display random image image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, _, _, _ = modellib.load_image_gt(dataset, crop_config, image_id) # Generate Anchors backbone_shapes = modellib.compute_backbone_shapes(config, image.shape) anchors = utils.generate_pyramid_anchors(config.RPN_ANCHOR_SCALES, config.RPN_ANCHOR_RATIOS, backbone_shapes, config.BACKBONE_STRIDES, config.RPN_ANCHOR_STRIDE) # Print summary of anchors num_levels = len(backbone_shapes) anchors_per_cell = len(config.RPN_ANCHOR_RATIOS) print("Count: ", anchors.shape[0]) print("Scales: ", config.RPN_ANCHOR_SCALES) print("ratios: ", config.RPN_ANCHOR_RATIOS) print("Anchors per Cell: ", anchors_per_cell) print("Levels: ", num_levels) anchors_per_level = [] for l in range(num_levels): num_cells = backbone_shapes[l][0] * backbone_shapes[l][1] anchors_per_level.append(anchors_per_cell * num_cells // config.RPN_ANCHOR_STRIDE**2) print("Anchors in Level {}: {}".format(l, anchors_per_level[l])) # Display fig, ax = plt.subplots(1, figsize=(10, 10)) ax.imshow(image) levels = len(backbone_shapes) for level in range(levels): colors = visualize.random_colors(levels) # Compute the index of the anchors at the center of the image level_start = sum(anchors_per_level[:level]) # sum of anchors of previous levels level_anchors = anchors[level_start:level_start+anchors_per_level[level]] print("Level {}. Anchors: {:6} Feature map Shape: {}".format(level, level_anchors.shape[0], backbone_shapes[level])) center_cell = backbone_shapes[level] // 2 center_cell_index = (center_cell[0] * backbone_shapes[level][1] + center_cell[1]) level_center = center_cell_index * anchors_per_cell center_anchor = anchors_per_cell * ( (center_cell[0] * backbone_shapes[level][1] / config.RPN_ANCHOR_STRIDE**2) \ + center_cell[1] / config.RPN_ANCHOR_STRIDE) level_center = int(center_anchor) # Draw anchors. Brightness show the order in the array, dark to bright. for i, rect in enumerate(level_anchors[level_center:level_center+anchors_per_cell]): y1, x1, y2, x2 = rect p = patches.Rectangle((x1, y1), x2-x1, y2-y1, linewidth=2, facecolor='none', edgecolor=(i+1)*np.array(colors[level]) / anchors_per_cell) ax.add_patch(p) ###Output _____no_output_____ ###Markdown Data Generator ###Code # Create data generator random_rois = 2000 g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=random_rois, batch_size=4, detection_targets=True) # Uncomment to run the generator through a lot of images # to catch rare errors # for i in range(1000): # print(i) # _, _ = next(g) # Get Next Image if random_rois: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_class_ids, gt_boxes, gt_masks, rpn_rois, rois], \ [mrcnn_class_ids, mrcnn_bbox, mrcnn_mask] = next(g) log("rois", rois) log("mrcnn_class_ids", mrcnn_class_ids) log("mrcnn_bbox", mrcnn_bbox) log("mrcnn_mask", mrcnn_mask) else: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_boxes, gt_masks], _ = next(g) log("gt_class_ids", gt_class_ids) log("gt_boxes", gt_boxes) log("gt_masks", gt_masks) log("rpn_match", rpn_match, ) log("rpn_bbox", rpn_bbox) image_id = modellib.parse_image_meta(image_meta)["image_id"][0] print("image_id: ", image_id, dataset.image_reference(image_id)) # Remove the last dim in mrcnn_class_ids. It's only added # to satisfy Keras restriction on target shape. mrcnn_class_ids = mrcnn_class_ids[:,:,0] b = 0 # Restore original image (reverse normalization) sample_image = modellib.unmold_image(normalized_images[b], config) # Compute anchor shifts. indices = np.where(rpn_match[b] == 1)[0] refined_anchors = utils.apply_box_deltas(anchors[indices], rpn_bbox[b, :len(indices)] * config.RPN_BBOX_STD_DEV) log("anchors", anchors) log("refined_anchors", refined_anchors) # Get list of positive anchors positive_anchor_ids = np.where(rpn_match[b] == 1)[0] print("Positive anchors: {}".format(len(positive_anchor_ids))) negative_anchor_ids = np.where(rpn_match[b] == -1)[0] print("Negative anchors: {}".format(len(negative_anchor_ids))) neutral_anchor_ids = np.where(rpn_match[b] == 0)[0] print("Neutral anchors: {}".format(len(neutral_anchor_ids))) # ROI breakdown by class for c, n in zip(dataset.class_names, np.bincount(mrcnn_class_ids[b].flatten())): if n: print("{:23}: {}".format(c[:20], n)) # Show positive anchors fig, ax = plt.subplots(1, figsize=(16, 16)) visualize.draw_boxes(sample_image, boxes=anchors[positive_anchor_ids], refined_boxes=refined_anchors, ax=ax) # Show negative anchors visualize.draw_boxes(sample_image, boxes=anchors[negative_anchor_ids]) # Show neutral anchors. They don't contribute to training. visualize.draw_boxes(sample_image, boxes=anchors[np.random.choice(neutral_anchor_ids, 100)]) ###Output _____no_output_____ ###Markdown ROIsTypically, the RPN network generates region proposals (a.k.a. Regions of Interest, or ROIs). The data generator has the ability to generate proposals as well for illustration and testing purposes. These are controlled by the `random_rois` parameter. ###Code if random_rois: # Class aware bboxes bbox_specific = mrcnn_bbox[b, np.arange(mrcnn_bbox.shape[1]), mrcnn_class_ids[b], :] # Refined ROIs refined_rois = utils.apply_box_deltas(rois[b].astype(np.float32), bbox_specific[:,:4] * config.BBOX_STD_DEV) # Class aware masks mask_specific = mrcnn_mask[b, np.arange(mrcnn_mask.shape[1]), :, :, mrcnn_class_ids[b]] visualize.draw_rois(sample_image, rois[b], refined_rois, mask_specific, mrcnn_class_ids[b], dataset.class_names) # Any repeated ROIs? rows = np.ascontiguousarray(rois[b]).view(np.dtype((np.void, rois.dtype.itemsize * rois.shape[-1]))) _, idx = np.unique(rows, return_index=True) print("Unique ROIs: {} out of {}".format(len(idx), rois.shape[1])) if random_rois: # Dispalay ROIs and corresponding masks and bounding boxes ids = random.sample(range(rois.shape[1]), 8) images = [] titles = [] for i in ids: image = visualize.draw_box(sample_image.copy(), rois[b,i,:4].astype(np.int32), [255, 0, 0]) image = visualize.draw_box(image, refined_rois[i].astype(np.int64), [0, 255, 0]) images.append(image) titles.append("ROI {}".format(i)) images.append(mask_specific[i] * 255) titles.append(dataset.class_names[mrcnn_class_ids[b,i]][:20]) display_images(images, titles, cols=4, cmap="Blues", interpolation="none") # Check ratio of positive ROIs in a set of images. if random_rois: limit = 10 temp_g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=10000, batch_size=1, detection_targets=True) total = 0 for i in range(limit): _, [ids, _, _] = next(temp_g) positive_rois = np.sum(ids[0] > 0) total += positive_rois print("{:5} {:5.2f}".format(positive_rois, positive_rois/ids.shape[1])) print("Average percent: {:.2f}".format(total/(limit*ids.shape[1]))) ###Output _____no_output_____ ###Markdown Inspect Nucleus Training DataInspect and visualize data loading and pre-processing code.https://www.kaggle.com/c/data-science-bowl-2018 ###Code import os import sys import itertools import math import logging import json import re import random import time import concurrent.futures import numpy as np import matplotlib import matplotlib.pyplot as plt import matplotlib.patches as patches import matplotlib.lines as lines from matplotlib.patches import Polygon import imgaug from imgaug import augmenters as iaa # Root directory of the project ROOT_DIR = os.getcwd() if ROOT_DIR.endswith("samples/nucleus"): # Go up two levels to the repo root ROOT_DIR = os.path.dirname(os.path.dirname(ROOT_DIR)) # Import Mask RCNN sys.path.append(ROOT_DIR) from mrcnn import utils from mrcnn import visualize from mrcnn.visualize import display_images from mrcnn import model as modellib from mrcnn.model import log import nucleus %matplotlib inline # Comment out to reload imported modules if they change # %load_ext autoreload # %autoreload 2 ###Output _____no_output_____ ###Markdown Configurations ###Code # Dataset directory DATASET_DIR = os.path.join(ROOT_DIR, "datasets/nucleus") # Use configuation from nucleus.py, but override # image resizing so we see the real sizes here class NoResizeConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "none" config = NoResizeConfig() ###Output _____no_output_____ ###Markdown Notebook Preferences ###Code def get_ax(rows=1, cols=1, size=16): """Return a Matplotlib Axes array to be used in all visualizations in the notebook. Provide a central point to control graph sizes. Adjust the size attribute to control how big to render images """ _, ax = plt.subplots(rows, cols, figsize=(size*cols, size*rows)) return ax ###Output _____no_output_____ ###Markdown DatasetDownload the dataset from the competition Website. Unzip it and save it in `mask_rcnn/datasets/nucleus`. If you prefer a different directory then change the `DATASET_DIR` variable above.https://www.kaggle.com/c/data-science-bowl-2018/data ###Code # Load dataset dataset = nucleus.NucleusDataset() # The subset is the name of the sub-directory, such as stage1_train, # stage1_test, ...etc. You can also use these special values: # train: loads stage1_train but excludes validation images # val: loads validation images from stage1_train. For a list # of validation images see nucleus.py dataset.load_nucleus(DATASET_DIR, subset="train") # Must call before using the dataset dataset.prepare() print("Image Count: {}".format(len(dataset.image_ids))) print("Class Count: {}".format(dataset.num_classes)) for i, info in enumerate(dataset.class_info): print("{:3}. {:50}".format(i, info['name'])) ###Output _____no_output_____ ###Markdown Display Samples ###Code # Load and display random samples image_ids = np.random.choice(dataset.image_ids, 4) for image_id in image_ids: image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) visualize.display_top_masks(image, mask, class_ids, dataset.class_names, limit=1) # Example of loading a specific image by its source ID source_id = "ed5be4b63e9506ad64660dd92a098ffcc0325195298c13c815a73773f1efc279" # Map source ID to Dataset image_id # Notice the nucleus prefix: it's the name given to the dataset in NucleusDataset image_id = dataset.image_from_source_map["nucleus.{}".format(source_id)] # Load and display image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("molded_image", image) log("mask", mask) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, show_bbox=False) ###Output _____no_output_____ ###Markdown Dataset StatsLoop through all images in the dataset and collect aggregate stats. ###Code def image_stats(image_id): """Returns a dict of stats for one image.""" image = dataset.load_image(image_id) mask, _ = dataset.load_mask(image_id) bbox = utils.extract_bboxes(mask) # Sanity check assert mask.shape[:2] == image.shape[:2] # Return stats dict return { "id": image_id, "shape": list(image.shape), "bbox": [[b[2] - b[0], b[3] - b[1]] for b in bbox # Uncomment to exclude nuclei with 1 pixel width # or height (often on edges) # if b[2] - b[0] > 1 and b[3] - b[1] > 1 ], "color": np.mean(image, axis=(0, 1)), } # Loop through the dataset and compute stats over multiple threads # This might take a few minutes t_start = time.time() with concurrent.futures.ThreadPoolExecutor() as e: stats = list(e.map(image_stats, dataset.image_ids)) t_total = time.time() - t_start print("Total time: {:.1f} seconds".format(t_total)) ###Output _____no_output_____ ###Markdown Image Size Stats ###Code # Image stats image_shape = np.array([s['shape'] for s in stats]) image_color = np.array([s['color'] for s in stats]) print("Image Count: ", image_shape.shape[0]) print("Height mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 0]), np.median(image_shape[:, 0]), np.min(image_shape[:, 0]), np.max(image_shape[:, 0]))) print("Width mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 1]), np.median(image_shape[:, 1]), np.min(image_shape[:, 1]), np.max(image_shape[:, 1]))) print("Color mean (RGB): {:.2f} {:.2f} {:.2f}".format(*np.mean(image_color, axis=0))) # Histograms fig, ax = plt.subplots(1, 3, figsize=(16, 4)) ax[0].set_title("Height") _ = ax[0].hist(image_shape[:, 0], bins=20) ax[1].set_title("Width") _ = ax[1].hist(image_shape[:, 1], bins=20) ax[2].set_title("Height & Width") _ = ax[2].hist2d(image_shape[:, 1], image_shape[:, 0], bins=10, cmap="Blues") ###Output _____no_output_____ ###Markdown Nuclei per Image Stats ###Code # Segment by image area image_area_bins = [256**2, 600**2, 1300**2] print("Nuclei/Image") fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nuclei_per_image = np.array([len(s['bbox']) for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area]) area_threshold = image_area if len(nuclei_per_image) == 0: print("Image area <= {:4}**2: None".format(np.sqrt(image_area))) continue print("Image area <= {:4.0f}**2: mean: {:.1f} median: {:.1f} min: {:.1f} max: {:.1f}".format( np.sqrt(image_area), nuclei_per_image.mean(), np.median(nuclei_per_image), nuclei_per_image.min(), nuclei_per_image.max())) ax[i].set_title("Image Area <= {:4}**2".format(np.sqrt(image_area))) _ = ax[i].hist(nuclei_per_image, bins=10) ###Output _____no_output_____ ###Markdown Nuclei Size Stats ###Code # Nuclei size stats fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nucleus_shape = np.array([ b for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area for b in s['bbox']]) nucleus_area = nucleus_shape[:, 0] * nucleus_shape[:, 1] area_threshold = image_area print("\nImage Area <= {:.0f}**2".format(np.sqrt(image_area))) print(" Total Nuclei: ", nucleus_shape.shape[0]) print(" Nucleus Height. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 0]), np.median(nucleus_shape[:, 0]), np.min(nucleus_shape[:, 0]), np.max(nucleus_shape[:, 0]))) print(" Nucleus Width. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 1]), np.median(nucleus_shape[:, 1]), np.min(nucleus_shape[:, 1]), np.max(nucleus_shape[:, 1]))) print(" Nucleus Area. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_area), np.median(nucleus_area), np.min(nucleus_area), np.max(nucleus_area))) # Show 2D histogram _ = ax[i].hist2d(nucleus_shape[:, 1], nucleus_shape[:, 0], bins=20, cmap="Blues") # Nuclei height/width ratio nucleus_aspect_ratio = nucleus_shape[:, 0] / nucleus_shape[:, 1] print("Nucleus Aspect Ratio. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_aspect_ratio), np.median(nucleus_aspect_ratio), np.min(nucleus_aspect_ratio), np.max(nucleus_aspect_ratio))) plt.figure(figsize=(15, 5)) _ = plt.hist(nucleus_aspect_ratio, bins=100, range=[0, 5]) ###Output _____no_output_____ ###Markdown Image AugmentationTest out different augmentation methods ###Code # List of augmentations # http://imgaug.readthedocs.io/en/latest/source/augmenters.html augmentation = iaa.Sometimes(0.9, [ iaa.Fliplr(0.5), iaa.Flipud(0.5), iaa.Multiply((0.8, 1.2)), iaa.GaussianBlur(sigma=(0.0, 5.0)) ]) # Load the image multiple times to show augmentations limit = 4 ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False, augment=False, augmentation=augmentation) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Image CropsMicroscoy images tend to be large, but nuclei are small. So it's more efficient to train on random crops from large images. This is handled by `config.IMAGE_RESIZE_MODE = "crop"`. ###Code class RandomCropConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "crop" IMAGE_MIN_DIM = 256 IMAGE_MAX_DIM = 256 crop_config = RandomCropConfig() # Load the image multiple times to show augmentations limit = 4 image_id = np.random.choice(dataset.image_ids, 1)[0] ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, crop_config, image_id, use_mini_mask=False) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Mini MasksInstance binary masks can get large when training with high resolution images. For example, if training with 1024x1024 image then the mask of a single instance requires 1MB of memory (Numpy uses bytes for boolean values). If an image has 100 instances then that's 100MB for the masks alone. To improve training speed, we optimize masks:* We store mask pixels that are inside the object bounding box, rather than a mask of the full image. Most objects are small compared to the image size, so we save space by not storing a lot of zeros around the object.* We resize the mask to a smaller size (e.g. 56x56). For objects that are larger than the selected size we lose a bit of accuracy. But most object annotations are not very accuracy to begin with, so this loss is negligable for most practical purposes. Thie size of the mini_mask can be set in the config class.To visualize the effect of mask resizing, and to verify the code correctness, we visualize some examples. ###Code # Load random image and mask. image_id = np.random.choice(dataset.image_ids, 1)[0] image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) original_shape = image.shape # Resize image, window, scale, padding, _ = utils.resize_image( image, min_dim=config.IMAGE_MIN_DIM, max_dim=config.IMAGE_MAX_DIM, mode=config.IMAGE_RESIZE_MODE) mask = utils.resize_mask(mask, scale, padding) # Compute Bounding box bbox = utils.extract_bboxes(mask) # Display image and additional stats print("image_id: ", image_id, dataset.image_reference(image_id)) print("Original shape: ", original_shape) log("image", image) log("mask", mask) log("class_ids", class_ids) log("bbox", bbox) # Display image and instances visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("image", image) log("image_meta", image_meta) log("class_ids", class_ids) log("bbox", bbox) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) # Add augmentation and mask resizing. image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, augment=True, use_mini_mask=True) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) mask = utils.expand_mask(bbox, mask, image.shape) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) ###Output _____no_output_____ ###Markdown AnchorsFor an FPN network, the anchors must be ordered in a way that makes it easy to match anchors to the output of the convolution layers that predict anchor scores and shifts. * Sort by pyramid level first. All anchors of the first level, then all of the second and so on. This makes it easier to separate anchors by level.* Within each level, sort anchors by feature map processing sequence. Typically, a convolution layer processes a feature map starting from top-left and moving right row by row. * For each feature map cell, pick any sorting order for the anchors of different ratios. Here we match the order of ratios passed to the function. ###Code ## Visualize anchors of one cell at the center of the feature map # Load and display random image image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, _, _, _ = modellib.load_image_gt(dataset, crop_config, image_id) # Generate Anchors backbone_shapes = modellib.compute_backbone_shapes(config, image.shape) anchors = utils.generate_pyramid_anchors(config.RPN_ANCHOR_SCALES, config.RPN_ANCHOR_RATIOS, backbone_shapes, config.BACKBONE_STRIDES, config.RPN_ANCHOR_STRIDE) # Print summary of anchors num_levels = len(backbone_shapes) anchors_per_cell = len(config.RPN_ANCHOR_RATIOS) print("Count: ", anchors.shape[0]) print("Scales: ", config.RPN_ANCHOR_SCALES) print("ratios: ", config.RPN_ANCHOR_RATIOS) print("Anchors per Cell: ", anchors_per_cell) print("Levels: ", num_levels) anchors_per_level = [] for l in range(num_levels): num_cells = backbone_shapes[l][0] * backbone_shapes[l][1] anchors_per_level.append(anchors_per_cell * num_cells // config.RPN_ANCHOR_STRIDE**2) print("Anchors in Level {}: {}".format(l, anchors_per_level[l])) # Display fig, ax = plt.subplots(1, figsize=(10, 10)) ax.imshow(image) levels = len(backbone_shapes) for level in range(levels): colors = visualize.random_colors(levels) # Compute the index of the anchors at the center of the image level_start = sum(anchors_per_level[:level]) # sum of anchors of previous levels level_anchors = anchors[level_start:level_start+anchors_per_level[level]] print("Level {}. Anchors: {:6} Feature map Shape: {}".format(level, level_anchors.shape[0], backbone_shapes[level])) center_cell = backbone_shapes[level] // 2 center_cell_index = (center_cell[0] * backbone_shapes[level][1] + center_cell[1]) level_center = center_cell_index * anchors_per_cell center_anchor = anchors_per_cell * ( (center_cell[0] * backbone_shapes[level][1] / config.RPN_ANCHOR_STRIDE**2) \ + center_cell[1] / config.RPN_ANCHOR_STRIDE) level_center = int(center_anchor) # Draw anchors. Brightness show the order in the array, dark to bright. for i, rect in enumerate(level_anchors[level_center:level_center+anchors_per_cell]): y1, x1, y2, x2 = rect p = patches.Rectangle((x1, y1), x2-x1, y2-y1, linewidth=2, facecolor='none', edgecolor=(i+1)*np.array(colors[level]) / anchors_per_cell) ax.add_patch(p) ###Output _____no_output_____ ###Markdown Data Generator ###Code # Create data generator random_rois = 2000 g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=random_rois, batch_size=4, detection_targets=True) # Uncomment to run the generator through a lot of images # to catch rare errors # for i in range(1000): # print(i) # _, _ = next(g) # Get Next Image if random_rois: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_class_ids, gt_boxes, gt_masks, rpn_rois, rois], \ [mrcnn_class_ids, mrcnn_bbox, mrcnn_mask] = next(g) log("rois", rois) log("mrcnn_class_ids", mrcnn_class_ids) log("mrcnn_bbox", mrcnn_bbox) log("mrcnn_mask", mrcnn_mask) else: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_boxes, gt_masks], _ = next(g) log("gt_class_ids", gt_class_ids) log("gt_boxes", gt_boxes) log("gt_masks", gt_masks) log("rpn_match", rpn_match, ) log("rpn_bbox", rpn_bbox) image_id = modellib.parse_image_meta(image_meta)["image_id"][0] print("image_id: ", image_id, dataset.image_reference(image_id)) # Remove the last dim in mrcnn_class_ids. It's only added # to satisfy Keras restriction on target shape. mrcnn_class_ids = mrcnn_class_ids[:,:,0] b = 0 # Restore original image (reverse normalization) sample_image = modellib.unmold_image(normalized_images[b], config) # Compute anchor shifts. indices = np.where(rpn_match[b] == 1)[0] refined_anchors = utils.apply_box_deltas(anchors[indices], rpn_bbox[b, :len(indices)] * config.RPN_BBOX_STD_DEV) log("anchors", anchors) log("refined_anchors", refined_anchors) # Get list of positive anchors positive_anchor_ids = np.where(rpn_match[b] == 1)[0] print("Positive anchors: {}".format(len(positive_anchor_ids))) negative_anchor_ids = np.where(rpn_match[b] == -1)[0] print("Negative anchors: {}".format(len(negative_anchor_ids))) neutral_anchor_ids = np.where(rpn_match[b] == 0)[0] print("Neutral anchors: {}".format(len(neutral_anchor_ids))) # ROI breakdown by class for c, n in zip(dataset.class_names, np.bincount(mrcnn_class_ids[b].flatten())): if n: print("{:23}: {}".format(c[:20], n)) # Show positive anchors fig, ax = plt.subplots(1, figsize=(16, 16)) visualize.draw_boxes(sample_image, boxes=anchors[positive_anchor_ids], refined_boxes=refined_anchors, ax=ax) # Show negative anchors visualize.draw_boxes(sample_image, boxes=anchors[negative_anchor_ids]) # Show neutral anchors. They don't contribute to training. visualize.draw_boxes(sample_image, boxes=anchors[np.random.choice(neutral_anchor_ids, 100)]) ###Output _____no_output_____ ###Markdown ROIsTypically, the RPN network generates region proposals (a.k.a. Regions of Interest, or ROIs). The data generator has the ability to generate proposals as well for illustration and testing purposes. These are controlled by the `random_rois` parameter. ###Code if random_rois: # Class aware bboxes bbox_specific = mrcnn_bbox[b, np.arange(mrcnn_bbox.shape[1]), mrcnn_class_ids[b], :] # Refined ROIs refined_rois = utils.apply_box_deltas(rois[b].astype(np.float32), bbox_specific[:,:4] * config.BBOX_STD_DEV) # Class aware masks mask_specific = mrcnn_mask[b, np.arange(mrcnn_mask.shape[1]), :, :, mrcnn_class_ids[b]] visualize.draw_rois(sample_image, rois[b], refined_rois, mask_specific, mrcnn_class_ids[b], dataset.class_names) # Any repeated ROIs? rows = np.ascontiguousarray(rois[b]).view(np.dtype((np.void, rois.dtype.itemsize * rois.shape[-1]))) _, idx = np.unique(rows, return_index=True) print("Unique ROIs: {} out of {}".format(len(idx), rois.shape[1])) if random_rois: # Dispalay ROIs and corresponding masks and bounding boxes ids = random.sample(range(rois.shape[1]), 8) images = [] titles = [] for i in ids: image = visualize.draw_box(sample_image.copy(), rois[b,i,:4].astype(np.int32), [255, 0, 0]) image = visualize.draw_box(image, refined_rois[i].astype(np.int64), [0, 255, 0]) images.append(image) titles.append("ROI {}".format(i)) images.append(mask_specific[i] * 255) titles.append(dataset.class_names[mrcnn_class_ids[b,i]][:20]) display_images(images, titles, cols=4, cmap="Blues", interpolation="none") # Check ratio of positive ROIs in a set of images. if random_rois: limit = 10 temp_g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=10000, batch_size=1, detection_targets=True) total = 0 for i in range(limit): _, [ids, _, _] = next(temp_g) positive_rois = np.sum(ids[0] > 0) total += positive_rois print("{:5} {:5.2f}".format(positive_rois, positive_rois/ids.shape[1])) print("Average percent: {:.2f}".format(total/(limit*ids.shape[1]))) ###Output _____no_output_____ ###Markdown Inspect Nucleus Training DataInspect and visualize data loading and pre-processing code.https://www.kaggle.com/c/data-science-bowl-2018 ###Code import os import sys import itertools import math import logging import json import re import random import time import concurrent.futures import numpy as np import matplotlib import matplotlib.pyplot as plt import matplotlib.patches as patches import matplotlib.lines as lines from matplotlib.patches import Polygon import imgaug from imgaug import augmenters as iaa # Root directory of the project ROOT_DIR = os.getcwd() if ROOT_DIR.endswith("samples/nucleus"): # Go up two levels to the repo root ROOT_DIR = os.path.dirname(os.path.dirname(ROOT_DIR)) # Import Mask RCNN sys.path.append(ROOT_DIR) from mrcnn import utils from mrcnn import visualize from mrcnn.visualize import display_images from mrcnn import model as modellib from mrcnn.model import log import nucleus %matplotlib inline # Comment out to reload imported modules if they change # %load_ext autoreload # %autoreload 2 ###Output _____no_output_____ ###Markdown Configurations ###Code # Dataset directory DATASET_DIR = os.path.join(ROOT_DIR, "datasets/nucleus") # Use configuation from nucleus.py, but override # image resizing so we see the real sizes here class NoResizeConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "none" config = NoResizeConfig() ###Output _____no_output_____ ###Markdown Notebook Preferences ###Code def get_ax(rows=1, cols=1, size=16): """Return a Matplotlib Axes array to be used in all visualizations in the notebook. Provide a central point to control graph sizes. Adjust the size attribute to control how big to render images """ _, ax = plt.subplots(rows, cols, figsize=(size*cols, size*rows)) return ax ###Output _____no_output_____ ###Markdown DatasetDownload the dataset from the competition Website. Unzip it and save it in `mask_rcnn/datasets/nucleus`. If you prefer a different directory then change the `DATASET_DIR` variable above.https://www.kaggle.com/c/data-science-bowl-2018/data ###Code # Load dataset dataset = nucleus.NucleusDataset() # The subset is the name of the sub-directory, such as stage1_train, # stage1_test, ...etc. You can also use these special values: # train: loads stage1_train but excludes validation images # val: loads validation images from stage1_train. For a list # of validation images see nucleus.py dataset.load_nucleus(DATASET_DIR, subset="train") # Must call before using the dataset dataset.prepare() print("Image Count: {}".format(len(dataset.image_ids))) print("Class Count: {}".format(dataset.num_classes)) for i, info in enumerate(dataset.class_info): print("{:3}. {:50}".format(i, info['name'])) ###Output /Users/anb32/Mask_RCNN/datasets/nucleus/stage1_train ###Markdown Display Samples ###Code # Load and display random samples image_ids = np.random.choice(dataset.image_ids, 4) for image_id in image_ids: image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) visualize.display_top_masks(image, mask, class_ids, dataset.class_names, limit=1) # Example of loading a specific image by its source ID source_id = "ed5be4b63e9506ad64660dd92a098ffcc0325195298c13c815a73773f1efc279" # Map source ID to Dataset image_id # Notice the nucleus prefix: it's the name given to the dataset in NucleusDataset image_id = dataset.image_from_source_map["nucleus.{}".format(source_id)] # Load and display image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("molded_image", image) log("mask", mask) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, show_bbox=False) ###Output _____no_output_____ ###Markdown Dataset StatsLoop through all images in the dataset and collect aggregate stats. ###Code def image_stats(image_id): """Returns a dict of stats for one image.""" image = dataset.load_image(image_id) mask, _ = dataset.load_mask(image_id) bbox = utils.extract_bboxes(mask) # Sanity check assert mask.shape[:2] == image.shape[:2] # Return stats dict return { "id": image_id, "shape": list(image.shape), "bbox": [[b[2] - b[0], b[3] - b[1]] for b in bbox # Uncomment to exclude nuclei with 1 pixel width # or height (often on edges) # if b[2] - b[0] > 1 and b[3] - b[1] > 1 ], "color": np.mean(image, axis=(0, 1)), } # Loop through the dataset and compute stats over multiple threads # This might take a few minutes t_start = time.time() with concurrent.futures.ThreadPoolExecutor() as e: stats = list(e.map(image_stats, dataset.image_ids)) t_total = time.time() - t_start print("Total time: {:.1f} seconds".format(t_total)) ###Output _____no_output_____ ###Markdown Image Size Stats ###Code # Image stats image_shape = np.array([s['shape'] for s in stats]) image_color = np.array([s['color'] for s in stats]) print("Image Count: ", image_shape.shape[0]) print("Height mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 0]), np.median(image_shape[:, 0]), np.min(image_shape[:, 0]), np.max(image_shape[:, 0]))) print("Width mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 1]), np.median(image_shape[:, 1]), np.min(image_shape[:, 1]), np.max(image_shape[:, 1]))) print("Color mean (RGB): {:.2f} {:.2f} {:.2f}".format(*np.mean(image_color, axis=0))) # Histograms fig, ax = plt.subplots(1, 3, figsize=(16, 4)) ax[0].set_title("Height") _ = ax[0].hist(image_shape[:, 0], bins=20) ax[1].set_title("Width") _ = ax[1].hist(image_shape[:, 1], bins=20) ax[2].set_title("Height & Width") _ = ax[2].hist2d(image_shape[:, 1], image_shape[:, 0], bins=10, cmap="Blues") ###Output _____no_output_____ ###Markdown Nuclei per Image Stats ###Code # Segment by image area image_area_bins = [256**2, 600**2, 1300**2] print("Nuclei/Image") fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nuclei_per_image = np.array([len(s['bbox']) for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area]) area_threshold = image_area if len(nuclei_per_image) == 0: print("Image area <= {:4}**2: None".format(np.sqrt(image_area))) continue print("Image area <= {:4.0f}**2: mean: {:.1f} median: {:.1f} min: {:.1f} max: {:.1f}".format( np.sqrt(image_area), nuclei_per_image.mean(), np.median(nuclei_per_image), nuclei_per_image.min(), nuclei_per_image.max())) ax[i].set_title("Image Area <= {:4}**2".format(np.sqrt(image_area))) _ = ax[i].hist(nuclei_per_image, bins=10) ###Output _____no_output_____ ###Markdown Nuclei Size Stats ###Code # Nuclei size stats fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nucleus_shape = np.array([ b for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area for b in s['bbox']]) nucleus_area = nucleus_shape[:, 0] * nucleus_shape[:, 1] area_threshold = image_area print("\nImage Area <= {:.0f}**2".format(np.sqrt(image_area))) print(" Total Nuclei: ", nucleus_shape.shape[0]) print(" Nucleus Height. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 0]), np.median(nucleus_shape[:, 0]), np.min(nucleus_shape[:, 0]), np.max(nucleus_shape[:, 0]))) print(" Nucleus Width. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 1]), np.median(nucleus_shape[:, 1]), np.min(nucleus_shape[:, 1]), np.max(nucleus_shape[:, 1]))) print(" Nucleus Area. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_area), np.median(nucleus_area), np.min(nucleus_area), np.max(nucleus_area))) # Show 2D histogram _ = ax[i].hist2d(nucleus_shape[:, 1], nucleus_shape[:, 0], bins=20, cmap="Blues") # Nuclei height/width ratio nucleus_aspect_ratio = nucleus_shape[:, 0] / nucleus_shape[:, 1] print("Nucleus Aspect Ratio. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_aspect_ratio), np.median(nucleus_aspect_ratio), np.min(nucleus_aspect_ratio), np.max(nucleus_aspect_ratio))) plt.figure(figsize=(15, 5)) _ = plt.hist(nucleus_aspect_ratio, bins=100, range=[0, 5]) ###Output _____no_output_____ ###Markdown Image AugmentationTest out different augmentation methods ###Code # List of augmentations # http://imgaug.readthedocs.io/en/latest/source/augmenters.html augmentation = iaa.Sometimes(0.9, [ iaa.Fliplr(0.5), iaa.Flipud(0.5), iaa.Multiply((0.8, 1.2)), iaa.GaussianBlur(sigma=(0.0, 5.0)) ]) # Load the image multiple times to show augmentations limit = 4 ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False, augment=False, augmentation=augmentation) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Image CropsMicroscoy images tend to be large, but nuclei are small. So it's more efficient to train on random crops from large images. This is handled by `config.IMAGE_RESIZE_MODE = "crop"`. ###Code class RandomCropConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "crop" IMAGE_MIN_DIM = 256 IMAGE_MAX_DIM = 256 crop_config = RandomCropConfig() # Load the image multiple times to show augmentations limit = 4 image_id = np.random.choice(dataset.image_ids, 1)[0] ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, crop_config, image_id, use_mini_mask=False) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Mini MasksInstance binary masks can get large when training with high resolution images. For example, if training with 1024x1024 image then the mask of a single instance requires 1MB of memory (Numpy uses bytes for boolean values). If an image has 100 instances then that's 100MB for the masks alone. To improve training speed, we optimize masks:* We store mask pixels that are inside the object bounding box, rather than a mask of the full image. Most objects are small compared to the image size, so we save space by not storing a lot of zeros around the object.* We resize the mask to a smaller size (e.g. 56x56). For objects that are larger than the selected size we lose a bit of accuracy. But most object annotations are not very accuracy to begin with, so this loss is negligable for most practical purposes. Thie size of the mini_mask can be set in the config class.To visualize the effect of mask resizing, and to verify the code correctness, we visualize some examples. ###Code # Load random image and mask. image_id = np.random.choice(dataset.image_ids, 1)[0] image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) original_shape = image.shape # Resize image, window, scale, padding, _ = utils.resize_image( image, min_dim=config.IMAGE_MIN_DIM, max_dim=config.IMAGE_MAX_DIM, mode=config.IMAGE_RESIZE_MODE) mask = utils.resize_mask(mask, scale, padding) # Compute Bounding box bbox = utils.extract_bboxes(mask) # Display image and additional stats print("image_id: ", image_id, dataset.image_reference(image_id)) print("Original shape: ", original_shape) log("image", image) log("mask", mask) log("class_ids", class_ids) log("bbox", bbox) # Display image and instances visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("image", image) log("image_meta", image_meta) log("class_ids", class_ids) log("bbox", bbox) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) # Add augmentation and mask resizing. image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, augment=True, use_mini_mask=True) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) mask = utils.expand_mask(bbox, mask, image.shape) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) ###Output _____no_output_____ ###Markdown AnchorsFor an FPN network, the anchors must be ordered in a way that makes it easy to match anchors to the output of the convolution layers that predict anchor scores and shifts. * Sort by pyramid level first. All anchors of the first level, then all of the second and so on. This makes it easier to separate anchors by level.* Within each level, sort anchors by feature map processing sequence. Typically, a convolution layer processes a feature map starting from top-left and moving right row by row. * For each feature map cell, pick any sorting order for the anchors of different ratios. Here we match the order of ratios passed to the function. ###Code ## Visualize anchors of one cell at the center of the feature map # Load and display random image image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, _, _, _ = modellib.load_image_gt(dataset, crop_config, image_id) # Generate Anchors backbone_shapes = modellib.compute_backbone_shapes(config, image.shape) anchors = utils.generate_pyramid_anchors(config.RPN_ANCHOR_SCALES, config.RPN_ANCHOR_RATIOS, backbone_shapes, config.BACKBONE_STRIDES, config.RPN_ANCHOR_STRIDE) # Print summary of anchors num_levels = len(backbone_shapes) anchors_per_cell = len(config.RPN_ANCHOR_RATIOS) print("Count: ", anchors.shape[0]) print("Scales: ", config.RPN_ANCHOR_SCALES) print("ratios: ", config.RPN_ANCHOR_RATIOS) print("Anchors per Cell: ", anchors_per_cell) print("Levels: ", num_levels) anchors_per_level = [] for l in range(num_levels): num_cells = backbone_shapes[l][0] * backbone_shapes[l][1] anchors_per_level.append(anchors_per_cell * num_cells // config.RPN_ANCHOR_STRIDE**2) print("Anchors in Level {}: {}".format(l, anchors_per_level[l])) # Display fig, ax = plt.subplots(1, figsize=(10, 10)) ax.imshow(image) levels = len(backbone_shapes) for level in range(levels): colors = visualize.random_colors(levels) # Compute the index of the anchors at the center of the image level_start = sum(anchors_per_level[:level]) # sum of anchors of previous levels level_anchors = anchors[level_start:level_start+anchors_per_level[level]] print("Level {}. Anchors: {:6} Feature map Shape: {}".format(level, level_anchors.shape[0], backbone_shapes[level])) center_cell = backbone_shapes[level] // 2 center_cell_index = (center_cell[0] * backbone_shapes[level][1] + center_cell[1]) level_center = center_cell_index * anchors_per_cell center_anchor = anchors_per_cell * ( (center_cell[0] * backbone_shapes[level][1] / config.RPN_ANCHOR_STRIDE**2) \ + center_cell[1] / config.RPN_ANCHOR_STRIDE) level_center = int(center_anchor) # Draw anchors. Brightness show the order in the array, dark to bright. for i, rect in enumerate(level_anchors[level_center:level_center+anchors_per_cell]): y1, x1, y2, x2 = rect p = patches.Rectangle((x1, y1), x2-x1, y2-y1, linewidth=2, facecolor='none', edgecolor=(i+1)*np.array(colors[level]) / anchors_per_cell) ax.add_patch(p) ###Output _____no_output_____ ###Markdown Data Generator ###Code # Create data generator random_rois = 2000 g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=random_rois, batch_size=4, detection_targets=True) # Uncomment to run the generator through a lot of images # to catch rare errors # for i in range(1000): # print(i) # _, _ = next(g) # Get Next Image if random_rois: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_class_ids, gt_boxes, gt_masks, rpn_rois, rois], \ [mrcnn_class_ids, mrcnn_bbox, mrcnn_mask] = next(g) log("rois", rois) log("mrcnn_class_ids", mrcnn_class_ids) log("mrcnn_bbox", mrcnn_bbox) log("mrcnn_mask", mrcnn_mask) else: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_boxes, gt_masks], _ = next(g) log("gt_class_ids", gt_class_ids) log("gt_boxes", gt_boxes) log("gt_masks", gt_masks) log("rpn_match", rpn_match, ) log("rpn_bbox", rpn_bbox) image_id = modellib.parse_image_meta(image_meta)["image_id"][0] print("image_id: ", image_id, dataset.image_reference(image_id)) # Remove the last dim in mrcnn_class_ids. It's only added # to satisfy Keras restriction on target shape. mrcnn_class_ids = mrcnn_class_ids[:,:,0] b = 0 # Restore original image (reverse normalization) sample_image = modellib.unmold_image(normalized_images[b], config) # Compute anchor shifts. indices = np.where(rpn_match[b] == 1)[0] refined_anchors = utils.apply_box_deltas(anchors[indices], rpn_bbox[b, :len(indices)] * config.RPN_BBOX_STD_DEV) log("anchors", anchors) log("refined_anchors", refined_anchors) # Get list of positive anchors positive_anchor_ids = np.where(rpn_match[b] == 1)[0] print("Positive anchors: {}".format(len(positive_anchor_ids))) negative_anchor_ids = np.where(rpn_match[b] == -1)[0] print("Negative anchors: {}".format(len(negative_anchor_ids))) neutral_anchor_ids = np.where(rpn_match[b] == 0)[0] print("Neutral anchors: {}".format(len(neutral_anchor_ids))) # ROI breakdown by class for c, n in zip(dataset.class_names, np.bincount(mrcnn_class_ids[b].flatten())): if n: print("{:23}: {}".format(c[:20], n)) # Show positive anchors fig, ax = plt.subplots(1, figsize=(16, 16)) visualize.draw_boxes(sample_image, boxes=anchors[positive_anchor_ids], refined_boxes=refined_anchors, ax=ax) # Show negative anchors visualize.draw_boxes(sample_image, boxes=anchors[negative_anchor_ids]) # Show neutral anchors. They don't contribute to training. visualize.draw_boxes(sample_image, boxes=anchors[np.random.choice(neutral_anchor_ids, 100)]) ###Output _____no_output_____ ###Markdown ROIsTypically, the RPN network generates region proposals (a.k.a. Regions of Interest, or ROIs). The data generator has the ability to generate proposals as well for illustration and testing purposes. These are controlled by the `random_rois` parameter. ###Code if random_rois: # Class aware bboxes bbox_specific = mrcnn_bbox[b, np.arange(mrcnn_bbox.shape[1]), mrcnn_class_ids[b], :] # Refined ROIs refined_rois = utils.apply_box_deltas(rois[b].astype(np.float32), bbox_specific[:,:4] * config.BBOX_STD_DEV) # Class aware masks mask_specific = mrcnn_mask[b, np.arange(mrcnn_mask.shape[1]), :, :, mrcnn_class_ids[b]] visualize.draw_rois(sample_image, rois[b], refined_rois, mask_specific, mrcnn_class_ids[b], dataset.class_names) # Any repeated ROIs? rows = np.ascontiguousarray(rois[b]).view(np.dtype((np.void, rois.dtype.itemsize * rois.shape[-1]))) _, idx = np.unique(rows, return_index=True) print("Unique ROIs: {} out of {}".format(len(idx), rois.shape[1])) if random_rois: # Dispalay ROIs and corresponding masks and bounding boxes ids = random.sample(range(rois.shape[1]), 8) images = [] titles = [] for i in ids: image = visualize.draw_box(sample_image.copy(), rois[b,i,:4].astype(np.int32), [255, 0, 0]) image = visualize.draw_box(image, refined_rois[i].astype(np.int64), [0, 255, 0]) images.append(image) titles.append("ROI {}".format(i)) images.append(mask_specific[i] * 255) titles.append(dataset.class_names[mrcnn_class_ids[b,i]][:20]) display_images(images, titles, cols=4, cmap="Blues", interpolation="none") # Check ratio of positive ROIs in a set of images. if random_rois: limit = 10 temp_g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=10000, batch_size=1, detection_targets=True) total = 0 for i in range(limit): _, [ids, _, _] = next(temp_g) positive_rois = np.sum(ids[0] > 0) total += positive_rois print("{:5} {:5.2f}".format(positive_rois, positive_rois/ids.shape[1])) print("Average percent: {:.2f}".format(total/(limit*ids.shape[1]))) ###Output _____no_output_____ ###Markdown Inspect Nucleus Training DataInspect and visualize data loading and pre-processing code.https://www.kaggle.com/c/data-science-bowl-2018 ###Code import os import sys import itertools import math import logging import json import re import random import time import concurrent.futures import numpy as np import matplotlib import matplotlib.pyplot as plt import matplotlib.patches as patches import matplotlib.lines as lines from matplotlib.patches import Polygon import imgaug from imgaug import augmenters as iaa # Root directory of the project ROOT_DIR = os.getcwd() print("ROOT_DIR",ROOT_DIR) if ROOT_DIR.endswith("nucleus"): # Go up two levels to the repo root ROOT_DIR = os.path.dirname(os.path.dirname(ROOT_DIR)) print("ROOT_DIR",ROOT_DIR) # Import Mask RCNN sys.path.append(ROOT_DIR) from mrcnn import utils from mrcnn import visualize from mrcnn.visualize import display_images from mrcnn import model as modellib from mrcnn.model import log import nucleus %matplotlib inline # Comment out to reload imported modules if they change # %load_ext autoreload # %autoreload 2 ###Output _____no_output_____ ###Markdown Configurations ###Code # Dataset directory DATASET_DIR = os.path.join(ROOT_DIR, "datasets/nucleus") # Use configuation from nucleus.py, but override # image resizing so we see the real sizes here class NoResizeConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "none" config = NoResizeConfig() ###Output _____no_output_____ ###Markdown Notebook Preferences ###Code def get_ax(rows=1, cols=1, size=16): """Return a Matplotlib Axes array to be used in all visualizations in the notebook. Provide a central point to control graph sizes. Adjust the size attribute to control how big to render images """ _, ax = plt.subplots(rows, cols, figsize=(size*cols, size*rows)) return ax ###Output _____no_output_____ ###Markdown DatasetDownload the dataset from the competition Website. Unzip it and save it in `mask_rcnn/datasets/nucleus`. If you prefer a different directory then change the `DATASET_DIR` variable above.https://www.kaggle.com/c/data-science-bowl-2018/data ###Code # Load dataset dataset = nucleus.NucleusDataset() # The subset is the name of the sub-directory, such as stage1_train, # stage1_test, ...etc. You can also use these special values: # train: loads stage1_train but excludes validation images # val: loads validation images from stage1_train. For a list # of validation images see nucleus.py dataset.load_nucleus(DATASET_DIR, subset="train") # Must call before using the dataset dataset.prepare() print("Image Count: {}".format(len(dataset.image_ids))) print("Class Count: {}".format(dataset.num_classes)) for i, info in enumerate(dataset.class_info): print("{:3}. {:50}".format(i, info['name'])) ###Output _____no_output_____ ###Markdown Display Samples ###Code # Load and display random samples image_ids = np.random.choice(dataset.image_ids, 4) for image_id in image_ids: image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) visualize.display_top_masks(image, mask, class_ids, dataset.class_names, limit=1) # Example of loading a specific image by its source ID source_id = "ed5be4b63e9506ad64660dd92a098ffcc0325195298c13c815a73773f1efc279" # Map source ID to Dataset image_id # Notice the nucleus prefix: it's the name given to the dataset in NucleusDataset image_id = dataset.image_from_source_map["nucleus.{}".format(source_id)] # Load and display image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("molded_image", image) log("mask", mask) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, show_bbox=False) ###Output _____no_output_____ ###Markdown Dataset StatsLoop through all images in the dataset and collect aggregate stats. ###Code def image_stats(image_id): """Returns a dict of stats for one image.""" image = dataset.load_image(image_id) mask, _ = dataset.load_mask(image_id) bbox = utils.extract_bboxes(mask) # Sanity check assert mask.shape[:2] == image.shape[:2] # Return stats dict return { "id": image_id, "shape": list(image.shape), "bbox": [[b[2] - b[0], b[3] - b[1]] for b in bbox # Uncomment to exclude nuclei with 1 pixel width # or height (often on edges) # if b[2] - b[0] > 1 and b[3] - b[1] > 1 ], "color": np.mean(image, axis=(0, 1)), } # Loop through the dataset and compute stats over multiple threads # This might take a few minutes t_start = time.time() with concurrent.futures.ThreadPoolExecutor() as e: stats = list(e.map(image_stats, dataset.image_ids)) t_total = time.time() - t_start print("Total time: {:.1f} seconds".format(t_total)) ###Output _____no_output_____ ###Markdown Image Size Stats ###Code # Image stats image_shape = np.array([s['shape'] for s in stats]) image_color = np.array([s['color'] for s in stats]) print("Image Count: ", image_shape.shape[0]) print("Height mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 0]), np.median(image_shape[:, 0]), np.min(image_shape[:, 0]), np.max(image_shape[:, 0]))) print("Width mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(image_shape[:, 1]), np.median(image_shape[:, 1]), np.min(image_shape[:, 1]), np.max(image_shape[:, 1]))) print("Color mean (RGB): {:.2f} {:.2f} {:.2f}".format(*np.mean(image_color, axis=0))) # Histograms fig, ax = plt.subplots(1, 3, figsize=(16, 4)) ax[0].set_title("Height") _ = ax[0].hist(image_shape[:, 0], bins=20) ax[1].set_title("Width") _ = ax[1].hist(image_shape[:, 1], bins=20) ax[2].set_title("Height & Width") _ = ax[2].hist2d(image_shape[:, 1], image_shape[:, 0], bins=10, cmap="Blues") ###Output _____no_output_____ ###Markdown Nuclei per Image Stats ###Code # Segment by image area image_area_bins = [256**2, 600**2, 1300**2] print("Nuclei/Image") fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nuclei_per_image = np.array([len(s['bbox']) for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area]) area_threshold = image_area if len(nuclei_per_image) == 0: print("Image area <= {:4}**2: None".format(np.sqrt(image_area))) continue print("Image area <= {:4.0f}**2: mean: {:.1f} median: {:.1f} min: {:.1f} max: {:.1f}".format( np.sqrt(image_area), nuclei_per_image.mean(), np.median(nuclei_per_image), nuclei_per_image.min(), nuclei_per_image.max())) ax[i].set_title("Image Area <= {:4}**2".format(np.sqrt(image_area))) _ = ax[i].hist(nuclei_per_image, bins=10) ###Output _____no_output_____ ###Markdown Nuclei Size Stats ###Code # Nuclei size stats fig, ax = plt.subplots(1, len(image_area_bins), figsize=(16, 4)) area_threshold = 0 for i, image_area in enumerate(image_area_bins): nucleus_shape = np.array([ b for s in stats if area_threshold < (s['shape'][0] * s['shape'][1]) <= image_area for b in s['bbox']]) nucleus_area = nucleus_shape[:, 0] * nucleus_shape[:, 1] area_threshold = image_area print("\nImage Area <= {:.0f}**2".format(np.sqrt(image_area))) print(" Total Nuclei: ", nucleus_shape.shape[0]) print(" Nucleus Height. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 0]), np.median(nucleus_shape[:, 0]), np.min(nucleus_shape[:, 0]), np.max(nucleus_shape[:, 0]))) print(" Nucleus Width. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_shape[:, 1]), np.median(nucleus_shape[:, 1]), np.min(nucleus_shape[:, 1]), np.max(nucleus_shape[:, 1]))) print(" Nucleus Area. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_area), np.median(nucleus_area), np.min(nucleus_area), np.max(nucleus_area))) # Show 2D histogram _ = ax[i].hist2d(nucleus_shape[:, 1], nucleus_shape[:, 0], bins=20, cmap="Blues") # Nuclei height/width ratio nucleus_aspect_ratio = nucleus_shape[:, 0] / nucleus_shape[:, 1] print("Nucleus Aspect Ratio. mean: {:.2f} median: {:.2f} min: {:.2f} max: {:.2f}".format( np.mean(nucleus_aspect_ratio), np.median(nucleus_aspect_ratio), np.min(nucleus_aspect_ratio), np.max(nucleus_aspect_ratio))) plt.figure(figsize=(15, 5)) _ = plt.hist(nucleus_aspect_ratio, bins=100, range=[0, 5]) ###Output _____no_output_____ ###Markdown Image AugmentationTest out different augmentation methods ###Code # List of augmentations # http://imgaug.readthedocs.io/en/latest/source/augmenters.html augmentation = iaa.Sometimes(0.9, [ iaa.Fliplr(0.5), iaa.Flipud(0.5), iaa.Multiply((0.8, 1.2)), iaa.GaussianBlur(sigma=(0.0, 5.0)) ]) # Load the image multiple times to show augmentations limit = 4 ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False, augment=False, augmentation=augmentation) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Image CropsMicroscoy images tend to be large, but nuclei are small. So it's more efficient to train on random crops from large images. This is handled by `config.IMAGE_RESIZE_MODE = "crop"`. ###Code class RandomCropConfig(nucleus.NucleusConfig): IMAGE_RESIZE_MODE = "crop" IMAGE_MIN_DIM = 256 IMAGE_MAX_DIM = 256 crop_config = RandomCropConfig() # Load the image multiple times to show augmentations limit = 4 image_id = np.random.choice(dataset.image_ids, 1)[0] ax = get_ax(rows=2, cols=limit//2) for i in range(limit): image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, crop_config, image_id, use_mini_mask=False) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names, ax=ax[i//2, i % 2], show_mask=False, show_bbox=False) ###Output _____no_output_____ ###Markdown Mini MasksInstance binary masks can get large when training with high resolution images. For example, if training with 1024x1024 image then the mask of a single instance requires 1MB of memory (Numpy uses bytes for boolean values). If an image has 100 instances then that's 100MB for the masks alone. To improve training speed, we optimize masks:* We store mask pixels that are inside the object bounding box, rather than a mask of the full image. Most objects are small compared to the image size, so we save space by not storing a lot of zeros around the object.* We resize the mask to a smaller size (e.g. 56x56). For objects that are larger than the selected size we lose a bit of accuracy. But most object annotations are not very accuracy to begin with, so this loss is negligable for most practical purposes. Thie size of the mini_mask can be set in the config class.To visualize the effect of mask resizing, and to verify the code correctness, we visualize some examples. ###Code # Load random image and mask. image_id = np.random.choice(dataset.image_ids, 1)[0] image = dataset.load_image(image_id) mask, class_ids = dataset.load_mask(image_id) original_shape = image.shape # Resize image, window, scale, padding, _ = utils.resize_image( image, min_dim=config.IMAGE_MIN_DIM, max_dim=config.IMAGE_MAX_DIM, mode=config.IMAGE_RESIZE_MODE) mask = utils.resize_mask(mask, scale, padding) # Compute Bounding box bbox = utils.extract_bboxes(mask) # Display image and additional stats print("image_id: ", image_id, dataset.image_reference(image_id)) print("Original shape: ", original_shape) log("image", image) log("mask", mask) log("class_ids", class_ids) log("bbox", bbox) # Display image and instances visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, use_mini_mask=False) log("image", image) log("image_meta", image_meta) log("class_ids", class_ids) log("bbox", bbox) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) # Add augmentation and mask resizing. image, image_meta, class_ids, bbox, mask = modellib.load_image_gt( dataset, config, image_id, augment=True, use_mini_mask=True) log("mask", mask) display_images([image]+[mask[:,:,i] for i in range(min(mask.shape[-1], 7))]) mask = utils.expand_mask(bbox, mask, image.shape) visualize.display_instances(image, bbox, mask, class_ids, dataset.class_names) ###Output _____no_output_____ ###Markdown AnchorsFor an FPN network, the anchors must be ordered in a way that makes it easy to match anchors to the output of the convolution layers that predict anchor scores and shifts. * Sort by pyramid level first. All anchors of the first level, then all of the second and so on. This makes it easier to separate anchors by level.* Within each level, sort anchors by feature map processing sequence. Typically, a convolution layer processes a feature map starting from top-left and moving right row by row. * For each feature map cell, pick any sorting order for the anchors of different ratios. Here we match the order of ratios passed to the function. ###Code ## Visualize anchors of one cell at the center of the feature map # Load and display random image image_id = np.random.choice(dataset.image_ids, 1)[0] image, image_meta, _, _, _ = modellib.load_image_gt(dataset, crop_config, image_id) # Generate Anchors backbone_shapes = modellib.compute_backbone_shapes(config, image.shape) anchors = utils.generate_pyramid_anchors(config.RPN_ANCHOR_SCALES, config.RPN_ANCHOR_RATIOS, backbone_shapes, config.BACKBONE_STRIDES, config.RPN_ANCHOR_STRIDE) # Print summary of anchors num_levels = len(backbone_shapes) anchors_per_cell = len(config.RPN_ANCHOR_RATIOS) print("Count: ", anchors.shape[0]) print("Scales: ", config.RPN_ANCHOR_SCALES) print("ratios: ", config.RPN_ANCHOR_RATIOS) print("Anchors per Cell: ", anchors_per_cell) print("Levels: ", num_levels) anchors_per_level = [] for l in range(num_levels): num_cells = backbone_shapes[l][0] * backbone_shapes[l][1] anchors_per_level.append(anchors_per_cell * num_cells // config.RPN_ANCHOR_STRIDE**2) print("Anchors in Level {}: {}".format(l, anchors_per_level[l])) # Display fig, ax = plt.subplots(1, figsize=(10, 10)) ax.imshow(image) levels = len(backbone_shapes) for level in range(levels): colors = visualize.random_colors(levels) # Compute the index of the anchors at the center of the image level_start = sum(anchors_per_level[:level]) # sum of anchors of previous levels level_anchors = anchors[level_start:level_start+anchors_per_level[level]] print("Level {}. Anchors: {:6} Feature map Shape: {}".format(level, level_anchors.shape[0], backbone_shapes[level])) center_cell = backbone_shapes[level] // 2 center_cell_index = (center_cell[0] * backbone_shapes[level][1] + center_cell[1]) level_center = center_cell_index * anchors_per_cell center_anchor = anchors_per_cell * ( (center_cell[0] * backbone_shapes[level][1] / config.RPN_ANCHOR_STRIDE**2) \ + center_cell[1] / config.RPN_ANCHOR_STRIDE) level_center = int(center_anchor) # Draw anchors. Brightness show the order in the array, dark to bright. for i, rect in enumerate(level_anchors[level_center:level_center+anchors_per_cell]): y1, x1, y2, x2 = rect p = patches.Rectangle((x1, y1), x2-x1, y2-y1, linewidth=2, facecolor='none', edgecolor=(i+1)*np.array(colors[level]) / anchors_per_cell) ax.add_patch(p) ###Output _____no_output_____ ###Markdown Data Generator ###Code # Create data generator random_rois = 2000 g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=random_rois, batch_size=4, detection_targets=True) # Uncomment to run the generator through a lot of images # to catch rare errors # for i in range(1000): # print(i) # _, _ = next(g) # Get Next Image if random_rois: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_class_ids, gt_boxes, gt_masks, rpn_rois, rois], \ [mrcnn_class_ids, mrcnn_bbox, mrcnn_mask] = next(g) log("rois", rois) log("mrcnn_class_ids", mrcnn_class_ids) log("mrcnn_bbox", mrcnn_bbox) log("mrcnn_mask", mrcnn_mask) else: [normalized_images, image_meta, rpn_match, rpn_bbox, gt_boxes, gt_masks], _ = next(g) log("gt_class_ids", gt_class_ids) log("gt_boxes", gt_boxes) log("gt_masks", gt_masks) log("rpn_match", rpn_match, ) log("rpn_bbox", rpn_bbox) image_id = modellib.parse_image_meta(image_meta)["image_id"][0] print("image_id: ", image_id, dataset.image_reference(image_id)) # Remove the last dim in mrcnn_class_ids. It's only added # to satisfy Keras restriction on target shape. mrcnn_class_ids = mrcnn_class_ids[:,:,0] b = 0 # Restore original image (reverse normalization) sample_image = modellib.unmold_image(normalized_images[b], config) # Compute anchor shifts. indices = np.where(rpn_match[b] == 1)[0] refined_anchors = utils.apply_box_deltas(anchors[indices], rpn_bbox[b, :len(indices)] * config.RPN_BBOX_STD_DEV) log("anchors", anchors) log("refined_anchors", refined_anchors) # Get list of positive anchors positive_anchor_ids = np.where(rpn_match[b] == 1)[0] print("Positive anchors: {}".format(len(positive_anchor_ids))) negative_anchor_ids = np.where(rpn_match[b] == -1)[0] print("Negative anchors: {}".format(len(negative_anchor_ids))) neutral_anchor_ids = np.where(rpn_match[b] == 0)[0] print("Neutral anchors: {}".format(len(neutral_anchor_ids))) # ROI breakdown by class for c, n in zip(dataset.class_names, np.bincount(mrcnn_class_ids[b].flatten())): if n: print("{:23}: {}".format(c[:20], n)) # Show positive anchors fig, ax = plt.subplots(1, figsize=(16, 16)) visualize.draw_boxes(sample_image, boxes=anchors[positive_anchor_ids], refined_boxes=refined_anchors, ax=ax) # Show negative anchors visualize.draw_boxes(sample_image, boxes=anchors[negative_anchor_ids]) # Show neutral anchors. They don't contribute to training. visualize.draw_boxes(sample_image, boxes=anchors[np.random.choice(neutral_anchor_ids, 100)]) ###Output _____no_output_____ ###Markdown ROIsTypically, the RPN network generates region proposals (a.k.a. Regions of Interest, or ROIs). The data generator has the ability to generate proposals as well for illustration and testing purposes. These are controlled by the `random_rois` parameter. ###Code if random_rois: # Class aware bboxes bbox_specific = mrcnn_bbox[b, np.arange(mrcnn_bbox.shape[1]), mrcnn_class_ids[b], :] # Refined ROIs refined_rois = utils.apply_box_deltas(rois[b].astype(np.float32), bbox_specific[:,:4] * config.BBOX_STD_DEV) # Class aware masks mask_specific = mrcnn_mask[b, np.arange(mrcnn_mask.shape[1]), :, :, mrcnn_class_ids[b]] visualize.draw_rois(sample_image, rois[b], refined_rois, mask_specific, mrcnn_class_ids[b], dataset.class_names) # Any repeated ROIs? rows = np.ascontiguousarray(rois[b]).view(np.dtype((np.void, rois.dtype.itemsize * rois.shape[-1]))) _, idx = np.unique(rows, return_index=True) print("Unique ROIs: {} out of {}".format(len(idx), rois.shape[1])) if random_rois: # Dispalay ROIs and corresponding masks and bounding boxes ids = random.sample(range(rois.shape[1]), 8) images = [] titles = [] for i in ids: image = visualize.draw_box(sample_image.copy(), rois[b,i,:4].astype(np.int32), [255, 0, 0]) image = visualize.draw_box(image, refined_rois[i].astype(np.int64), [0, 255, 0]) images.append(image) titles.append("ROI {}".format(i)) images.append(mask_specific[i] * 255) titles.append(dataset.class_names[mrcnn_class_ids[b,i]][:20]) display_images(images, titles, cols=4, cmap="Blues", interpolation="none") # Check ratio of positive ROIs in a set of images. if random_rois: limit = 10 temp_g = modellib.data_generator( dataset, crop_config, shuffle=True, random_rois=10000, batch_size=1, detection_targets=True) total = 0 for i in range(limit): _, [ids, _, _] = next(temp_g) positive_rois = np.sum(ids[0] > 0) total += positive_rois print("{:5} {:5.2f}".format(positive_rois, positive_rois/ids.shape[1])) print("Average percent: {:.2f}".format(total/(limit*ids.shape[1]))) ###Output _____no_output_____

PMFG_diagnostics.ipynb

###Markdown PMFG -- testing runtime and convergence ###Code import numpy as np import pandas as pd import networkx # as nx from time import time import timeit #%matplotlib inline import matplotlib.pyplot as plt raw_asset_prices_df = pd.read_csv("IVV_historical.csv", index_col='Date') log_returns_df = np.log(raw_asset_prices_df).diff().dropna() # drop first row of raw prices so it has the same dimensions as the log-returns DF raw_asset_prices_df = raw_asset_prices_df.iloc[1:] stock_names = log_returns_df.columns df_shape = (raw_asset_prices_df.shape) print(f"There are {df_shape[0]} rows and {df_shape[1]} columns in the dataset.") print(f"Data timeperiod covers: {raw_asset_prices_df.index[0]} to {raw_asset_prices_df.index[-1]}") raw_corr = log_returns_df.corr() shr_coef = 1e-4 #shr_target=np.ones((df_shape[1], df_shape[1])) shr_target=np.eye(df_shape[1]) correlation_matrix = raw_corr*(1-shr_coef) + shr_target*shr_coef print('Condition number of sample correlation matrix: %.2e' %np.linalg.cond(raw_corr)) print('Condition number of shrunk correlation matrix: %.2e' %np.linalg.cond(correlation_matrix)) G0 = networkx.from_pandas_adjacency(correlation_matrix-np.diag(np.diag(correlation_matrix))) print(networkx.info(G0)) ###Output Condition number of sample correlation matrix: 1.13e+19 Condition number of shrunk correlation matrix: 1.49e+06 Name: Type: Graph Number of nodes: 504 Number of edges: 126756 Average degree: 503.0000 ###Markdown Diagnostic version of PMFG.pyTemporary version of PMFG algorithm for debugging, as well as inspecting the convergence process. ###Code from typing import List import planarity class edge(): """ Create an edge from `src` to `dst` with weight `wt` @params src: source node dst: destination node wt: weight """ def __init__(self, src, dst, wt): self.src = src self.dst = dst self.wt = wt class PMFG(): def __init__(self, graph: networkx.Graph, planarity_check_lib: str="default", verbose: int=0, tol_ratio: float=0.): self.origin_graph = graph self.sort_edges = None self.pmfg_graph = None self.planarity_check_lib = planarity_check_lib self.verbose = verbose self.tol_ratio = tol_ratio def sort_edge(self) -> List[edge]: sort_edges = [] for src, dst, data in sorted(self.origin_graph.edges(data=True), key=lambda x: x[2]["weight"], reverse=True): sort_edges.append(edge(src, dst, data["weight"])) self.sort_edges = sort_edges return sort_edges def compute(self) -> networkx.Graph: if self.sort_edges == None: self.sort_edge() number_of_nodes = self.origin_graph.number_of_nodes() pmfg_graph = networkx.Graph() loop_counter = 0 cum_pct = [] timestamp = time() for edge in self.sort_edges: loop_counter += 1 # Adding edge and check the planarity pmfg_graph.add_edge(edge.src, edge.dst, weight=edge.wt) # If the graph is not planar, then remove the edge if not self.is_planar(pmfg_graph, self.planarity_check_lib): pmfg_graph.remove_edge(edge.src, edge.dst) cum_pct.append(pmfg_graph.number_of_edges()/(3 * (number_of_nodes - 2))) if self.verbose == 1: print(f"Number of edges added = {pmfg_graph.number_of_edges()}, Number of edges to be added = {3 * (number_of_nodes - 2) - pmfg_graph.number_of_edges()}") if self.verbose == 2 and (loop_counter%1000 == 0): print(f"Number of edges to be added = {3 * (number_of_nodes - 2) - pmfg_graph.number_of_edges()}, time taken = {time() - timestamp}") timestamp = time() if pmfg_graph.number_of_edges() >= 3 * (number_of_nodes - 2) * (1-self.tol_ratio): break self.pmfg_graph = pmfg_graph return pmfg_graph, np.array(cum_pct) @staticmethod def is_planar(graph: networkx.Graph, planarity_check_lib: str="default") -> bool: if planarity_check_lib == "networkx": return networkx.algorithms.planarity.check_planarity(graph)[0] return planarity.is_planar(graph) #timestamp = time() G0_filtered, cum_pct = PMFG(G0, verbose=2).compute() #print('Time taken to construct PMFG graph: %.2f s\n' %(time()-timestamp)) print(networkx.info(G0_filtered)) for i in range(95, 100): print(i,'pct: argmin' , np.min(np.where(cum_pct>=i*.01))) plt.figure(figsize=(12,6)) plt.axhline(.95, linestyle='--', c='r') plt.plot(cum_pct); tstamp=time() G0_filtered, _ = PMFG(G0, verbose=0, tol_ratio=.03).compute() print('Time taken: %.2f s' %(time()-tstamp)) print(networkx.info(G0_filtered)) ###Output Name: Type: Graph Number of nodes: 503 Number of edges: 1461 Average degree: 5.8091 ###Markdown FindingsIt takes progressively longer to find the successive edge to be added to PMFG. The last few edges take more than twice the time than to find the rest (total ~120s, $97\%$ of the edges are found at ~40s and $40\%$ iteration). We are thinking in terms of running this algorithm on years worth of daily data. If we take the cutoff at 97% (so a planar-97%-filtered-graph instead of p-M-f-g), we cut runtime down to one-third.Still, 40s ($=\epsilon$ for the other graph operations that we have to perform) per run mean a year's worth of business data would take ~3 hours to process. Relatively better and more manageable, but we can do better.Proposal: use graph sampling method to compute centrality features of a random subgraph og the correlation network; do this multiple times to get some kind of sampled/ensembled centrality feature that hopefully captures most of the underlying structure of the corr. network, but runs way faster. (TBD) Centrality fFeature AnalysisRunning the same plots to check that the distribution of centrality features of our approx. PMFG are in-line with the actual PMFG. ###Code import networkx as nx G1 = nx.Graph() weight_map = lambda w: 1+w for u,v,d in G0_filtered.edges(data=True): G1.add_edge(u,v,weight=weight_map(d['weight'])) print(nx.info(G1)) deg= pd.DataFrame.from_dict(dict(G1.degree(weight='weight')), orient='index', columns = ['D']) EC = pd.DataFrame.from_dict(nx.eigenvector_centrality(G1), orient='index', columns = ['EC']) PG = pd.DataFrame.from_dict(nx.pagerank(G1), orient='index', columns = ['PG']) G1 = nx.Graph() weight_map = lambda w: np.sqrt(2*(1-w)) for u,v,d in G0_filtered.edges(data=True): G1.add_edge(u,v,weight=weight_map(d['weight'])) print(nx.info(G1)) ecc= pd.DataFrame.from_dict(nx.eccentricity(G1), orient='index', columns = ['E']) clo= pd.DataFrame.from_dict(nx.closeness_centrality(G1), orient='index', columns = ['C']) BC = pd.DataFrame.from_dict(nx.betweenness_centrality(G1), orient='index', columns = ['BC']) #centralities_names = ['BC', 'C', 'D', 'E', 'EC'] #centralities_names = ['D', 'BC', 'E', 'C', 'EC'] centralities_names = ['D', 'BC', 'nE', 'C', 'EC', 'PG'] centralities = deg.copy() centralities['BC'] = BC centralities['nE'] = -ecc centralities['C'] = clo centralities['EC'] = EC centralities['PG'] = PG print(centralities.head()) centralities.corr() import seaborn as sns sns.clustermap(centralities.corr(), cmap="RdYlGn", center=0.) plt.show() corr_plot = sns.pairplot(data=centralities); #corr_plot.map_lower(sns.kdeplot, levels=4, color=".2"); print(BC.idxmax()) BC.hist(); ###Output BC EMR dtype: object

9-pyecharts_tutorial.ipynb

###Markdown 简介在这个教程中，我们将介绍pyecharts包。 Echarts是百度开发的一个javascript可视化脚本，他的特点在于可交互（就是你鼠标移动上去，图片可以作出相应的变化）。小旭学长在echarts gallery发布了多款图表，累计12万的浏览量，获得300+赞，可以点击[这个链接](https://gallery.echartsjs.com/explore.html?u=bd-167860219&type=worksort=rank~timeframe=all~author=all)查看 echarts属于门槛比较高的一种可视化方法，需要写javascript，而javascript又是基于html网页，另外数据的处理还要用python，等于说你要熟练使用得同时会js，html，python三种语言。现在pyecharts出现了，直接在python里就可以调用生成echarts图片，大部分的图表只需要用python就可以生成，非常方便！ 相比我们之前介绍的几种画图方法，各有各的优势，小旭学长的总结如下： >matplotlib：纯python出图，可批量出图，缺点是出的图片为静态图片无法交互 folium：主要功能是绘制地图，javascript出图可交互，坐标系为wgs84，数据不需要转坐标 echarts：可绘制各种图表，也能绘制地图，javascript出图可交互，但绘制地图时底图一般采用百度地图，需要转坐标系那么，我们赶紧开始学习python的pyecharts包吧！ 最近新冠肺炎的疫情是相当的不妙。 小旭学长观察到，一些大型网站的疫情发布地图都是基于echarts的，那么我们基于pyecharts来实现一下数据地图可视化的操作吧 提供的基础数据是：提供的基础数据是： 数据： 不提供，我们数据从网上抓，无中生有 数据获取 很多网站都提供了疫情分布情况，数据都是公开的我们直接抓就行。这里以腾讯新闻的疫情发布链接为例，观察网络链接可以找到数据获取的访问请求 好的我们用最简单的方式把它抓下来，我们做省份的可视化 ###Code import urllib import json url = 'https://view.inews.qq.com/g2/getOnsInfo?name=disease_h5' request = urllib.request.Request(url) response = urllib.request.urlopen(request) datajson=json.loads(response.read().decode('utf8')) datajson=json.loads(datajson['data']) #数据就存放在这个变量里 datajson #提取各省份的数据 import pandas as pd provincedata = pd.DataFrame(datajson['areaTree'][0]['children']) provincedata.head(5) #整理一下数据，把total里面的数据展开 data1 = pd.DataFrame(list(provincedata['total'])) data1['name'] = provincedata['name'] data1.head(5) ###Output _____no_output_____ ###Markdown 好的，到这一步我们已经获取了数据 可视化 全国数据可视化 官方配置文档：[pyecharts的地理图表教程](https://pyecharts.org//zh-cn/geography_charts) 首先我们要把数据整理成echarts认识的格式，就是如下： ###Code data1[['name','confirm']].values from pyecharts import options as opts from pyecharts.charts import Map #创建echarts对象c c = ( Map()#告诉echarts这个是Map形式的图表 .add("确诊", data1[['name','confirm']].values, "china")#加一个数据，这个数据名叫”确诊“，数据的地图是echarts自带的china .set_global_opts(#对图表添加设置 title_opts=opts.TitleOpts(title='疫情地图')#设置图表的名称 ) ) #导出为html文件 c.render('疫情地图.html') ###Output _____no_output_____ ###Markdown 打开目录下的 [疫情地图.html](疫情地图.html) 文件，效果如下 但是，我们还要在加一些美化调整，一些参数可以看[echarts官方的配置项手册](https://www.echartsjs.com/zh/option.htmltitle) ###Code from pyecharts import options as opts from pyecharts.charts import Map c = ( Map() .add("确诊", data1[['name','confirm']].values, "china", is_roam = False,#不可鼠标缩放和平移漫游 zoom = 1.2,#当前视角的缩放比例 is_map_symbol_show = False, # 是否显示标记图形 label_opts = opts.LabelOpts(position = 'inside'),#标签尽量放在图形区域内 ) .set_global_opts( title_opts=opts.TitleOpts(title='疫情地图'), visualmap_opts=opts.VisualMapOpts(is_piecewise=True,#设定分段颜色显示 pieces=[{'min': 10000,'label':'10000人以上'}, #设定分段的值 {'min': 1000, 'max': 9999,'label':'1000-9999人'}, {'min': 500, 'max': 999,'label':'500-999人'}, {'min': 100, 'max': 499,'label':'100-499人'}, {'min': 10, 'max': 99,'label':'10-99人'}, {'min': 1, 'max': 9,'label':'1-9人'}], range_color=["#b4e0f3","#70b4eb","#1482e5","#1c3fbf","#070093" ] #调整显示颜色 ), ) ) c.render('疫情地图.html') ###Output _____no_output_____ ###Markdown 打开目录下的 [疫情地图.html](疫情地图.html) 文件，效果如下 单个省份数据可视化 ###Code import pandas as pd #提取省份的数据 province = '广东' guangdongdata = pd.DataFrame(provincedata[provincedata['name'] == province]['children'].iloc[0]) #整理一下数据，把total里面的数据展开 data2 = pd.DataFrame(list(guangdongdata['total'])) data2['name'] = guangdongdata['name']+'市' data2.head(5) from pyecharts import options as opts from pyecharts.charts import Map c = ( Map() .add("确诊", data2[['name','confirm']].values, province, is_roam = False,#不可鼠标缩放和平移漫游 zoom = 1.2,#当前视角的缩放比例 is_map_symbol_show = False, # 是否显示标记图形 label_opts = opts.LabelOpts(position = 'inside'),#标签尽量放在图形区域内 ) .set_global_opts( title_opts=opts.TitleOpts(title=province+'疫情地图'), visualmap_opts=opts.VisualMapOpts(is_piecewise=True,#设定分段颜色显示 pieces=[{'min': 200, 'label':'200人以上'},#设定分段的值 {'min': 100, 'max': 199,'label':'100-199人'}, {'min': 50, 'max': 99,'label':'50-99人'}, {'min': 10, 'max': 49,'label':'10-49人'}, {'min': 1, 'max': 9,'label':'1-9人'}], range_color=["#b4e0f3","#70b4eb","#1482e5","#1c3fbf","#070093" ] #调整显示颜色 ), ) ) c.render(province+'疫情地图.html') ###Output _____no_output_____

data/preprocessing/.ipynb_checkpoints/TCGA-PANCAN-checkpoint.ipynb

###Markdown TCGA-PANCAN Data Set- **Input:** 20502 gene expression - **Output:** Classification, BRCA (300), KIRC (146), LUAD (141), PRAD (136), COAD (78). Preprocess Data ###Code raw_data = pd.read_csv(RAW_DATA_PATH) raw_data.drop(columns=[raw_data.columns[0]], inplace=True) raw_data.head(2) # List of input features feature_col_names = list(raw_data.columns) feature_col_names.remove(target_col_name) # Encode target data # class_0 = 'BRCA' # class_1 = 'KIRC' # class_2 ='LUAD' # class_3 = 'PRAD' # class_4 = 'COAD' raw_data[target_col_name].replace({'BRCA':0, 'KIRC':1, 'LUAD':2, 'PRAD':3, 'COAD':4}, inplace=True) # Seperate input features and target column X = raw_data.drop(columns=[target_col_name]).values y = raw_data[target_col_name].values # Normalise input features i.e. scale attributes so that theyre 0-1 so that larger weights do not carry more signifcance in the network from sklearn.preprocessing import MinMaxScaler scaler = MinMaxScaler() X = scaler.fit_transform(X) # Store preprocessed data data = pd.DataFrame(X, columns=feature_col_names) data[target_col_name] = y data.head(3) assert data.columns[-1]==target_col_name, 'Target column must be last column in DataFrame' ###Output _____no_output_____ ###Markdown Save Clean Data ###Code # Initialise new empty dataset folder from model.generation.helpers import init_dataset_dir path_to_data_folder = '../' init_dataset_dir.run(dataset_name=dataset_name, path_to_data_folder=path_to_data_folder) data_path = '../' + dataset_name + '/' # Save cleaned data data.to_csv(data_path + 'data.csv', index=False) ###Output _____no_output_____

xcorr_test.ipynb

###Markdown ###Code !git clone https://github.com/rsh2458/dragonfly.git !cd dragonfly && git pull import sys import os import pandas as pd # Plot values import plotly.graph_objects as go from plotly.subplots import make_subplots events=os.listdir('dragonfly/csv') events ###Output _____no_output_____ ###Markdown 3D plotsHere are some examples of getting some data into our system, and plotting them in 3d. ###Code def getPE(p, e): p=str(p) e=str(e) data = pd.read_csv('dragonfly/csv/'+p+'-'+e+'_CSV.txt',sep=';') df = pd.DataFrame(data) return df ###Output _____no_output_____ ###Markdown It's hard to create this plots with now real examples, [Scattter3d Examples](https://www.programcreek.com/python/example/103209/plotly.graph_objs.Scatter3d) shows some examples. ###Code p=str(34) e=str(53) df=getPE(p,e) import plotly.graph_objects as go from plotly.subplots import make_subplots layout = go.Layout( # width=1024, # height=1024, scene = dict( aspectmode='data', xaxis = dict(title='x'), yaxis = dict(title='y'), zaxis = dict(title='height')) ) fig=go.Figure(layout=layout) fig1=go.Scatter3d(x=df['xt_avg_' + p], y=df['yt_avg_' + p], z=df['zt_avg_' + p]) fig.add_trace(fig1) fig.add_scatter3d( x=df['xt_avg_' + e], y=df['yt_avg_' + e], z=df['zt_avg_' + e]) #fig.add_scatter3d(df, # x='xt_' + p, # y='yt_' + p, # z='zt_' + p) #fig1.show() ###Output _____no_output_____ ###Markdown GITHUB Library integrationThis example shows how you can add external, github libraries into your notebook. The idea is that, besides cloning the data, you need to append the new github data into the path where python searches for it's libraries. ###Code !git clone https://github.com/trichter/xcorr.git foobar sys.path.append('foobar') sys.path ###Output fatal: destination path 'foobar' already exists and is not an empty directory. ###Markdown Now, you can import functions from the library that you've already defined above. The example below, imports some functions from the `xcorr.py` file that's found in the `foobar` directory that we've added. ###Code import matplotlib.pyplot as plt import numpy as np from xcorr import correlate_maxlag, correlate_template, get_lags np.random.seed(26) N = 200 maxlag = 50 a = np.random.random(N) start = N // 4 b = a[start:-start] cc1 = correlate_maxlag(a, b, maxlag) cc2 = correlate_template(a, b) grid = plt.GridSpec(2, 2, wspace=0.4, hspace=0.3) ax1 = plt.subplot(grid[0, 0:]) ax2 = plt.subplot(grid[1, 0]) ax3 = plt.subplot(grid[1, 1], sharey=ax2) ax1.plot(np.arange(len(a)), a, label='signal a') ax1.plot(np.arange(len(b)) + start, b, label='signal b') ax2.plot(get_lags(cc1), cc1) ax3.plot(cc2) ax1.legend(loc=3) kw = dict(xy=(0.05, 0.95), xycoords='axes fraction', va='top') ax2.annotate('correlate_maxlag(a, b, {})'.format(maxlag), **kw) ax3.annotate('correlate_template(a, b)', **kw) plt.savefig('xcorr_example.png') plt.show() ###Output _____no_output_____

match cpr and eddy info and output file_updatexarray.ipynb

###Markdown Put files together ###Code file1 = filename_cpr_expanded+'aviso'+'.nc' file2 = filename_cpr_expanded+'wnd'+'.nc' file3 = filename_cpr_expanded+'sst'+'.nc' ds = xr.open_dataset(file1) ds2 = xr.open_dataset(file2) for var in ds2: if not var in ds: ds[var]=ds2[var] ds2 = xr.open_dataset(file3) for var in ds2: if not var in ds: ds[var]=ds2[var] ds.to_netcdf(filename_cpr_expanded+'.nc') df_bird = ds.to_dataframe() df_bird.to_csv(filename_cpr_expanded+'.csv') ds ###Output _____no_output_____ ###Markdown collocate with eddies ###Code ds_npac_eddy = xr.open_dataset(filename_northpac_eddies).rename({'Longitude':'lon','Latitude':'lat'}) for var in ds_npac_eddy: ds_npac_eddy = ds_npac_eddy.rename({var:str('cpr_eddy_data_'+var)}) ds_cpr_eddy = xr.open_dataset(filename_cpr_eddy) for var in ds_cpr_eddy: if var[0]=='s': ds_cpr_eddy = ds_cpr_eddy.rename({var:str('cpr_eddy_data_'+var[10:])}) else: ds_cpr_eddy = ds_cpr_eddy.rename({var:str('cpr_eddy_data_'+var[4:])}) ds_npac_eddy.close() ds_cpr_eddy.close() print(ds_npac_eddy) print(ds_cpr_eddy) ###Output _____no_output_____ ###Markdown make single array with all info ###Code ilen = len(ds_cpr_eddy.cpr_eddy_data_index) for var in ds_npac_eddy: if not var=='cpr_eddy_data_time': ds_cpr_eddy[var]=xr.DataArray(np.nan*np.empty(ilen, dtype=str(ds_npac_eddy[var].dtype)), dims=('z')) ds_cpr_eddy[var].attrs=ds_npac_eddy[var].attrs else: ds_cpr_eddy[var]=xr.DataArray(np.empty(ilen, dtype=str(ds_npac_eddy[var].dtype)), dims=('z')) for i in range(ilen): ii = ds_cpr_eddy.cpr_eddy_data_index[i] for var in ds_npac_eddy: ds_cpr_eddy[var][i]=ds_npac_eddy[var][ii] ###Output _____no_output_____ ###Markdown check where double crossing ###Code #proc_cpr ==1 whre distance is GREATER than radius of eddy #proc_cpr = np.where(ds_cpr_eddy.cpr_eddy_data_distance>ds_cpr_eddy.cpr_eddy_data_radius,1,0) #proc_cpr ilen = len(ds_cpr_eddy.cpr_eddy_data_track) ds_cpr_eddy['num_cross']=xr.DataArray(np.zeros(ilen, dtype='int32'), dims=('z')) ds_cpr_eddy['num_cross'].attrs={'description':'how many times eddy crossed by cpr data'} #calculate where cpr in eddy radius, put nan where not in eddy subset = ds_cpr_eddy.where(ds_cpr_eddy.cpr_eddy_data_distance<ds_cpr_eddy.cpr_eddy_data_radius) #find unique eddy track ids u, indices = np.unique(ds_cpr_eddy.cpr_eddy_data_track, return_index=True) #cycle through each unique eddy id to find unique years for i in range(len(u)): ind = np.where(subset.cpr_eddy_data_track==u[i]) ind_tem = np.where(ds_cpr_eddy.cpr_eddy_data_track==u[i]) tem = subset.cpr_eddy_data_year[ind] u1, indices1 = np.unique(tem, return_index=True) ds_cpr_eddy.num_cross[ind_tem]=len(u1) ds_cpr_eddy.num_cross.plot() ds_cpr_eddy ds_env = xr.open_dataset(filename_cpr_expanded+'.nc') ds_env.close() ds_env = ds_env.rename({'index':'z'}) ds_env for var in ds_env: var_tem = var if not var_tem[0:3]=='cpr': var_tem = 'cpr_sample_'+var ds_cpr_eddy[var_tem]=xr.DataArray(ds_env[var].data, dims=('z')) ds_cpr_eddy[var_tem].attrs=ds_env[var].attrs ds_cpr_eddy filename_cpr_expanded='F:/data/project_data/NASA_biophysical/collocated_data/CPR/All CPR Sample catalogue with eddy info_2020_10_06' ds_cpr_eddy.to_netcdf(filename_cpr_expanded+'.nc') df_bird = ds_cpr_eddy.to_dataframe() df_bird.to_csv(filename_cpr_expanded+'.csv') filename_cpr_expanded_netcdf='F:/data/project_data/NASA_biophysical/collocated_data/CPR/All CPR Sample catalogue with eddy info4.nc' ds_tem = xr.open_dataset(filename_cpr_expanded_netcdf) ds_tem.close() ds_tem.num_cross.plot() print(ds_tem) #chech on subset #subset = ds_cpr_eddy.where(ds_cpr_eddy.cpr_eddy_data_distance<ds_cpr_eddy.cpr_eddy_data_radius) #for i in range(100): # print(subset.cpr_eddy_data_track[i].data,ds_cpr_eddy.cpr_eddy_data_distance[i].data,ds_cpr_eddy.cpr_eddy_data_radius[i].data) #print(filename_eddy) #ds_unique = xr.open_dataset(filename_eddy,group='eddy_data') #ds_unique.close() #ds_unique ds_cpr_eddy.cpr_eddy_data_cyclonic_type.plot() plt.plot(ds_cpr_eddy.cpr_eddy_data_distance) plt.plot(ds_cpr_eddy.cpr_eddy_data_radius) for i in range(10): print(ds_cpr_eddy.cpr_eddy_data_distance[i].data,ds_cpr_eddy.cpr_eddy_data_radius[i].data) #cpr_eddy_data_speed_radius_deg[index]=speed_radius_eddy[index_eddy]*cos(radians(lats_eddy[index_eddy]))/111.0 #proc_cpr ==1 whre distance is GREATER than radius of eddy proc_cpr = np.where(ds_cpr_eddy.cpr_eddy_data_distance>ds_cpr_eddy.cpr_eddy_data_radius,1,0) proc_cpr import numpy.ma as ma from numpy import * #remove masked values from data data = np.ma.filled(cpr_sample_ucur, np.nan) data[isnan(data)] = -9999 cpr_sample_ucur2=data data = np.ma.filled(cpr_sample_vcur, np.nan) data[isnan(data)] = -9999 cpr_sample_vcur2=data data = np.ma.filled(cpr_sample_ucur_clim, np.nan) data[isnan(data)] = -9999 cpr_sample_ucur_clim2=data data = np.ma.filled(cpr_sample_vcur_clim, np.nan) data[isnan(data)] = -9999 cpr_sample_vcur_clim2=data data = np.ma.filled(cpr_sample_sst, np.nan) data[isnan(data)] = -9999 cpr_sample_sst2=data data = np.ma.filled(cpr_sample_sst_clim, np.nan) data[isnan(data)] = -9999 cpr_sample_sst_clim2=data data = np.ma.filled(cpr_sample_uwnd, np.nan) data[isnan(data)] = -9999 cpr_sample_uwnd2=data data = np.ma.filled(cpr_sample_uwnd_clim, np.nan) data[isnan(data)] = -9999 cpr_sample_uwnd_clim2=data data = np.ma.filled(cpr_sample_vwnd, np.nan) data[isnan(data)] = -9999 cpr_sample_vwnd2=data data = np.ma.filled(cpr_sample_vwnd_clim, np.nan) data[isnan(data)] = -9999 cpr_sample_vwnd_clim2=data #print(shape(df)) #print(shape(cpr_sample_jday)) #df_time=[0] * (ilen_cpr) #print(ilen_cpr) #for index in range(0,ilen_cpr): # df_time[index] = dt.datetime(cpr_sample_year[index],cpr_sample_month[index],cpr_sample_day[index]) #df_vars=['Sample ID','day','month','year','lat','lon','already processed?','ETOPO_depth (m) nearest neighbor','ETOPO_depth (m) interp','SST CMC 2.0','SST Climatology CMC 2.0','U_wnd CCMC m/s','V_wnd CCMC m/s','Climatology U_wnd CCMC m/s','Climatology V_wnd CCMC m/s','U_cur oscar m/s','V_cur oscar m/s','Climatology U_cur oscar m/s','Climatology V_cur oscar m/s'] #print(shape(df_time)) #print(shape(df_vars)) #print(type(df_time)) #type(df) #print(type(df)) #print(shape(df)) ##print(shape(df_time)) #print(shape(df_vars)) #df_out = xr.DataArray(df, coords=[df_time,df_vars]) #, dims=['time' 'vars']) #df_out.to_netcdf(filename_cpr_expanded_netcdf) #df_test=xr.open_dataset(filename_cpr_expanded_netcdf) #df_test print(len(cpr_sample_sst2)) print(cpr_sample_sst2[-11:-1]) #output in netcdf #get the values for a given column #f.close() filename_cpr_expanded_netcdf='f:/data/eddy/collocated_data/All CPR Sample catalogue with eddy info4.nc' print(type(cpr_sample_id)) print(len(cpr_sample_id)) print(cpr_sample_ucur_clim[9:10]) print(cpr_sample_ucur[9:10]) #f.close() ilen_cpr=len(cpr_sample_id) f = Dataset(filename_cpr_expanded_netcdf,'w', format='NETCDF4') #'w' stands for write #tempgrp = f.createGroup('CPR_data') f.createDimension('z', ilen_cpr) cpr_sample_id_netcdf = f.createVariable('cpr_sample_id', 'str', 'z') cpr_sample_day_netcdf = f.createVariable('cpr_sample_day', 'i4', 'z') cpr_sample_month_netcdf = f.createVariable('cpr_sample_month', 'i4', 'z') cpr_sample_year_netcdf =f.createVariable('cpr_sample_year', 'i4', 'z') cpr_sample_lat_netcdf = f.createVariable('cpr_sample_lat', 'f4', 'z') cpr_sample_lon_netcdf = f.createVariable('cpr_sample_lon', 'f4', 'z') cpr_sample_proc_netcdf = f.createVariable('cpr_sample_proc', 'c', 'z') eddy_dist_netcdf = f.createVariable('cpr_eddy_data_distance', 'f4', 'z') eddy_dist_from_land_netcdf = f.createVariable('cpr_eddy_data_distance_from_land', 'f4', 'z') eddy_rad_netcdf = f.createVariable('cpr_eddy_data_radius', 'f4', 'z') eddy_lon_netcdf = f.createVariable('cpr_eddy_data_lons', 'f4', 'z') eddy_lat_netcdf = f.createVariable('cpr_eddy_data_lats', 'f4', 'z') eddy_time_netcdf = f.createVariable('cpr_eddy_data_time', 'f4', 'z') eddy_amp_netcdf = f.createVariable('cpr_eddy_data_amplitude', 'f4', 'z') eddy_spd_netcdf = f.createVariable('cpr_eddy_data_speed_average', 'f4', 'z') eddy_rad2_netcdf = f.createVariable('cpr_eddy_data_speed_radius', 'f4', 'z') eddy_cyc_netcdf = f.createVariable('cpr_eddy_data_cyclonic_type', 'i4', 'z') eddy_id_netcdf = f.createVariable('cpr_eddy_data_track_id', 'i4', 'z') eddy_tdy_netcdf = f.createVariable('cpr_eddy_data_total_days', 'i4', 'z') eddy_ob_netcdf = f.createVariable('cpr_eddy_data_ob_num', 'i4', 'z') eddy_yr_netcdf = f.createVariable('cpr_eddy_data_year', 'i4', 'z') eddy_dy_netcdf = f.createVariable('cpr_eddy_data_idyjl', 'i4', 'z') eddy_crossings_netcdf = f.createVariable('num_cross', 'i4', 'z') ucur_netcdf = f.createVariable('cpr_sample_oscar_ucur', 'f4', 'z') vcur_netcdf = f.createVariable('cpr_sample_oscar_vcur', 'f4', 'z') ucur_clim_netcdf = f.createVariable('cpr_sample_oscar_ucur_clim', 'f4', 'z') vcur_clim_netcdf = f.createVariable('cpr_sample_oscar_vcur_clim', 'f4', 'z') sst_netcdf = f.createVariable('cpr_sample_cmc_sst', 'f4', 'z') sst_clim_netcdf = f.createVariable('cpr_sample_cmc_sst_clim', 'f4', 'z') uwnd_netcdf = f.createVariable('cpr_sample_ccmp_uwnd', 'f4', 'z') uwnd_clim_netcdf = f.createVariable('cpr_sample_ccmp_uwnd_clim', 'f4', 'z') vwnd_netcdf = f.createVariable('cpr_sample_ccmp_vwnd', 'f4', 'z') vwnd_clim_netcdf = f.createVariable('cpr_sample_ccmp_vwnd_clim', 'f4', 'z') depth_netcdf = f.createVariable('cpr_sample_ETOPO_depth', 'f4', 'z') tem=cpr_sample_id.tolist() print(type(tem)) print(tem[0:10]) cpr_sample_id_netcdf[:] = cpr_sample_id #tem cpr_sample_day_netcdf[:] = cpr_sample_day cpr_sample_month_netcdf[:] = cpr_sample_month cpr_sample_year_netcdf[:] = cpr_sample_year cpr_sample_lat_netcdf[:] = cpr_sample_lat cpr_sample_lon_netcdf[:] = cpr_sample_lon cpr_sample_proc_netcdf[:] = cpr_sample_proc eddy_dist_netcdf[:] = cpr_eddy_data_distance eddy_dist_from_land_netcdf[:] = cpr_eddy_data_distance_from_land eddy_rad_netcdf[:] = cpr_eddy_data_radius eddy_lon_netcdf[:] = cpr_eddy_data_lons eddy_lat_netcdf[:] = cpr_eddy_data_lats eddy_time_netcdf[:] = cpr_eddy_data_time eddy_amp_netcdf[:] = cpr_eddy_data_amplitude eddy_spd_netcdf[:] = cpr_eddy_data_speed_average eddy_rad2_netcdf[:] = cpr_eddy_data_speed_radius eddy_cyc_netcdf[:] = cpr_eddy_data_cyclonic_type eddy_id_netcdf[:] = cpr_eddy_data_track_id eddy_tdy_netcdf[:] = cpr_eddy_data_total_days eddy_ob_netcdf[:] = cpr_eddy_data_ob_num eddy_yr_netcdf[:] = cpr_eddy_data_year eddy_dy_netcdf[:] = cpr_eddy_data_idyjl eddy_crossings_netcdf[:] = num_cross ucur_netcdf[:] =cpr_sample_ucur2 vcur_netcdf[:] =cpr_sample_vcur2 ucur_clim_netcdf[:] = cpr_sample_ucur_clim2 vcur_clim_netcdf[:] = cpr_sample_vcur_clim2 sst_netcdf[:] =cpr_sample_sst2 sst_clim_netcdf[:] =cpr_sample_sst_clim2 uwnd_netcdf[:] =cpr_sample_uwnd2 uwnd_clim_netcdf[:] =cpr_sample_uwnd_clim2 vwnd_netcdf[:] =cpr_sample_vwnd2 vwnd_clim_netcdf[:] =cpr_sample_vwnd_clim2 depth_netcdf[:] =cpr_sample_depth_exact f.close() df_test=xr.open_dataset(filename_cpr_expanded_netcdf) df_test.cpr_sample_id #into excel file #from pandas import DataFrame #tem=cpr_sample_id.tolist() #df = DataFrame({'CPR Sample ID': tem, 'CPR sample day': cpr_sample_day}) #print(filename_cpr_expanded) #df.to_excel('filename_cpr_expanded,', sheet_name='sheet1', index=False) #find number of crossings print(cpr_eddy_data_speed_radius[1],cpr_eddy_data_speed_radius_deg[1]) filename_cpr wb = openpyxl.load_workbook(filename_cpr) sheet=wb['2000_2016'] #sheet = wb.get_sheet_by_name('2000_2016') for i in range(0,1): sheet['A' + str(i + 1)].value = 'cpr_sample_id' sheet['B' + str(i + 1)].value = 'cpr_sample_day' sheet['C' + str(i + 1)].value = 'cpr_sample_month' sheet['D' + str(i + 1)].value = 'cpr_sample_year' sheet['E' + str(i + 1)].value = 'cpr_sample_lat' sheet['F' + str(i + 1)].value = 'cpr_sample_lon' sheet['G' + str(i + 1)].value = 'cpr_sample_proc' sheet['H' + str(i + 1)].value = 'eddy_data_track_id' sheet['I' + str(i + 1)].value = 'eddy_data_distance' sheet['J' + str(i + 1)].value = 'eddy_data_distance_from_land' sheet['K' + str(i + 1)].value = 'eddy_data_radius' sheet['L' + str(i + 1)].value = 'eddy_data_lons' sheet['M' + str(i + 1)].value = 'eddy_data_lats' sheet['N' + str(i + 1)].value = 'eddy_data_time' sheet['O' + str(i + 1)].value = 'eddy_data_amplitude' sheet['P' + str(i + 1)].value = 'eddy_data_speed_average' sheet['Q' + str(i + 1)].value = 'eddy_data_speed_radius' sheet['R' + str(i + 1)].value = 'eddy_data_cyclonic_type' sheet['S' + str(i + 1)].value = 'eddy_data_total_days' sheet['T' + str(i + 1)].value = 'eddy_data_ob_num' sheet['U' + str(i + 1)].value = 'eddy_data_year' sheet['V' + str(i + 1)].value = 'eddy_data_idyjl' sheet['W' + str(i + 1)].value = 'number_times_cpr_crosses_this_eddy' sheet['X' + str(i + 1)].value = 'cpr_sample_oscar_ucur' sheet['Y' + str(i + 1)].value = 'cpr_sample_oscar_vcur' sheet['Z' + str(i + 1)].value = 'cpr_sample_oscar_ucur_clim' sheet['AA' + str(i + 1)].value = 'cpr_sample_oscar_vcur_clim' sheet['AB' + str(i + 1)].value = 'cpr_sample_cmc_sst' sheet['AC' + str(i + 1)].value = 'cpr_sample_cmc_sst_clim' sheet['AD' + str(i + 1)].value = 'cpr_sample_ccmp_uwnd' sheet['AE' + str(i + 1)].value = 'cpr_sample_ccmp_uwnd_clim' sheet['AF' + str(i + 1)].value = 'cpr_sample_ccmp_vwnd' sheet['AG' + str(i + 1)].value = 'cpr_sample_ccmp_vwnd_clim' sheet['AH' + str(i + 1)].value = 'cpr_sample_ETOPO_depth' ilen_cpr=len(cpr_sample_id) cpr_eddy_data_lons2=cpr_eddy_data_lons for i in range(0,ilen): if cpr_eddy_data_lons[i]>180.: cpr_eddy_data_lons2[i]=cpr_eddy_data_lons[i]-360. for i in range(0,ilen_cpr): sheet['A' + str(i + 2)].value = cpr_sample_id[i] sheet['B' + str(i + 2)].value = cpr_sample_day[i] sheet['C' + str(i + 2)].value = cpr_sample_month[i] sheet['D' + str(i + 2)].value = cpr_sample_year[i] sheet['E' + str(i + 2)].value = cpr_sample_lat[i] sheet['F' + str(i + 2)].value = cpr_sample_lon[i] sheet['G' + str(i + 2)].value = cpr_sample_proc[i] sheet['H' + str(i + 2)].value = cpr_eddy_data_track_id[i] sheet['I' + str(i + 2)].value = cpr_eddy_data_distance[i] sheet['J' + str(i + 2)].value = cpr_eddy_data_distance_from_land[i] sheet['K' + str(i + 2)].value = cpr_eddy_data_radius[i] sheet['L' + str(i + 2)].value = cpr_eddy_data_lons2[i] sheet['M' + str(i + 2)].value = cpr_eddy_data_lats[i] sheet['N' + str(i + 2)].value = cpr_eddy_data_time[i] sheet['O' + str(i + 2)].value = cpr_eddy_data_amplitude[i] sheet['P' + str(i + 2)].value = cpr_eddy_data_speed_average[i] sheet['Q' + str(i + 2)].value = cpr_eddy_data_speed_radius[i] sheet['R' + str(i + 2)].value = cpr_eddy_data_cyclonic_type[i] sheet['S' + str(i + 2)].value = cpr_eddy_data_total_days[i] sheet['T' + str(i + 2)].value = cpr_eddy_data_ob_num[i] sheet['U' + str(i + 2)].value = cpr_eddy_data_year[i] sheet['V' + str(i + 2)].value = cpr_eddy_data_idyjl[i] sheet['W' + str(i + 2)].value = num_cross[i] sheet['X' + str(i + 2)].value = cpr_sample_ucur2[i] sheet['Y' + str(i + 2)].value = cpr_sample_vcur2[i] sheet['Z' + str(i + 2)].value = cpr_sample_ucur_clim2[i] sheet['AA' + str(i + 2)].value = cpr_sample_vcur_clim2[i] sheet['AB' + str(i + 2)].value = cpr_sample_sst2[i] sheet['AC' + str(i + 2)].value = cpr_sample_sst_clim2[i] sheet['AD' + str(i + 2)].value = cpr_sample_uwnd2[i] sheet['AE' + str(i + 2)].value = cpr_sample_uwnd_clim2[i] sheet['AF' + str(i + 2)].value = cpr_sample_vwnd2[i] sheet['AG' + str(i + 2)].value = cpr_sample_vwnd_clim2[i] sheet['AH' + str(i + 2)].value = cpr_sample_depth_exact[i] wb.save(filename_cpr_expanded) f = plt.figure() clats=[] clons=[] clats2=[] clons2=[] for i in range(0,len(cpr_sample_lat)): tem=cpr_sample_proc[i] if cpr_eddy_data_distance[i]<=cpr_eddy_data_radius[i] and tem=='Yes' : clats.append(cpr_sample_lat[i]) clons.append(cpr_sample_lon[i]) elif cpr_eddy_data_distance[i]<=cpr_eddy_data_radius[i] and tem=='No' : clats2.append(cpr_sample_lat[i]) clons2.append(cpr_sample_lon[i]) map = Basemap(projection='merc', lat_0 = 45, lon_0 = -130, resolution = 'l', area_thresh = 0.1, llcrnrlon=-180.25, llcrnrlat=30.0,urcrnrlon=-115.25, urcrnrlat=62.75) #map.drawcoastlines() #map.drawcountries() map.fillcontinents(color = 'coral') #map.drawmapboundary() #xx=cpr_sample_lon[i] #map.plot(xx,yy,'ko',markersize=24) x,y = map(clons,clats) map.plot(x, y, 'bo', markersize=.2) x,y = map(clons2,clats2) map.plot(x, y, 'ro', markersize=.2) plt.show() f.savefig("F:/data/eddy/figures/all_collocated_cpr_data.pdf", bbox_inches='tight') print(cpr_eddy_data_speed_radius[1],cpr_eddy_data_speed_radius_deg[1]) f = plt.figure() clats=[] clons=[] clats2=[] clons2=[] elats=[] elons=[] erads=[] erads2=[] espokes=[] ecross=[] for i in range(0,len(cpr_sample_lat)): tem=cpr_sample_proc[i] if cpr_eddy_data_distance[i]<=cpr_eddy_data_radius[i] and tem=='Yes' : clats.append(cpr_sample_lat[i]) clons.append(cpr_sample_lon[i]) elats.append(cpr_eddy_data_lats[i]) elons.append(cpr_eddy_data_lons2[i]) erads.append(cpr_eddy_data_speed_radius[i]) erads2.append(cpr_eddy_data_speed_radius_deg[i]) ecross.append(num_cross[i]) espokes.append(50) elif cpr_eddy_data_distance[i]<=cpr_eddy_data_radius[i] and tem=='No' : clats2.append(cpr_sample_lat[i]) clons2.append(cpr_sample_lon[i]) elats.append(cpr_eddy_data_lats[i]) elons.append(cpr_eddy_data_lons2[i]) erads.append(cpr_eddy_data_speed_radius[i]) erads2.append(cpr_eddy_data_speed_radius_deg[i]) ecross.append(num_cross[i]) espokes.append(50) print(cpr_eddy_data_speed_radius[1],cpr_eddy_data_speed_radius_deg[1]) def shoot(lon, lat, azimuth, maxdist=None): """Shooter Function Original javascript on http://williams.best.vwh.net/gccalc.htm Translated to python by Thomas Lecocq """ glat1 = lat * np.pi / 180. glon1 = lon * np.pi / 180. s = maxdist / 1.852 faz = azimuth * np.pi / 180. EPS= 0.00000000005 if ((np.abs(np.cos(glat1))<EPS) and not (np.abs(np.sin(faz))<EPS)): alert("Only N-S courses are meaningful, starting at a pole!") a=6378.13/1.852 f=1/298.257223563 r = 1 - f tu = r * np.tan(glat1) sf = np.sin(faz) cf = np.cos(faz) if (cf==0): b=0. else: b=2. * np.arctan2 (tu, cf) cu = 1. / np.sqrt(1 + tu * tu) su = tu * cu sa = cu * sf c2a = 1 - sa * sa x = 1. + np.sqrt(1. + c2a * (1. / (r * r) - 1.)) x = (x - 2.) / x c = 1. - x c = (x * x / 4. + 1.) / c d = (0.375 * x * x - 1.) * x tu = s / (r * a * c) y = tu c = y + 1 while (np.abs (y - c) > EPS): sy = np.sin(y) cy = np.cos(y) cz = np.cos(b + y) e = 2. * cz * cz - 1. c = y x = e * cy y = e + e - 1. y = (((sy * sy * 4. - 3.) * y * cz * d / 6. + x) * d / 4. - cz) * sy * d + tu b = cu * cy * cf - su * sy c = r * np.sqrt(sa * sa + b * b) d = su * cy + cu * sy * cf glat2 = (np.arctan2(d, c) + np.pi) % (2*np.pi) - np.pi c = cu * cy - su * sy * cf x = np.arctan2(sy * sf, c) c = ((-3. * c2a + 4.) * f + 4.) * c2a * f / 16. d = ((e * cy * c + cz) * sy * c + y) * sa glon2 = ((glon1 + x - (1. - c) * d * f + np.pi) % (2*np.pi)) - np.pi baz = (np.arctan2(sa, b) + np.pi) % (2 * np.pi) glon2 *= 180./np.pi glat2 *= 180./np.pi baz *= 180./np.pi return (glon2, glat2, baz) def equi(m, centerlon, centerlat, radius, *args, **kwargs): glon1 = centerlon glat1 = centerlat X = [] Y = [] for azimuth in range(0, 360): glon2, glat2, baz = shoot(glon1, glat1, azimuth, radius) X.append(glon2) Y.append(glat2) X.append(X[0]) Y.append(Y[0]) #m.plot(X,Y,**kwargs) #Should work, but doesn't... X,Y = m(X,Y) plt.plot(X,Y,**kwargs) fig = plt.figure(figsize=(11.7,8.3)) #Custom adjust of the subplots plt.subplots_adjust(left=0.05,right=0.95,top=0.90,bottom=0.05,wspace=0.15,hspace=0.05) ax = plt.subplot(111) print(cpr_eddy_data_speed_radius[1],cpr_eddy_data_speed_radius_deg[1]) #Let's create a basemap of the world m = Basemap(projection='merc', lat_0 = 45, lon_0 = -130, resolution = 'l', area_thresh = 0.1, llcrnrlon=-180.25, llcrnrlat=30.0,urcrnrlon=-115.25, urcrnrlat=62.75) m.fillcontinents(color='coral',lake_color='white') x,y = m(clons,clats) m.plot(x, y, 'bo', markersize=.2) x,y = m(clons2,clats2) m.plot(x, y, 'ro', markersize=.2) for i in range(0,len(erads)): centerlon = elons[i] centerlat = elats[i] radius = erads[i] if abs(centerlon-erads2[i])<177: equi(m, centerlon, centerlat, radius,lw=1.) plt.savefig("F:/data/eddy/figures/all_collocated_cpr_data3.pdf",dpi=300) plt.show() #make a list of eddy id that have two visits #make icheck have a 1 where trackid has more than two visits icheck=[] for i in range(0,len(cpr_sample_lat)): if num_cross[i]>1: itest=0 for i2 in range(0,len(icheck)): if icheck[i2]==cpr_eddy_data_track_id[i]: itest=1 if itest==0: icheck.append(cpr_eddy_data_track_id[i]) print(icheck) #now just do for eddies that have 2 visits for i_tem in range(0,len(icheck)): tem_id=icheck[i_tem] #get all lat/lon for specific eddy to pring alats=[] alons=[] for i in range(0,len(lons_eddy)): if tem_id==track_eddy[i]: alats.append(lats_eddy[i]) if lons_eddy[i]<=180: alons.append(lons_eddy[i]) if lons_eddy[i]>180: alons.append(lons_eddy[i]-360) clats=[] clons=[] clats2=[] clons2=[] elats=[] elons=[] erads=[] erads2=[] for i in range(0,len(cpr_sample_lat)): tem=cpr_sample_proc[i] if cpr_sample_lon[i]>0: continue if cpr_eddy_data_distance[i]<=cpr_eddy_data_radius[i] \ and tem=='Yes' and cpr_eddy_data_track_id[i]==tem_id: clats.append(cpr_sample_lat[i]) clons.append(cpr_sample_lon[i]) elats.append(cpr_eddy_data_lats[i]) elons.append(cpr_eddy_data_lons2[i]) erads.append(cpr_eddy_data_speed_radius[i]) erads2.append(cpr_eddy_data_speed_radius_deg[i]) elif cpr_eddy_data_distance[i]<=cpr_eddy_data_radius[i] \ and tem=='No' and cpr_eddy_data_track_id[i]==tem_id: clats2.append(cpr_sample_lat[i]) clons2.append(cpr_sample_lon[i]) elats.append(cpr_eddy_data_lats[i]) elons.append(cpr_eddy_data_lons2[i]) erads.append(cpr_eddy_data_speed_radius[i]) erads2.append(cpr_eddy_data_speed_radius_deg[i]) if len(clons2)<1 and len(clats)<1: continue fig = plt.figure(figsize=(11.7,8.3)) #Custom adjust of the subplots plt.subplots_adjust(left=0.05,right=0.95,top=0.90,bottom=0.05,wspace=0.15,hspace=0.05) ax = plt.subplot(111) print(cpr_eddy_data_speed_radius[1],cpr_eddy_data_speed_radius_deg[1]) #Let's create a basemap of the world m = Basemap(projection='merc', lat_0 = 45, lon_0 = -130, resolution = 'l', area_thresh = 0.1, llcrnrlon=-180.25, llcrnrlat=30.0,urcrnrlon=-115.25, urcrnrlat=62.75) m.fillcontinents(color='coral',lake_color='white') x,y = m(clons,clats) m.plot(x, y, 'bo', markersize=.2) x,y = m(clons2,clats2) m.plot(x, y, 'ro', markersize=.2) x,y = m(alons,alats) m.plot(x, y, 'k') for i in range(0,len(erads)): centerlon = elons[i] centerlat = elats[i] radius = erads[i] if abs(centerlon-erads2[i])<177: equi(m, centerlon, centerlat, radius,lw=1.) # plt.show() fig_fname="F:/data/eddy/figures/all_collocated_cpr_data_doubles" + str(tem_id) + ".pdf" plt.savefig(fig_fname,dpi=300) print(fig_fname) print(len(alons)) print(alons[1:200]) for i in range(0,len(cpr_sample_lat)): tem=cpr_sample_proc[i] if cpr_eddy_data_track_id[i]==tem_id: print(i,cpr_eddy_data_distance[i],cpr_eddy_data_radius[i],tem) print('clons2',clons2) print('clats2',clats2) print(len(clons)) print('clons',clons) print('clats',clats) filename='F:/data/eddy/collocated_data/All CPR Sample catalogue with eddy info4.nc' ds_eddy = xr.open_dataset(filename) ds_eddy ds_eddy.cpr_sample_id[2].values print(type(ds_eddy)) fig, (ax1) = plt.subplots(nrows=1, figsize=(6, 5.4)) #f = plt.figure() #map = Basemap(projection='merc', lat_0 = 45, lon_0 = -130, resolution = 'l', area_thresh = 0.1, # llcrnrlon=-180.25, llcrnrlat=30.0,urcrnrlon=-115.25, urcrnrlat=62.75) #map.fillcontinents(color = 'coral') #x,y = map(ds_eddy.cpr_sample_lon.values,ds_eddy.cpr_sample_lat.values) d2=ds_eddy.where(ds_eddy.cpr_sample_lon<0) print(len(d2)) print(type(d2)) ax1.scatter(d2.cpr_sample_lon.values,d2.cpr_sample_lat.values, c = cpr_sample_depth_exact,s=1) #plt.scatter(ds_eddy.cpr_sample_lon.values,ds_eddy.cpr_sample_lat.values, c = ds_eddy.cpr_sample_ETOPO_depth.values) #plt.plot(ds_eddy.cpr_sample_lon.values[0:1000],ds_eddy.cpr_sample_ETOPO_depth.values[0:1000],'.') plt.show() f.savefig('F:/data/eddy/collocated_data/depth_image.png', transparent=False, format='png') fig, (ax1) = plt.subplots(nrows=1, figsize=(6, 5.4)) im = ax1.imshow(ds_topo.z[7000:9500,0:4500], interpolation='bilinear',vmin=-7000.0, vmax=1.0,aspect='auto',origin='lower') plt.show() ds_eddy.cpr_sample_ETOPO_depth.values[0:10] ds_eddy.cpr_sample_id[0:1000] dir_pattern_zarr = 'F:/data/sat_data/sst/cmc/zarr/' ds_sst= xr.open_zarr(dir_pattern_zarr) ds_sst ###Output _____no_output_____

Preco_a_termo.ipynb

###Markdown ###Code #encoding: utf-8 #encoding: iso-8859-1 #encoding: win-1252 #Atividade desenvolvida para a Curso Derivativos e Gestão de Carteiras #The University of Campinas -UNICAMP #Desenvolvido por: José Wellington Albuquerque # encoding: utf-8 # encoding: iso-8859-1 # encoding: win-1252 from math import e S_o = input("Qual o valor do contrato a termo sobre o ativo de investimento em R$? \n") t_inicial = input("Quantos meses: \n") t_final = 12 juros_aa = input("Digite um valor do juros ao ano: \n") n=((float(juros_aa))*(int(t_inicial))/(int(t_final))) F_o=(float(S_o))*(e**n) print ('O preço futuro é de R$',("%.2f"% F_o), 'Reais!\n\n') if (F_o > (float(S_o))*(e**(float(juros_aa))*(int(t_final)))): print ("Compre o ativo e venda a descoberto com contratos a termo sobre o ativo!!") else: print ("Venda o ativo a descoberto e faça contratos a termo comprados sobre ele.!!\n") ###Output Qual o valor do contrato a termo sobre o ativo de investimento em R$? 32 Quantos meses: 3 Digite um valor do juros ao ano: 0.05 O preço futuro é de R$ 32.40 Reais! Venda o ativo a descoberto e faça contratos a termo comprados sobre ele.!!

Fase 2 - Manejo de datos y optimizacion/Tema 06 - Programacion de funciones/Ejercicios/Enunciados.ipynb

###Markdown Tema 06: Programación de funciones (Enunciados)*Nota: Estos ejercicios son optativos para hacer al final de la unidad y están pensados para apoyar tu aprendizaje*. **1) Realiza una función llamada area_rectangulo() que devuelva el área del rectangulo a partir de una base y una altura. Calcula el área de un rectángulo de 15 de base y 10 de altura.***Nota: El área de un rectángulo se obtiene al multiplicar la base por la altura.* ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **2) Realiza una función llamada area_circulo() que devuelva el área de un círculo a partir de un radio. Calcula el área de un círculo de 5 de radio: **Nota: El área de un círculo se obtiene al elevar el radio a dos y multiplicando el resultado por el número pi. Puedes utilizar el valor 3.14159 como pi o importarlo del módulo math:```pythonimport mathprint(math.pi)> 3.1415...``` ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **3) Realiza una función llamada relacion() que a partir de dos números cumpla lo siguiente**:* Si el primer número es mayor que el segundo, debe devolver 1.* Si el primer número es menor que el segundo, debe devolver -1.* Si ambos números son iguales, debe devolver un 0.** Comprueba la relación entre los números: '5 y 10', '10 y 5' y '5 y 5'** ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **4) Realiza una función llamada intermedio() que a partir de dos números, devuelva su punto intermedio:***Nota: El número intermedio de dos números corresponde a la suma de los dos números dividida entre 2*** Comprueba el punto intermedio entre -12 y 24** ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **5) Realiza una función llamada recortar() que reciba tres parámetros. El primero es el número a recortar, el segundo es el límite inferior y el tercero el límite superior. La función tendrá que cumplir lo siguiente:*** Devolver el límite inferior si el número es menor que éste* Devolver el límite superior si el número es mayor que éste.* Devolver el número sin cambios si no se supera ningún límite.** Comprueba el resultado de recortar 15 entre los límites 0 y 10** ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **6) Realiza una función separar() que tome una lista de números enteros y devuelva dos listas ordenadas. La primera con los números pares, y la segunda con los números impares:**Por ejemplo: ```pythonpares, impares = separar([6,5,2,1,7])print(pares) valdría [2, 6]print(impares) valdría [1, 5, 7]```*Nota: Para ordenar una lista automáticamente puedes usar el método .sort().* ###Code numeros = [-12, 84, 13, 20, -33, 101, 9] # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown Tema 06: Programación de funciones (Enunciados)*Nota: Estos ejercicios son optativos para hacer al final de la unidad y están pensados para apoyar tu aprendizaje*. **1) Realiza una función llamada area_rectangulo() que devuelva el área del rectangulo a partir de una base y una altura. Calcula el área de un rectángulo de 15 de base y 10 de altura.***Nota: El área de un rectángulo se obtiene al multiplicar la base por la altura.* ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **2) Realiza una función llamada area_circulo() que devuelva el área de un círculo a partir de un radio. Calcula el área de un círculo de 5 de radio: **Nota: El área de un círculo se obtiene al elevar el radio a dos y multiplicando el resultado por el número pi. Puedes utilizar el valor 3.14159 como pi o importarlo del módulo math:```pythonimport mathprint(math.pi)> 3.1415...``` ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **3) Realiza una función llamada relacion() que a partir de dos números cumpla lo siguiente**:* Si el primer número es mayor que el segundo, debe devolver 1.* Si el primer número es menor que el segundo, debe devolver -1.* Si ambos números son iguales, debe devolver un 0.** Comprueba la relación entre los números: '5 y 10', '10 y 5' y '5 y 5'** ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **4) Realiza una función llamada intermedio() que a partir de dos números, devuelva su punto intermedio:***Nota: El número intermedio de dos números corresponde a la suma de los dos números dividida entre 2*** Comprueba el punto intermedio entre -12 y 24** ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **5) Realiza una función llamada recortar() que reciba tres parámetros. El primero es el número a recortar, el segundo es el límite inferior y el tercero el límite superior. La función tendrá que cumplir lo siguiente:*** Devolver el límite inferior si el número es menor que éste* Devolver el límite superior si el número es mayor que éste.* Devolver el número sin cambios si no se supera ningún límite.** Comprueba el resultado de recortar 15 entre los límites 0 y 10** ###Code # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown **6) Realiza una función separar() que tome una lista de números enteros y devuelva dos listas ordenadas. La primera con los números pares, y la segunda con los números impares:**Por ejemplo: ```pythonpares, impares = separar([6,5,2,1,7])print(pares) valdría [2, 6]print(impares) valdría [1, 5, 7]```*Nota: Para ordenar una lista automáticamente puedes usar el método .sort().* ###Code numeros = [-12, 84, 13, 20, -33, 101, 9] # Completa el ejercicio aquí ###Output _____no_output_____ ###Markdown Tema 06: Programación de funciones (Enunciados)*Nota: Estos ejercicios son optativos para hacer al final de la unidad y están pensados para apoyar tu aprendizaje*. **1) Realiza una función llamada area_rectangulo() que devuelva el área del rectangulo a partir de una base y una altura. Calcula el área de un rectángulo de 15 de base y 10 de altura.***Nota: El área de un rectángulo se obtiene al multiplicar la base por la altura.* ###Code # Completa el ejercicio aquí def area_rectangulo(base, altura): return base * altura resultado = area_rectangulo(15, 10) print("El área de un rectangulo que tiene 15 de base y 10 de altura es la siguiente:", resultado) ###Output El área de un rectangulo que tiene 15 de base y 10 de altura es la siguiente: 150 ###Markdown **2) Realiza una función llamada area_circulo() que devuelva el área de un círculo a partir de un radio. Calcula el área de un círculo de 5 de radio: **Nota: El área de un círculo se obtiene al elevar el radio a dos y multiplicando el resultado por el número pi. Puedes utilizar el valor 3.14159 como pi o importarlo del módulo math:```pythonimport mathprint(math.pi)> 3.1415...``` ###Code # Completa el ejercicio aquí import math def area_circulo(radio): return (radio**2) * math.pi resultado = area_circulo(radio = 5) print("El área de un círculo con un radio de 5 es la siguiente:", resultado) ###Output El área de un círculo con un radio de 5 es la siguiente: 78.53981633974483 ###Markdown **3) Realiza una función llamada relacion() que a partir de dos números cumpla lo siguiente**:* Si el primer número es mayor que el segundo, debe devolver 1.* Si el primer número es menor que el segundo, debe devolver -1.* Si ambos números son iguales, debe devolver un 0.** Comprueba la relación entre los números: '5 y 10', '10 y 5' y '5 y 5'** ###Code # Completa el ejercicio aquí def relacion(num1, num2): result = 0 if num1 > num2: result = 1 elif num2 > num1: result = -1 return result print("Entre 5 y 10:", relacion(5, 10)) print("Entre 10 y 5:", relacion(10, 5)) print("Entre 5 y 5:", relacion(5, 5)) ###Output Entre 5 y 10: -1 Entre 10 y 5: 1 Entre 5 y 5: 0 ###Markdown **4) Realiza una función llamada intermedio() que a partir de dos números, devuelva su punto intermedio:***Nota: El número intermedio de dos números corresponde a la suma de los dos números dividida entre 2*** Comprueba el punto intermedio entre -12 y 24** ###Code # Completa el ejercicio aquí def intermedio(num1, num2): return (num1 + num2) / 2 print("El numero intermedio es el siguiente", intermedio(-12, 24)) ###Output El numero intermedio es el siguiente 6.0 ###Markdown **5) Realiza una función llamada recortar() que reciba tres parámetros. El primero es el número a recortar, el segundo es el límite inferior y el tercero el límite superior. La función tendrá que cumplir lo siguiente:*** Devolver el límite inferior si el número es menor que éste* Devolver el límite superior si el número es mayor que éste.* Devolver el número sin cambios si no se supera ningún límite.** Comprueba el resultado de recortar 15 entre los límites 0 y 10** ###Code # Completa el ejercicio aquí def recortar(num, limiteInferior, limiteSuperior): if num < limiteInferior: return limiteInferior elif num > limiteSuperior: return limiteSuperior else: return num print("Recortar numero 15 entre limites 0 y 10: ", recortar(15, 0, 10)) ###Output Recortar numero 15 entre limites 0 y 10: 10 ###Markdown **6) Realiza una función separar() que tome una lista de números enteros y devuelva dos listas ordenadas. La primera con los números pares, y la segunda con los números impares:**Por ejemplo: ```pythonpares, impares = separar([6,5,2,1,7])print(pares) valdría [2, 6]print(impares) valdría [1, 5, 7]```*Nota: Para ordenar una lista automáticamente puedes usar el método .sort().* ###Code numeros = [-12, 84, 13, 20, -33, 101, 9] # Completa el ejercicio aquí def separar(numeros): pares = [] impares = [] numeros.sort() for num in numeros: if num % 2 == 0: pares.append(num) else: impares.append(num) return pares, impares pares, impares = separar([6,5,2,1,7]) print(pares) print(impares) pares, impares = separar([1, 5, 7, 3, 9, 2, 0, 1, -45, -12, 34, 98, 290]) print(pares) print(impares) ###Output [2, 6] [1, 5, 7] [-12, 0, 2, 34, 98, 290] [-45, 1, 1, 3, 5, 7, 9]

nb4a_3d_structuring_elements.ipynb

###Markdown Structuing elements ###Code %%capture_png $cell_normal arrray = scipy.ndimage.generate_binary_structure(3, 1) plot_voxels(arrray) %%capture_png $cell_normal arrray = scipy.ndimage.generate_binary_structure(3, 2) plot_voxels(arrray) %%capture_png $cell_normal arrray = scipy.ndimage.generate_binary_structure(3, 3) plot_voxels(arrray) %%capture_png $cell_normal arrray = cube(5) plot_voxels(arrray) %%capture_png $cell_normal arrray = octahedron(3) plot_voxels(arrray) %%capture_png $cell_normal arrray = ball(3) plot_voxels(arrray) %%capture_png $cell_normal import matplotlib.pyplot as plt import numpy as np grids = 2 boxs = 5 voxelarray = np.zeros((boxs * grids, boxs * grids, boxs * grids)) i = 1 for xi in range(0, 2): for yi in range(0, 2): for zi in range(0, 2): voxelarray[ xi * boxs : xi * boxs + boxs, yi * boxs : yi * boxs + boxs, zi * boxs : zi * boxs + boxs, ] = i i += 1 voxelarray = np.uint8(voxelarray * 255 / i) plot_voxels(voxelarray) %%capture_png $cell_normal voxelarray = data.binary_blobs(length=110, volume_fraction=0.6, n_dim=3, seed=9) voxelarray = voxelarray[90:, 90:, 90:] # plt.imshow(voxelarray[:,:,3]) plot_voxels(voxelarray, linewidth=0.1) ###Output _____no_output_____

Week-1/CS6501_Lab_1_1.ipynb

###Markdown **Artificial Intelligence - MSc**CS6501 - MACHINE LEARNING AND APPLICATIONS Instructor: Enrique NaredoCS6501_Lab-0.1 Python Basics Markdown Examples This is **bold**. This is *italic*. This is ~strikethrough~. Mathematical Equations$\sqrt{3x-1}+(1+x)^2$$e^x=\sum_{i=0}^\infty \frac{1}{i!}x^i$ Python Comments ###Code # This is a single line comment ''' THIS IS A MULTILINE COMMENT USING STRING LITERALS! ''' """ This is a comment written in more than just one line """ ###Output _____no_output_____ ###Markdown Python Indentation ###Code ## Good indentation if 10 > 5: print("Ten is greater than five!") ## Wrong indentation # add blank spaces to get the right indentation if 10 > 5: print("Ten is greater than five!") ###Output _____no_output_____ ###Markdown Python Variables ###Code x = 10 y = "Hello, Friend!" z = "Celtics" # is the same as z = 'Celtics' a = 4 # is NOT the same as A = 4 # Legal variable names myvar = "Anything" my_var = "Anything" _my_var = "Anything" myVar = "Anything" MYVAR = "Anything" myvar2 = "Anything" # Camel Case myVariableName = "Something" # Pascal Case MyVariableName = "Something" # Snake Case my_variable_name = "Something" # Invent your own case my_Variable-NAME = "Something" # Many Values to Multiple Variables alpha, beta, gamma = "Anything", "Something", "Whatever" print(alpha) print(beta) print(gamma) # One Value to Multiple Variables alpha = beta = gamma = "Everything" print(alpha) print(beta) print(gamma) ###Output _____no_output_____

.ipynb_checkpoints/teste-checkpoint.ipynb

###Markdown New bussines location indicator Coursera project capstoneThis is the course captstone project for the coursera IBM machine learning specialization About the projectHaving a good location for your business is an important factor for it's prosperity. Although the hot spots in a city for a new venue are common knowledge, usually this places have a very high price given that it is correlated with higher demand. With some datamining and machine learning, some places cam be discovered as good opportunity’s that have not yet received enought attention from people on the business.This project uses python and some very helpfull libraries for machine learning, visualization and data colection, to give some insight on where you should open your business in a city, based on how "hot" the area is and how many competidors are on the same busines type, trying to maximize the fist and minimase the last. For the case study, the city chosen was Piracicaba, Brazil and the business type is a coffe shop, to the goal was to find a good place for a new coffe shop that has good location but not many competidors. To achive this objective we will start by ranking the places in city by how 'hot' they are for business and them finding what is the optimal place for a new business that does not collide with other similar business by location but also is on a "hot spot" in the city. The data on the amount of venues by location will be collected using the foursquare api for a given city. The app/notebook will be created in a generic way so that people using it can change the city name. A map of the city based on the amount of venues will be created and also another one for the similar venues as the person is looking to create.A score for a given location that will be created by adding value for number of venues using mahalanobis distance as a weight and the using the opposite (decreasing score) by having similar venues.In the end, points will be clustered together to have useful locations as a suggestion for the new business to be opened. Structure:This notebook is 6 parts: 1. Interest area organization. In this part, we will select the city and area of search as well as basic visualization, libraries imports and api/requests setup. 2. Data Gattering Using the fourshared api, we will get the data we need. 3. Data organization and cleanup Here we will treat the received data to be able to use it for visualization and the final machine learnig stage 4. Clustering We will find how many groups of coffe shop are there in the city by location and explore it also for the general venues. 5. Ranking Two scores, ranging from 0 to 100 will be created, and all positions on the city map will recieve this scores, one for ammount of venues (high is better - more general venues) and one for ammount of competition (high is worst - more coffe shops around). Let's start by importing the libraries we will need ###Code import pandas as pd import numpy as np import matplotlib.pyplot as plt import folium, requests, os, time, itertools, pickle import folium.plugins as plugins from bs4 import BeautifulSoup from urllib.request import urlopen from geopy.geocoders import Nominatim from IPython.display import Image ###Output _____no_output_____ ###Markdown 1. Interest area organization Defining the place of interest and search area ###Code # this will be our center point in the city lat_city_center, lng_city_center = -22.727482, -47.648811 # now, create a map with this lat and lng info map_city = folium.Map(location=[lat_city_center, lng_city_center], zoom_start=14) folium.CircleMarker( [lat_city_center, lng_city_center], radius=10, color='green', fill=True, fill_color='green', fill_opacity=0.7, parse_html=False).add_to(map_city) # check if it is correct map_city # Defining the search grid size and location number_x_points = 10 number_y_points = 10 lat_city_center, lng_city_center = -22.727482, -47.648811 # the farthest point of interest in the map x_max, y_max = -22.713566, -47.659758 # now we create a distance range in lat and lng distance measure lat_delta = 2*np.abs(x_max - lat_city_center) lng_delta = 2*np.abs(y_max - lng_city_center) # create the matrix of points for use in the map and foursquare lat_range = np.linspace(lat_city_center - lat_delta, lat_city_center + lat_delta, number_x_points) lng_range = np.linspace(lng_city_center - lng_delta, lng_city_center + lng_delta, number_y_points) lat_range for lat in lat_range: for lng in lng_range: folium.CircleMarker( [lat, lng], radius=10, color='red', fill=True, fill_color='red', fill_opacity=0.7, parse_html=False).add_to(map_city) map_city ###Output _____no_output_____ ###Markdown whe can see that we have covered most of the city with every point at around 200m from each other 2. Data Gattering Requesting the data from the location with foursquare api ###Code # Client ID and cliet secret key shoud never be stored in the notebook or other script, # so we read it from os enviroment variable. VERSION = '20180605' # Foursquare API version #CLIENT_ID = os.getenv('CLIENT_ID') # your Foursquare ID #CLIENT_SECRET = os.getenv('CLIENT_SECRET') # your Foursquare Secret ###Output _____no_output_____ ###Markdown Creating some help functions to get and treat the data received ###Code def get_info(lat, lng): ''' This function call foursquare api with given lattitude and longtude and returns the api response as ''' url = f'https://api.foursquare.com/v2/venues/search?&client_id={CLIENT_ID}&client_secret={CLIENT_SECRET}&v={VERSION}&ll={lat},{lng}&radius={250}&limit={500}' results = requests.get(url).json() if results['meta']['code'] == 200: return results['response'] return False def count_venues(response): ''' This function parse the response received from the get_info() function and treat it to filter only the number of venues in the area and retur it's number and a list of lat and lng data in a list o lists format ''' try: points = [] if response['venues']: for i in range(len(response['venues'])): try: lat = r['venues'][i]['location']['lat'] lng = r['venues'][i]['location']['lng'] points.append([lat, lng]) except: pass return len(response['venues']), points except: pass return 0, None def count_similar(response, similar=['Café', 'Cafe', 'Coffe', 'Coffee Shops']): ''' This function parse the response received from the get_info() function and count how many of then has similar text (eg: has the type we are looking for) and retur it's number ''' total = 0 # we start with 0 matchs try: points = [] for venue in response['venues']: for item in venue['categories']: if item['pluralName'] in similar or item['shortName'] in similar or item['name'] in similar: total += 1 try: lat = venue['location']['lat'] lng = venue['location']['lng'] points.append([lat, lng]) except: pass return total, points except: return 0, None # Let's just check the functions created r = get_info(lat_city_center, lng_city_center) print(f'number of coffe shops: {count_similar(r)[0]}') print(f'number of venues in the center of the city: {count_venues(r)[0]}') print(r['venues'][0]['location']['lat']) print(r['venues'][0]) ###Output _____no_output_____ ###Markdown Now, we will search in all the opoints in the map ###Code # the flag bellow is to avoid excess use of the api, loading the data if it already exists new_scrap = False filename = 'foursquare_data.pk' if new_scrap: full_response, points_coffe, points_venue = [], [], [] for lat in lat_range: line = [] for lng in lng_range: r = get_info(lat, lng) similar, pt_temp_cofee = count_similar(r) venues, pt_temp_venue = count_venues(r) if pt_temp_venue: points_venue.extend(pt_temp_venue) if pt_temp_cofee: points_coffe.extend(pt_temp_cofee) line.append((similar, venues)) time.sleep(1) full_response.append(line) outfile = open(filename, 'wb') pickle.dump([full_response, points_coffe, points_venue], outfile) outfile.close() else: infile = open(filename,'rb') full_response, points_coffe, points_venue = pickle.load(infile) infile.close() # let's check what we got: print(type(full_response),len(full_response), full_response[0]) ###Output <class 'list'> 10 [(0, 190), (0, 177), (0, 186), (0, 191), (0, 178), (0, 131), (0, 155), (0, 161), (0, 113), (0, 104)] ###Markdown 3. Data organization and cleanup Let's just see the data format and visualize the results ###Code # to plot a heatmap using folium.plugins.HeatMap, we will generate a data in the expected format venue_matrix = np.zeros([number_x_points*number_y_points, 3]) coffe_matrix = np.zeros([number_x_points*number_y_points, 3]) # flatten the full response for easy of use full_response_flat = list(itertools.chain(*full_response)) # now, populate the matrix with the info from "full_response" list from foursquare i = 0 for lat in lat_range: for lng in lng_range: coffe_matrix[i] = (lat, lng, full_response_flat[i][0]) venue_matrix[i] = (lat, lng, full_response_flat[i][1]) i += 1 # and do some data threatment and formating max_venue = venue_matrix[:,2].max() min_venue = venue_matrix[:,2].min() venue_matrix_normalized = (venue_matrix[:,2] - min_venue)/(max_venue - min_venue) ###Output _____no_output_____ ###Markdown To plot using folium heatmap, we will create a list of points in the expected format: ###Code points_venue = [] for venue in venue_matrix: for i in range(int((venue[2]/10))): points_venue.append([venue[0], venue[1]]) points_coffe = [] for venue in coffe_matrix: for i in range(int((venue[2]))): points_coffe.append([venue[0], venue[1]]) m_venues = folium.Map(location=[lat_city_center, lng_city_center], zoom_start=14) m_venues.add_child(folium.plugins.HeatMap(points_venue, radius=10, min_opacity=0.2, blur=8, control_scale=False)) m_venues m_cofee = folium.Map(location=[lat_city_center, lng_city_center], zoom_start=14) m_cofee.add_child(folium.plugins.HeatMap(points_coffe, radius=70, min_opacity=0.2, blur=35, control_scale=False)) m_cofee ###Output _____no_output_____ ###Markdown if both graphs where not able to render properly (the are some known bugs no mozilla for the heamap generation *), here are the plots as jped images* https://github.com/python-visualization/folium/issues/812 4. Clustering We will use k-means and the Elbow Method to see the ammount of clusters for existing coffe shops and general venues ###Code from sklearn.cluster import KMeans def find_elbow_k(point): sse = [] for k in range(1,10): kmeans = KMeans(n_clusters=k) kmeans.fit(points_coffe) pred_clusters = kmeans.predict(point) centroids = kmeans.cluster_centers_ curr_sse = 0 # calculate square of Euclidean distance of each point from its cluster center and add to current WSS for i in range(len(points_coffe)): curr_center = centroids[pred_clusters[i]] curr_sse += (point[i][0] - curr_center[0]) ** 2 + (point[i][1] - curr_center[1]) ** 2 sse.append(curr_sse) return sse point = points_coffe sse = find_elbow_k(point) plt.plot(sse) ###Output _____no_output_____ ###Markdown We can see that 4 or 5 blobs are a good start for places with coffe shops ###Code kmeans = KMeans(n_clusters=5) kmeans.fit(points_coffe) pred_clusters = kmeans.predict(point) centroids = kmeans.cluster_centers_ m_cofee2 = folium.Map(location=[lat_city_center, lng_city_center], zoom_start=14) m_cofee2.add_child(folium.plugins.HeatMap(points_coffe, radius=70, min_opacity=0.2, blur=35, control_scale=False)) for centroid in centroids: folium.CircleMarker( centroid, radius=10, color='red', fill=True, fill_color='red', fill_opacity=0.7, parse_html=False).add_to(m_cofee2) m_cofee2 point = points_venue sse = find_elbow_k(point) plt.plot(sse) ###Output _____no_output_____ ###Markdown Testes do módulo de verificação de perfis metálicos ###Code from material import * from secao import * from perfil_de_aco import * from perfil_i_laminado import * ###Output _____no_output_____ ###Markdown classe Material() ###Code #Criando um material com as propriedades do aço A572 # E, poisson, fy, fu A572 = Material(20000, 0.3, 34.5, 45) #imprimindo os parâmetros da classe print('modulo de elasticidade: ', A572.E, 'kgf/mm²') print('modulo de cisalhamento: ', A572.G, 'kgf/mm²') print('coeficiente de poisson: ', A572.poisson) print('Tensão de escoamento: ', A572.fy, 'kgf/mm²') print('Tensão de ruptura: ', A572.fu, 'kgf/mm²') ###Output modulo de elasticidade: 20000 kgf/mm² modulo de cisalhamento: 7692.307692307692 kgf/mm² coeficiente de poisson: 0.3 Tensão de escoamento: 34.5 kgf/mm² Tensão de ruptura: 45 kgf/mm² ###Markdown classes Secao(), PerfilDeAco() e PerfilILaminado() ###Code #Criando um instancia da classe PerfilILaminado() com as propriedades do perfil W530X74, com o aço #A572 criado anteriomente # nome do perfil, material P_W530X74 = PerfilILaminado( 'W530X74', A572 ) #imprimindo as propriedades do perfil print('Propriedades geométricas do perfil W530X74') print('-------------------------------------------') print('Altura total(ht): ', P_W530X74.ht, 'mm') print('Altura da alma(hw): ', P_W530X74.hw, 'mm') print('Distância entre as faces internas das mesas(h):', P_W530X74.ht, 'mm') print('Largura da mesa(bf): ', P_W530X74.bf, 'mm') print('Espessura da mesa(tf): ', P_W530X74.tf, 'mm') print('Espessura da alma(tw):', P_W530X74.tw, 'mm') print('Área Trasnversal(A):', P_W530X74.A, 'mm²') print('Momento de inécicia em x (Ix):', P_W530X74.Ix, 'mm4') print('Momento de inécicia em y (Iy):', P_W530X74.Iy, 'mm4') print('Constante de torção (J):', P_W530X74.J,'mm4') print('Raio de giração em x(rx): ', P_W530X74.rx, 'mm') print('Raio de giração em y(ry): ', P_W530X74.ry, 'mm') print('Módulo de resitência elástico em x (Wx): ', P_W530X74.Wx, 'mm³') print('Módulo de resitência elástico em y (Wy): ', P_W530X74.Wy, 'mm³') print('Módulo de resitência plástico em x (Zx): ', P_W530X74.Zx, 'mm³') print('Módulo de resitência elástico em y (Zy): ', P_W530X74.Zy, 'mm³') print('Constante de empenamento(Cw):', P_W530X74.Cw, 'mm6') print('Cordenada X do centro de cisalhamento em relação ao Xcg (xo):', P_W530X74.xo, 'mm') print('Cordenada Y do centro de cisalhamento em relação ao Ycg (yo):', P_W530X74.yo, 'mm') print('Raio de giração em relação ao centro de corte (ro):', P_W530X74.ro, 'mm') ###Output Propriedades geométricas do perfil W530X74 ------------------------------------------- Altura total(ht): 528.0 mm Altura da alma(hw): 500.8 mm Distância entre as faces internas das mesas(h): 528.0 mm Largura da mesa(bf): 166.0 mm Espessura da mesa(tf): 13.6 mm Espessura da alma(tw): 9.65 mm Área Trasnversal(A): 9480.0 mm² Momento de inécicia em x (Ix): 410000000.0 mm4 Momento de inécicia em y (Iy): 10400000.0 mm4 Constante de torção (J): 475000.0 mm4 Raio de giração em x(rx): 207.96380730232684 mm Raio de giração em y(ry): 33.121690981924665 mm Módulo de resitência elástico em x (Wx): 1550000.0 mm³ Módulo de resitência elástico em y (Wy): 125000.0 mm³ Módulo de resitência plástico em x (Zx): 1800000.0 mm³ Módulo de resitência elástico em y (Zy): 200000.0 mm³ Constante de empenamento(Cw): 690000000000.0 mm6 Cordenada X do centro de cisalhamento em relação ao Xcg (xo): 0 mm Cordenada Y do centro de cisalhamento em relação ao Ycg (yo): 0 mm Raio de giração em relação ao centro de corte (ro): 210.58487970692823 mm ###Markdown Algumas propriedades mecânicas- considerando uma barra com comprimentos de flambagem * klx = 3000 mm * kly = 3000 mm * klz = 3000 mm ###Code #Comprimentos de flambagem klx = 3000 kly = 3000 klz = 3000 print("Cargas criticas de flambagem") print("----------------------------") print('Nex:', P_W530X74.Nex(klx), 'kgf') print('Ney:', P_W530X74.Ney(kly), 'kgf') print('Nez', P_W530X74.Nez(klz), 'kgf') print('Ne:', P_W530X74.Ne(klx, kly, klz), 'kgf') #Indice de esbeltez print('Indices de esbeltez da barra') print('----------------------------') print('Indice de esbeltez em relação ao giro no eixo X:', P_W530X74.indice_esbeltez_X(100)) print('Indice de esbeltez em relação ao giro no eixo Y:', P_W530X74.indice_esbeltez_Y(100)) ###Output Indices de esbeltez da barra ---------------------------- Indice de esbeltez em relação ao giro no eixo X: 3.0191695241215943 Indice de esbeltez em relação ao giro no eixo Y: 0.48085290078684345 ###Markdown Métodos de verificação da capacidade resistente Tração - escoamento da seção bruta ###Code resb = P_W530X74.resist_esc_secao_bruta_NBR8800() print('Resistência ao escoamento da seção bruta =', resb, 'kgf') ###Output Resistência ao escoamento da seção bruta = 297327.2727272727 kgf ###Markdown Compressão- considerando os comprimentos de flambagem indicados anteriormente ###Code print('Ncrd = ', P_W530X74.Ncrd_NBR8800(klx, kly, klz), 'kgf') print('\n Parametros de cálculo:') print('-------------------------') ier = P_W530X74.ind_esbeltez_reduzido(klx, kly, klz) frc = P_W530X74.fator_reducao_compressao(ier) print('Indice de esbeltez reduzido', ier ) print('Fator Chi:', frc) print('Fator Q:', P_W530X74.fator_Q(frc)) ###Output Ncrd = 131445.0336998553 kgf Parametros de cálculo: ------------------------- Indice de esbeltez reduzido 1.3964851803036198 Fator Chi: 0.4420887209375675 Fator Q: 1.0 ###Markdown Cortante Em Y - maior inércia ###Code print('Força reistênte de corte') print('-----------------------') print('Vrd_y: ', P_W530X74.Vrdy_NBR8800(), 'kgf') print('\n Parametros de cálculo:') print('-------------------------') print('Awy: ', P_W530X74.Awy, ' mm²') print('Vpl: ', P_W530X74.Vpl(P_W530X74.Awy), ' kgf') print('kv: ', P_W530X74.kv_Vrdy()) print('Lambda_p: ', P_W530X74.par_esbeltez_limites_Vrd(P_W530X74.kv_Vrdy())[0]) print('Lambda_r: ', P_W530X74.par_esbeltez_limites_Vrd(P_W530X74.kv_Vrdy())[1]) ###Output Força reistênte de corte ----------------------- Vrd_y: 95882.4 kgf Parametros de cálculo: ------------------------- Awy: 5095.2 mm² Vpl: 105470.64 kgf kv: 5 Lambda_p: 59.222009226398214 Lambda_r: 73.75832058196869 ###Markdown Em X - menor inércia ###Code print('Força reistênte de corte') print('-----------------------') print('Vrd_x: ', P_W530X74.Vrdx_NBR8800(), 'kgf') print('\n Parametros de cálculo:') print('-------------------------') print('Aw: ', P_W530X74.Awx, ' mm²') print('Vpl: ', P_W530X74.Vpl(P_W530X74.Awx), ' kgf') print('kv: ', P_W530X74.kv_Vrdx()) print('Lambda_p: ', P_W530X74.par_esbeltez_limites_Vrd(P_W530X74.kv_Vrdx())[0]) print('Lambda_r: ', P_W530X74.par_esbeltez_limites_Vrd(P_W530X74.kv_Vrdx())[1]) ###Output Força reistênte de corte ----------------------- Vrd_x: 84967.85454545454 kgf Parametros de cálculo: ------------------------- Aw: 4515.2 mm² Vpl: 93464.64 kgf kv: 1.2 Lambda_p: 29.01274082941463 Lambda_r: 36.13404994208913 ###Markdown Momento fletor- considerando a barra contida em todo seu comprimento- coeficiente Cb = 1 Em X - eixo de maior inércia ###Code print('Momento resistente de cálculo') print('-----------------------------') print('Mrd_x:', P_W530X74.Mrdx_NBR8800(0), 'kgf.mm') print('\n Parametros de cálculo:') print('-------------------------\n') print('Mpl: ', P_W530X74.Mplx, 'kgf.mm \n') print('ELU - Flambagem lateral com torção') print('-----------------------------------') print('Lambda_p: ', P_W530X74.par_esbeltez_limite_Mrdx_FLT()[0]) print('Lambda_r: ', P_W530X74.par_esbeltez_limite_Mrdx_FLT()[1]) print('Mr:', P_W530X74.Mrx_FLT(), 'kgf.mm') print('Mcr:', P_W530X74.Mcrx_FLT(1, 1), 'kgf.mm') print('Mn:', P_W530X74.Mnx_FLT(1, 1), 'kgf.mm') print('\n') print('ELU - Flambagem local da mesa') print('-----------------------------------') print('Lambda_p: ', P_W530X74.par_esbeltez_limite_Mrdx_FLM()[0]) print('Lambda_r: ', P_W530X74.par_esbeltez_limite_Mrdx_FLM()[1]) print('Mr:', P_W530X74.Mrx_FLM(), 'kgf.mm') print('Mcr:', P_W530X74.Mcrx_FLM(), 'kgf.mm') print('Mn:', P_W530X74.Mnx_FLM(), 'kgf.mm') print('\n') print('ELU - Flambagem local da alma') print('-----------------------------------') print('Lambda_p: ', P_W530X74.par_esbeltez_limite_Mrdx_FLA()[0]) print('Lambda_r: ', P_W530X74.par_esbeltez_limite_Mrdx_FLA()[1]) print('Mr:', P_W530X74.Mrx_FLA(), 'kgf.mm') print('Mn:', P_W530X74.Mnx_FLA(), 'kgf.mm') print('\n') ###Output Momento resistente de cálculo ----------------------------- Mrd_x: 56454545.45454545 kgf.mm Parametros de cálculo: ------------------------- Mpl: 62100000.0 kgf.mm ELU - Flambagem lateral com torção ----------------------------------- Lambda_p: 42.37582028619076 Lambda_r: 124.85369974978447 Mr: 37432500.0 kgf.mm Mcr: 528775058423461.1 kgf.mm Mn: 62100000.0 kgf.mm ELU - Flambagem local da mesa ----------------------------------- Lambda_p: 9.14932483451846 Lambda_r: 23.885510217361595 Mr: 37432500.0 kgf.mm Mcr: 574291537.2332702 kgf.mm Mn: 62100000.0 kgf.mm ELU - Flambagem local da alma ----------------------------------- Lambda_p: 90.53016152049844 Lambda_r: 137.2398725177769 Mr: 53475000.0 kgf.mm Mn: 62100000.0 kgf.mm ###Markdown Em Y - eixo de menor inércia ###Code print('Momento resistente de cálculo') print('-----------------------------') print('Mrd_y:', P_W530X74.Mrdy_NBR8800(0), 'kgf.mm') print('\n Parametros de cálculo:') print('-------------------------\n') print('Mpl: ', P_W530X74.Mply, 'kgf.mm \n') print('ELU - Flambagem local da mesa') print('-----------------------------------') print('Lambda_p: ', P_W530X74.par_esbeltez_limite_Mrdy_FLM()[0]) print('Lambda_r: ', P_W530X74.par_esbeltez_limite_Mrdy_FLM()[1]) print('Mr:', P_W530X74.Mry_FLM(), 'kgf.mm') print('Mcr:', P_W530X74.Mcry_FLM(), 'kgf.mm') print('Mn:', P_W530X74.Mny_FLM(), 'kgf.mm') print('\n') ###Output Momento resistente de cálculo ----------------------------- Mrd_y: 6272727.2727272725 kgf.mm Parametros de cálculo: ------------------------- Mpl: 6900000.0 kgf.mm ELU - Flambagem local da mesa ----------------------------------- Lambda_p: 9.14932483451846 Lambda_r: 23.885510217361595 Mr: 3018750.0 kgf.mm Mcr: 46313833.647844374 kgf.mm Mn: 6900000.0 kgf.mm

arl-python/examples/arl/imaging-mfs.ipynb

###Markdown MFS demonstration This script makes a fake data set and then deconvolves it. Finally the full and residual visibility are plotted. ###Code %matplotlib inline import os import sys import multiprocessing sys.path.append(os.path.join('..', '..')) results_dir = './results' os.makedirs(results_dir, exist_ok=True) from matplotlib import pylab pylab.rcParams['figure.figsize'] = (10.0, 10.0) pylab.rcParams['image.cmap'] = 'rainbow' import numpy from astropy.coordinates import SkyCoord from astropy import units as u from astropy import constants as const from astropy.wcs.utils import pixel_to_skycoord from matplotlib import pyplot as plt from arl.data.polarisation import PolarisationFrame from arl.visibility.base import create_visibility from arl.skycomponent.operations import create_skycomponent from arl.image.operations import show_image, export_image_to_fits, smooth_image, \ calculate_image_frequency_moments, calculate_image_from_frequency_moments from arl.image.deconvolution import deconvolve_cube, restore_cube from arl.image.iterators import image_raster_iter from arl.image.solvers import solve_image from arl.visibility.iterators import vis_timeslice_iter from arl.util.testing_support import create_named_configuration, \ create_low_test_image_from_gleam, create_low_test_beam from arl.imaging import * from arl.imaging.weighting import weight_visibility import logging log = logging.getLogger() log.setLevel(logging.DEBUG) log.addHandler(logging.StreamHandler(sys.stdout)) ###Output _____no_output_____ ###Markdown Construct LOW configuration We create the visibility. This just makes the uvw, time, antenna1, antenna2, weight columns in a table ###Code config = 'full' if config == 'full': low = create_named_configuration('LOWBD2') b = 8e4 cellsize = 0.00001 npixel=5 * 2048 padding = 1 invert = invert_2d predict = predict_2d else: low = create_named_configuration('LOWBD2-CORE') b = 4e3 cellsize = 0.001 npixel=512 padding = 2 invert = invert_2d predict = predict_2d oversampling = 32 nchan = 7 frequency = numpy.linspace(0.8e8, 1.2e8, nchan) centre_frequency = numpy.array([numpy.average(frequency)]) channel_bandwidth=numpy.array(nchan * [frequency[1]-frequency[0]]) total_bandwidth = numpy.array([numpy.sum(channel_bandwidth)]) times = numpy.linspace(-3, +3, 5) * numpy.pi / 12.0 log.info('Observing times %s' % (times)) log.info("Observing frequencies %s Hz" % (frequency)) log.info("Channel bandwidths %s Hz" % (channel_bandwidth)) log.info("Centre frequency %s Hz" % (centre_frequency)) log.info("Cellsize = %.6f radians" % (cellsize)) phasecentre = SkyCoord(ra=+15.0 * u.deg, dec=-35.0 * u.deg, frame='icrs', equinox='J2000') vt = create_visibility(low, times, frequency, channel_bandwidth=channel_bandwidth, weight=1.0, phasecentre=phasecentre, polarisation_frame=PolarisationFrame('stokesI')) ###Output create_visibility: 4578560 rows, 0.478 GB create_visibility: 4578560 rows, 0.478 GB ###Markdown Plot the synthesized uv coverage ###Code plt.clf() plt.plot(vt.uvw[:,0], vt.uvw[:,1], '.', color='b') plt.plot(-vt.uvw[:,0], -vt.uvw[:,1], '.', color='b') plt.xlabel("U (wavelengths)") plt.ylabel("V (wavelengths)") plt.show() ###Output _____no_output_____ ###Markdown Make a test image ###Code model_centrechannel = create_low_test_image_from_gleam(npixel=npixel, frequency=centre_frequency, channel_bandwidth=total_bandwidth, cellsize=cellsize, phasecentre=phasecentre) export_image_to_fits(model_centrechannel, '%s/imaging-mfs-model_centre_channel.fits' % (results_dir)) model_multichannel = create_low_test_image_from_gleam(npixel=npixel, frequency=frequency, channel_bandwidth=channel_bandwidth, cellsize=cellsize, phasecentre=phasecentre) import time start = time.time() beam=create_low_test_beam(model_multichannel) model_multichannel.data*=beam.data print("Model * beam has %.3f Jy" % (numpy.sum(model_multichannel.data[0,0,:,:]))) cmodel = smooth_image(model_multichannel) show_image(cmodel) plt.title("Smoothed model image") plt.show() export_image_to_fits(cmodel, '%s/imaging-mfs-cmodel.fits' % (results_dir)) beam = None cmodel = None stop = time.time() print('beam time:', stop - start) export_image_to_fits(model_multichannel, '%s/imaging-mfs-multi_channel.fits' % (results_dir)) moment_cube = calculate_image_frequency_moments(model_multichannel,nmoments=3) export_image_to_fits(moment_cube, '%s/imaging-mfs-moment_cube.fits' % (results_dir)) reconstructed_cube = calculate_image_from_frequency_moments(model_multichannel, moment_cube) export_image_to_fits(reconstructed_cube, '%s/imaging-mfs-reconstructed_cube.fits' % (results_dir)) vt.data['vis'] *= 0.0 vt = predict(vt, model_multichannel) # To check that we got the prediction right, plot the amplitude of the visibility. uvdist=numpy.sqrt(vt.data['uvw'][:,0]**2+vt.data['uvw'][:,1]**2) plt.clf() plt.plot(uvdist, numpy.abs(vt.data['vis']), '.') plt.xlabel('uvdist') plt.ylabel('Amp Visibility') plt.show() ###Output _____no_output_____ ###Markdown Weight the data ###Code vt, density, densitygrid = weight_visibility(vt, model_centrechannel) plt.clf() plt.semilogy(uvdist, density, '.') plt.xlabel('uvdist') plt.ylabel('Sample density') plt.show() density = None densitygrid = None ###Output _____no_output_____ ###Markdown Make the dirty image and point spread function ###Code dirty, sumwt = invert(vt, model_multichannel, padding=1) show_image(dirty) psf, sumwt = invert(vt, model_multichannel, dopsf=True, padding=1) print("Max, min in dirty image = %.6f, %.6f, sumwt = %s" % (dirty.data.max(), dirty.data.min(), sumwt)) print("Max, min in PSF = %.6f, %.6f, sumwt = %s" % (psf.data.max(), psf.data.min(), sumwt)) export_image_to_fits(dirty, '%s/imaging-mfs-dirty.fits' % (results_dir)) export_image_to_fits(psf, '%s/imaging-mfs-psf.fits' % (results_dir)) comp, residual = deconvolve_cube(dirty, psf, niter=1000, gain=0.7, algorithm='msmfsclean', scales=[0, 3, 10, 30], threshold=0.01, fractional_threshold=0.001, nmoments=3) export_image_to_fits(comp, '%s/imaging-mfs-comp.fits' % (results_dir)) clean = restore_cube(model=comp, psf=psf, residual=residual) export_image_to_fits(residual, '%s/imaging-mfs-residual.fits' % (results_dir)) export_image_to_fits(clean, '%s/imaging-mfs-clean.fits' % (results_dir)) show_image(clean) plt.show() ###Output _____no_output_____ ###Markdown Predict the visibility of the model ###Code vtmodel = create_visibility(low, times, frequency, channel_bandwidth=channel_bandwidth, weight=1.0, phasecentre=phasecentre, polarisation_frame=PolarisationFrame('stokesI')) vtmodel=predict(vtmodel, comp) ###Output _____no_output_____ ###Markdown Now we will plot the original visibility and the residual visibility. ###Code uvdist=numpy.sqrt(vt.data['uvw'][:,0]**2+vt.data['uvw'][:,1]**2) plt.clf() plt.plot(uvdist, numpy.abs(vt.data['vis']), '.', color='b', label='Original') plt.plot(uvdist, numpy.abs(vt.data['vis']-vtmodel.data['vis']), '.', color='r', label='Residual') plt.xlabel('uvdist') plt.ylabel('Amp Visibility') plt.legend() plt.show() ###Output _____no_output_____

2-Working-With-Data/07-python/notebook-covidspread.ipynb

###Markdown Estimation of COVID-19 Pandemic Loading Data We will use data on COVID-19 infected individuals, provided by the [Center for Systems Science and Engineering](https://systems.jhu.edu/) (CSSE) at [Johns Hopkins University](https://jhu.edu/). Dataset is available in [this GitHub Repository](https://github.com/CSSEGISandData/COVID-19). ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = (10,3) # make figures larger ###Output _____no_output_____ ###Markdown We can load the most recent data directly from GitHub using `pd.read_csv`. If for some reason the data is not available, you can always use the copy available locally in the `data` folder - just uncomment the line below that defines `base_url`: ###Code base_url = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/" # loading from Internet # base_url = "../../data/COVID/" # loading from disk infected_dataset_url = base_url + "time_series_covid19_confirmed_global.csv" recovered_dataset_url = base_url + "time_series_covid19_recovered_global.csv" deaths_dataset_url = base_url + "time_series_covid19_deaths_global.csv" countries_dataset_url = base_url + "../UID_ISO_FIPS_LookUp_Table.csv" ###Output _____no_output_____ ###Markdown Let's now load the data for infected individuals and see how the data looks like: ###Code infected = pd.read_csv(infected_dataset_url) infected.head() ###Output _____no_output_____ ###Markdown We can see that each row of the table defines the number of infected individuals for each country and/or province, and columns correspond to dates. Similar tables can be loaded for other data, such as number of recovered and number of deaths. ###Code recovered = pd.read_csv(recovered_dataset_url) deaths = pd.read_csv(deaths_dataset_url) ###Output _____no_output_____ ###Markdown Making Sense of the Data From the table above the role of province column is not clear. Let's see the different values that are present in `Province/State` column: ###Code infected['Province/State'].value_counts() ###Output _____no_output_____ ###Markdown From the names we can deduce that countries like Australia and China have more detailed breakdown by provinces. Let's look for information on China to see the example: ###Code infected[infected['Country/Region']=='China'] ###Output _____no_output_____ ###Markdown Pre-processing the Data We are not interested in breaking countries down to further territories, thus we would first get rid of this breakdown and add information on all territories together, to get info for the whole country. This can be done using `groupby`: ###Code infected = infected.groupby('Country/Region').sum() recovered = recovered.groupby('Country/Region').sum() deaths = deaths.groupby('Country/Region').sum() infected.head() ###Output _____no_output_____ ###Markdown You can see that due to using `groupby` all DataFrames are now indexed by Country/Region. We can thus access the data for a specific country by using `.loc`:| ###Code infected.loc['US'][2:].plot() recovered.loc['US'][2:].plot() plt.show() ###Output _____no_output_____ ###Markdown > **Note** how we use `[2:]` to remove first two elements of a sequence that contain geolocation of a country. We can also drop those two columns altogether: ###Code infected.drop(columns=['Lat','Long'],inplace=True) recovered.drop(columns=['Lat','Long'],inplace=True) deaths.drop(columns=['Lat','Long'],inplace=True) ###Output _____no_output_____ ###Markdown Investigating the Data Let's now switch to investigating a specific country. Let's create a frame that contains the data on infections indexed by date: ###Code def mkframe(country): df = pd.DataFrame({ 'infected' : infected.loc[country] , 'recovered' : recovered.loc[country], 'deaths' : deaths.loc[country]}) df.index = pd.to_datetime(df.index) return df df = mkframe('US') df df.plot() plt.show() ###Output _____no_output_____ ###Markdown Now let's compute the number of new infected people each day. This will allow us to see the speed at which pandemic progresses. The easiest day to do it is to use `diff`: ###Code df['ninfected'] = df['infected'].diff() df['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown We can see high fluctuations in data. Let's look closer at one of the months: ###Code df[(df.index.year==2020) & (df.index.month==7)]['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown It clearly looks like there are weekly fluctuations in data. Because we want to be able to see the trends, it makes sense to smooth out the curve by computing running average (i.e. for each day we will compute the average value of the previous several days): ###Code df['ninfav'] = df['ninfected'].rolling(window=7).mean() df['ninfav'].plot() plt.show() ###Output _____no_output_____ ###Markdown In order to be able to compare several countries, we might want to take the country's population into account, and compare the percentage of infected individuals with respect to country's population. In order to get country's population, let's load the dataset of countries: ###Code countries = pd.read_csv(countries_dataset_url) countries ###Output _____no_output_____ ###Markdown Because this dataset contains information on both countries and provinces, to get the population of the whole country we need to be a little bit clever: ###Code countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()] pop = countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()]['Population'].iloc[0] df['pinfected'] = df['infected']*100 / pop df['pinfected'].plot(figsize=(10,3)) plt.show() ###Output _____no_output_____ ###Markdown Computing $R_t$ To see how infectuous is the disease, we look at the **basic reproduction number** $R_0$, which indicated the number of people that an infected person would further infect. When $R_0$ is more than 1, the epidemic is likely to spread. $R_0$ is a property of the disease itself, and does not take into account some protective measures that people may take to slow down the pandemic. During the pandemic progression, we can estimate the reproduction number $R_t$ at any given time $t$. It has been shown that this number can be roughly estimated by taking a window of 8 days, and computing $$R_t=\frac{I_{t-7}+I_{t-6}+I_{t-5}+I_{t-4}}{I_{t-3}+I_{t-2}+I_{t-1}+I_t}$$ where $I_t$ is the number of newly infected individuals on day $t$. Let's compute $R_t$ for our pandemic data. To do this, we will take a rolling window of 8 `ninfected` values, and apply the function to compute the ratio above: ###Code df['Rt'] = df['ninfected'].rolling(8).apply(lambda x: x[4:].sum()/x[:4].sum()) df['Rt'].plot() plt.show() ###Output _____no_output_____ ###Markdown You can see that there are some gaps in the graph. Those can be caused by either `NaN`, if `inf` values being present in the dataset. `inf` may be caused by division by 0, and `NaN` can indicate missing data, or no data available to compute the result (like in the very beginning of our frame, where rolling window of width 8 is not yet available). To make the graph nicer, we need to fill those values using `replace` and `fillna` function. Let's further look at the beginning of the pandemic. We will also limit the y-axis values to show only values below 6, in order to see better, and draw horizontal line at 1. ###Code ax = df[df.index<"2020-05-01"]['Rt'].replace(np.inf,np.nan).fillna(method='pad').plot(figsize=(10,3)) ax.set_ylim([0,6]) ax.axhline(1,linestyle='--',color='red') plt.show() ###Output _____no_output_____ ###Markdown Another interesting indicator of the pandemic is the **derivative**, or **daily difference** in new cases. It allows us to see clearly when pandemic is increasing or declining. ###Code df['ninfected'].diff().plot() plt.show() ###Output _____no_output_____ ###Markdown Given the fact that there are a lot of fluctuations in data caused by reporting, it makes sense to smooth the curve by running rolling average to get the overall picture. Let's again focus on the first months of the pandemic: ###Code ax=df[df.index<"2020-06-01"]['ninfected'].diff().rolling(7).mean().plot() ax.axhline(0,linestyle='-.',color='red') plt.show() ###Output _____no_output_____ ###Markdown Estimation of COVID-19 Pandemic Loading DataWe will use data on COVID-19 infected individuals, provided by the [Center for Systems Science and Engineering](https://systems.jhu.edu/) (CSSE) at [Johns Hopkins University](https://jhu.edu/). Dataset is available in [this GitHub Repository](https://github.com/CSSEGISandData/COVID-19). ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = (10,3) # make figures larger ###Output _____no_output_____ ###Markdown We can load the most recent data directly from GitHub using `pd.read_csv`. If for some reason the data is not available, you can always use the copy available locally in the `data` folder - just uncomment the line below that defines `base_url`: ###Code base_url = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/" # loading from Internet # base_url = "../../data/COVID/" # loading from disk infected_dataset_url = base_url + "time_series_covid19_confirmed_global.csv" recovered_dataset_url = base_url + "time_series_covid19_recovered_global.csv" deaths_dataset_url = base_url + "time_series_covid19_deaths_global.csv" countries_dataset_url = base_url + "../UID_ISO_FIPS_LookUp_Table.csv" ###Output _____no_output_____ ###Markdown Let's now load the data for infected individuals and see how the data looks like: ###Code infected = pd.read_csv(infected_dataset_url) infected.head() ###Output _____no_output_____ ###Markdown We can see that each row of the table defines the number of infected individuals for each country and/or province, and columns correspond to dates. Similar tables can be loaded for other data, such as number of recovered and number of deaths. ###Code recovered = pd.read_csv(recovered_dataset_url) deaths = pd.read_csv(deaths_dataset_url) ###Output _____no_output_____ ###Markdown Making Sense of the DataFrom the table above the role of province column is not clear. Let's see the different values that are present in `Province/State` column: ###Code infected['Province/State'].value_counts() ###Output _____no_output_____ ###Markdown From the names we can deduce that countries like Australia and China have more detailed breakdown by provinces. Let's look for information on China to see the example: ###Code infected[infected['Country/Region']=='China'] ###Output _____no_output_____ ###Markdown Pre-processing the Data We are not interested in breaking countries down to further territories, thus we would first get rid of this breakdown and add information on all territories together, to get info for the whole country. This can be done using `groupby`: ###Code infected = infected.groupby('Country/Region').sum() recovered = recovered.groupby('Country/Region').sum() deaths = deaths.groupby('Country/Region').sum() infected.head() ###Output _____no_output_____ ###Markdown You can see that due to using `groupby` all DataFrames are now indexed by Country/Region. We can thus access the data for a specific country by using `.loc`:| ###Code infected.loc['US'][2:].plot() recovered.loc['US'][2:].plot() plt.show() ###Output _____no_output_____ ###Markdown > **Note** how we use `[2:]` to remove first two elements of a sequence that contain geolocation of a country. We can also drop those two columns altogether: ###Code infected.drop(columns=['Lat','Long'],inplace=True) recovered.drop(columns=['Lat','Long'],inplace=True) deaths.drop(columns=['Lat','Long'],inplace=True) ###Output _____no_output_____ ###Markdown Investigating the DataLet's now switch to investigating a specific country. Let's create a frame that contains the data on infections indexed by date: ###Code def mkframe(country): df = pd.DataFrame({ 'infected' : infected.loc[country] , 'recovered' : recovered.loc[country], 'deaths' : deaths.loc[country]}) df.index = pd.to_datetime(df.index) return df df = mkframe('US') df df.plot() plt.show() ###Output _____no_output_____ ###Markdown Now let's compute the number of new infected people each day. This will allow us to see the speed at which pandemic progresses. The easiest day to do it is to use `diff`: ###Code df['ninfected'] = df['infected'].diff() df['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown We can see high fluctuations in data. Let's look closer at one of the months: ###Code df[(df.index.year==2020) & (df.index.month==7)]['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown It clearly looks like there are weekly fluctuations in data. Because we want to be able to see the trends, it makes sense to smooth out the curve by computing running average (i.e. for each day we will compute the average value of the previous several days): ###Code df['ninfav'] = df['ninfected'].rolling(window=7).mean() df['ninfav'].plot() plt.show() ###Output _____no_output_____ ###Markdown In order to be able to compare several countries, we might want to take the country's population into account, and compare the percentage of infected individuals with respect to country's population. In order to get country's population, let's load the dataset of countries: ###Code countries = pd.read_csv(countries_dataset_url) countries ###Output _____no_output_____ ###Markdown Because this dataset contains information on both countries and provinces, to get the population of the whole country we need to be a little bit clever: ###Code countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()] pop = countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()]['Population'].iloc[0] df['pinfected'] = df['infected']*100 / pop df['pinfected'].plot(figsize=(10,3)) plt.show() ###Output _____no_output_____ ###Markdown Computing $R_t$To see how infectious is the disease, we look at the **basic reproduction number** $R_0$, which indicated the number of people that an infected person would further infect. When $R_0$ is more than 1, the epidemic is likely to spread.$R_0$ is a property of the disease itself, and does not take into account some protective measures that people may take to slow down the pandemic. During the pandemic progression, we can estimate the reproduction number $R_t$ at any given time $t$. It has been shown that this number can be roughly estimated by taking a window of 8 days, and computing $$R_t=\frac{I_{t-7}+I_{t-6}+I_{t-5}+I_{t-4}}{I_{t-3}+I_{t-2}+I_{t-1}+I_t}$$where $I_t$ is the number of newly infected individuals on day $t$.Let's compute $R_t$ for our pandemic data. To do this, we will take a rolling window of 8 `ninfected` values, and apply the function to compute the ratio above: ###Code df['Rt'] = df['ninfected'].rolling(8).apply(lambda x: x[4:].sum()/x[:4].sum()) df['Rt'].plot() plt.show() ###Output _____no_output_____ ###Markdown You can see that there are some gaps in the graph. Those can be caused by either `NaN`, if `inf` values being present in the dataset. `inf` may be caused by division by 0, and `NaN` can indicate missing data, or no data available to compute the result (like in the very beginning of our frame, where rolling window of width 8 is not yet available). To make the graph nicer, we need to fill those values using `replace` and `fillna` function.Let's further look at the beginning of the pandemic. We will also limit the y-axis values to show only values below 6, in order to see better, and draw horizontal line at 1. ###Code ax = df[df.index<"2020-05-01"]['Rt'].replace(np.inf,np.nan).fillna(method='pad').plot(figsize=(10,3)) ax.set_ylim([0,6]) ax.axhline(1,linestyle='--',color='red') plt.show() ###Output _____no_output_____ ###Markdown Another interesting indicator of the pandemic is the **derivative**, or **daily difference** in new cases. It allows us to see clearly when pandemic is increasing or declining. ###Code df['ninfected'].diff().plot() plt.show() ###Output _____no_output_____ ###Markdown Given the fact that there are a lot of fluctuations in data caused by reporting, it makes sense to smooth the curve by running rolling average to get the overall picture. Let's again focus on the first months of the pandemic: ###Code ax=df[df.index<"2020-06-01"]['ninfected'].diff().rolling(7).mean().plot() ax.axhline(0,linestyle='-.',color='red') plt.show() ###Output _____no_output_____ ###Markdown Estimation of COVID-19 Pandemic Loading DataWe will use data on COVID-19 infected individuals, provided by the [Center for Systems Science and Engineering](https://systems.jhu.edu/) (CSSE) at [Johns Hopkins University](https://jhu.edu/). Dataset is available in [this GitHub Repository](https://github.com/CSSEGISandData/COVID-19). ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = (10,3) # make figures larger ###Output _____no_output_____ ###Markdown We can load the most recent data directly from GitHub using `pd.read_csv`. If for some reason the data is not available, you can always use the copy available locally in the `data` folder - just uncomment the line below that defines `base_url`: ###Code # base_url = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/" # loading from Internet base_url = "../../data/COVID/" # loading from disk infected_dataset_url = base_url + "time_series_covid19_confirmed_global.csv" recovered_dataset_url = base_url + "time_series_covid19_recovered_global.csv" deaths_dataset_url = base_url + "time_series_covid19_deaths_global.csv" countries_dataset_url = base_url + "../UID_ISO_FIPS_LookUp_Table.csv" ###Output _____no_output_____ ###Markdown Let's now load the data for infected individuals and see how the data looks like: ###Code infected = pd.read_csv(infected_dataset_url) infected.head() ###Output _____no_output_____ ###Markdown We can see that each row of the table defines the number of infected individuals for each country and/or province, and columns correspond to dates. Similar tables can be loaded for other data, such as number of recovered and number of deaths. ###Code recovered = pd.read_csv(recovered_dataset_url) deaths = pd.read_csv(deaths_dataset_url) ###Output _____no_output_____ ###Markdown Making Sense of the DataFrom the table above the role of province column is not clear. Let's see the different values that are present in `Province/State` column: ###Code infected['Province/State'].value_counts() ###Output _____no_output_____ ###Markdown From the names we can deduce that countries like Australia and China have more detailed breakdown by provinces. Let's look for information on China to see the example: ###Code infected[infected['Country/Region']=='China'] ###Output _____no_output_____ ###Markdown Pre-processing the Data We are not interested in breaking countries down to further territories, thus we would first get rid of this breakdown and add information on all territories together, to get info for the whole country. This can be done using `groupby`: ###Code infected = infected.groupby('Country/Region').sum() recovered = recovered.groupby('Country/Region').sum() deaths = deaths.groupby('Country/Region').sum() infected.head() ###Output _____no_output_____ ###Markdown You can see that due to using `groupby` all DataFrames are now indexed by Country/Region. We can thus access the data for a specific country by using `.loc`:| ###Code infected.loc['US'][2:].plot() recovered.loc['US'][2:].plot() plt.show() ###Output _____no_output_____ ###Markdown > **Note** how we use `[2:]` to remove first two elements of a sequence that contain geolocation of a country. We can also drop those two columns altogether: ###Code infected.drop(columns=['Lat','Long'],inplace=True) recovered.drop(columns=['Lat','Long'],inplace=True) deaths.drop(columns=['Lat','Long'],inplace=True) ###Output _____no_output_____ ###Markdown Investigating the DataLet's now switch to investigating a specific country. Let's create a frame that contains the data on infections indexed by date: ###Code def mkframe(country): df = pd.DataFrame({ 'infected' : infected.loc[country] , 'recovered' : recovered.loc[country], 'deaths' : deaths.loc[country]}) df.index = pd.to_datetime(df.index) return df df = mkframe('US') df df.plot() plt.show() ###Output _____no_output_____ ###Markdown Now let's compute the number of new infected people each day. This will allow us to see the speed at which pandemic progresses. The easiest day to do it is to use `diff`: ###Code df['ninfected'] = df['infected'].diff() df['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown We can see high fluctuations in data. Let's look closer at one of the months: ###Code df[(df.index.year==2020) & (df.index.month==7)]['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown It clearly looks like there are weekly fluctuations in data. Because we want to be able to see the trends, it makes sense to smooth out the curve by computing running average (i.e. for each day we will compute the average value of the previous several days): ###Code df['ninfav'] = df['ninfected'].rolling(window=7).mean() df['ninfav'].plot() plt.show() ###Output _____no_output_____ ###Markdown In order to be able to compare several countries, we might want to take the country's population into account, and compare the percentage of infected individuals with respect to country's population. In order to get country's population, let's load the dataset of countries: ###Code countries = pd.read_csv(countries_dataset_url) countries ###Output _____no_output_____ ###Markdown Because this dataset contains information on both countries and provinces, to get the population of the whole country we need to be a little bit clever: ###Code countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()] pop = countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()]['Population'].iloc[0] df['pinfected'] = df['infected']*100 / pop df['pinfected'].plot(figsize=(10,3)) plt.show() ###Output _____no_output_____ ###Markdown Computing $R_t$To see how infectuous is the disease, we look at the **basic repoduction number** $R_0$, which indicated the number of people that an infected person would further infect. When $R_0$ is more than 1, the epidemic is likely to spread.$R_0$ is a property of the disease itself, and does not take into account some protective measures that people may take to slow down the pandemic. During the pandemic progression, we can estimate the reproduction number $R_t$ at any given time $t$. It has been shown that this number can be roughly estimated by taking a window of 8 days, and computing $$R_t=\frac{I_{t-7}+I_{t-6}+I_{t-5}+I_{t-4}}{I_{t-3}+I_{t-2}+I_{t-1}+I_t}$$where $I_t$ is the number of newly infected individuals on day $t$.Let's compute $R_t$ for our pandemic data. To do this, we will take a rolling window of 8 `ninfected` values, and apply the function to compute the ratio above: ###Code df['Rt'] = df['ninfected'].rolling(8).apply(lambda x: x[4:].sum()/x[:4].sum()) df['Rt'].plot() plt.show() ###Output _____no_output_____ ###Markdown You can see that there are some gaps in the graph. Those can be caused by either `NaN`, if `inf` values being present in the dataset. `inf` may be caused by division by 0, and `NaN` can indicate missing data, or no data available to compute the result (like in the very beginning of our frame, where rolling window of width 8 is not yet available). To make the graph nicer, we need to fill those values using `replace` and `fillna` function.Let's further look at the beginning of the pandemic. We will also limit the y-axis values to show only values below 6, in order to see better, and draw horizontal line at 1. ###Code ax = df[df.index<"2020-05-01"]['Rt'].replace(np.inf,np.nan).fillna(method='pad').plot(figsize=(10,3)) ax.set_ylim([0,6]) ax.axhline(1,linestyle='--',color='red') plt.show() ###Output _____no_output_____ ###Markdown Another interesting indicator of the pandemic is the **derivative**, or **daily difference** in new cases. It allows us to see clearly when pandemic is increasing or declining. ###Code df['ninfected'].diff().plot() plt.show() ###Output _____no_output_____ ###Markdown Given the fact that there are a lot of fluctuations in data caused by reporting, it makes sense to smooth the curve by running rolling average to get the overall picture. Let's again focus on the first months of the pandemic: ###Code ax=df[df.index<"2020-06-01"]['ninfected'].diff().rolling(7).mean().plot() ax.axhline(0,linestyle='-.',color='red') plt.show() ###Output _____no_output_____ ###Markdown ChallengeNow it is time for you to play more with the code and data! Here are a few suggestions you can experiment with:* See the spread of the pandemic in different countries.* Plot $R_t$ graphs for several countries on one plot for comparison, or make several plots side-by-side* See how the number of deaths and recoveries correlate with number of infected cases.* Try to find out how long a typical disease lasts by visually correlating infection rate and deaths rate and looking for some anomalies. You may need to look at different countries to find that out.* Calculate the fatality rate and how it changes over time. You may want to take into account the length of the disease in days to shift one time series before doing calculations ###Code china = mkframe('China') france = mkframe('France') china['new_infected'] = china['infected'].diff().plot() france['new_infected'] = france['infected'].diff().plot(color='red') plt.show() def add_Rt(df): df['ninfected'] = df['infected'].diff() df['Rt'] = df['ninfected'].rolling(8).apply(lambda x: x[4:].sum()/x[:4].sum()) china = mkframe('China') france = mkframe('France') US = mkframe('US') UK = mkframe('United Kingdom') countries = [china,france,US,UK] color = ['red','blue','green','yellow'] for i,country in enumerate(countries): add_Rt(country) country['Rt'].plot(color = color[i]) plt.show() ###Output _____no_output_____ ###Markdown Estimation of COVID-19 Pandemic Loading DataWe will use data on COVID-19 infected individuals, provided by the [Center for Systems Science and Engineering](https://systems.jhu.edu/) (CSSE) at [Johns Hopkins University](https://jhu.edu/). Dataset is available in [this GitHub Repository](https://github.com/CSSEGISandData/COVID-19). ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = (10,3) # make figures larger ###Output _____no_output_____ ###Markdown We can load the most recent data directly from GitHub using `pd.read_csv`. If for some reason the data is not available, you can always use the copy available locally in the `data` folder - just uncomment the line below that defines `base_url`: ###Code base_url = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/" # loading from Internet # base_url = "../../data/COVID/" # loading from disk infected_dataset_url = base_url + "time_series_covid19_confirmed_global.csv" recovered_dataset_url = base_url + "time_series_covid19_recovered_global.csv" deaths_dataset_url = base_url + "time_series_covid19_deaths_global.csv" countries_dataset_url = base_url + "../UID_ISO_FIPS_LookUp_Table.csv" ###Output _____no_output_____ ###Markdown Let's now load the data for infected individuals and see how the data looks like: ###Code infected = pd.read_csv(infected_dataset_url) infected.head() ###Output _____no_output_____ ###Markdown We can see that each row of the table defines the number of infected individuals for each country and/or province, and columns correspond to dates. Similar tables can be loaded for other data, such as number of recovered and number of deaths. ###Code recovered = pd.read_csv(recovered_dataset_url) deaths = pd.read_csv(deaths_dataset_url) ###Output _____no_output_____ ###Markdown Making Sense of the DataFrom the table above the role of province column is not clear. Let's see the different values that are present in `Province/State` column: ###Code infected['Province/State'].value_counts() ###Output _____no_output_____ ###Markdown From the names we can deduce that countries like Australia and China have more detailed breakdown by provinces. Let's look for information on China to see the example: ###Code infected[infected['Country/Region']=='China'] ###Output _____no_output_____ ###Markdown Pre-processing the Data We are not interested in breaking countries down to further territories, thus we would first get rid of this breakdown and add information on all territories together, to get info for the whole country. This can be done using `groupby`: ###Code infected = infected.groupby('Country/Region').sum() recovered = recovered.groupby('Country/Region').sum() deaths = deaths.groupby('Country/Region').sum() infected.head() ###Output _____no_output_____ ###Markdown You can see that due to using `groupby` all DataFrames are now indexed by Country/Region. We can thus access the data for a specific country by using `.loc`:| ###Code infected.loc['US'][2:].plot() recovered.loc['US'][2:].plot() plt.show() ###Output _____no_output_____ ###Markdown > **Note** how we use `[2:]` to remove first two elements of a sequence that contain geolocation of a country. We can also drop those two columns altogether: ###Code infected.drop(columns=['Lat','Long'],inplace=True) recovered.drop(columns=['Lat','Long'],inplace=True) deaths.drop(columns=['Lat','Long'],inplace=True) ###Output _____no_output_____ ###Markdown Investigating the DataLet's now switch to investigating a specific country. Let's create a frame that contains the data on infections indexed by date: ###Code def mkframe(country): df = pd.DataFrame({ 'infected' : infected.loc[country] , 'recovered' : recovered.loc[country], 'deaths' : deaths.loc[country]}) df.index = pd.to_datetime(df.index) return df df = mkframe('US') df df.plot() plt.show() ###Output _____no_output_____ ###Markdown Now let's compute the number of new infected people each day. This will allow us to see the speed at which pandemic progresses. The easiest day to do it is to use `diff`: ###Code df['ninfected'] = df['infected'].diff() df['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown We can see high fluctuations in data. Let's look closer at one of the months: ###Code df[(df.index.year==2020) & (df.index.month==7)]['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown It clearly looks like there are weekly fluctuations in data. Because we want to be able to see the trends, it makes sense to smooth out the curve by computing running average (i.e. for each day we will compute the average value of the previous several days): ###Code df['ninfav'] = df['ninfected'].rolling(window=7).mean() df['ninfav'].plot() plt.show() ###Output _____no_output_____ ###Markdown In order to be able to compare several countries, we might want to take the country's population into account, and compare the percentage of infected individuals with respect to country's population. In order to get country's population, let's load the dataset of countries: ###Code countries = pd.read_csv(countries_dataset_url) countries ###Output _____no_output_____ ###Markdown Because this dataset contains information on both countries and provinces, to get the population of the whole country we need to be a little bit clever: ###Code countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()] pop = countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()]['Population'].iloc[0] df['pinfected'] = df['infected']*100 / pop df['pinfected'].plot(figsize=(10,3)) plt.show() ###Output _____no_output_____ ###Markdown Computing $R_t$To see how infectious is the disease, we look at the **basic reproduction number** $R_0$, which indicated the number of people that an infected person would further infect. When $R_0$ is more than 1, the epidemic is likely to spread.$R_0$ is a property of the disease itself, and does not take into account some protective measures that people may take to slow down the pandemic. During the pandemic progression, we can estimate the reproduction number $R_t$ at any given time $t$. It has been shown that this number can be roughly estimated by taking a window of 8 days, and computing $$R_t=\frac{I_{t-7}+I_{t-6}+I_{t-5}+I_{t-4}}{I_{t-3}+I_{t-2}+I_{t-1}+I_t}$$where $I_t$ is the number of newly infected individuals on day $t$.Let's compute $R_t$ for our pandemic data. To do this, we will take a rolling window of 8 `ninfected` values, and apply the function to compute the ratio above: ###Code df['Rt'] = df['ninfected'].rolling(8).apply(lambda x: x[4:].sum()/x[:4].sum()) df['Rt'].plot() plt.show() ###Output _____no_output_____ ###Markdown You can see that there are some gaps in the graph. Those can be caused by either `NaN`, if `inf` values being present in the dataset. `inf` may be caused by division by 0, and `NaN` can indicate missing data, or no data available to compute the result (like in the very beginning of our frame, where rolling window of width 8 is not yet available). To make the graph nicer, we need to fill those values using `replace` and `fillna` function.Let's further look at the beginning of the pandemic. We will also limit the y-axis values to show only values below 6, in order to see better, and draw horizontal line at 1. ###Code ax = df[df.index<"2020-05-01"]['Rt'].replace(np.inf,np.nan).fillna(method='pad').plot(figsize=(10,3)) ax.set_ylim([0,6]) ax.axhline(1,linestyle='--',color='red') plt.show() ###Output _____no_output_____ ###Markdown Another interesting indicator of the pandemic is the **derivative**, or **daily difference** in new cases. It allows us to see clearly when pandemic is increasing or declining. ###Code df['ninfected'].diff().plot() plt.show() ###Output _____no_output_____ ###Markdown Given the fact that there are a lot of fluctuations in data caused by reporting, it makes sense to smooth the curve by running rolling average to get the overall picture. Let's again focus on the first months of the pandemic: ###Code ax=df[df.index<"2020-06-01"]['ninfected'].diff().rolling(7).mean().plot() ax.axhline(0,linestyle='-.',color='red') plt.show() ###Output _____no_output_____ ###Markdown Estimation of COVID-19 Pandemic Loading Data We will use data on COVID-19 infected individuals, provided by the [Center for Systems Science and Engineering](https://systems.jhu.edu/) (CSSE) at [Johns Hopkins University](https://jhu.edu/). Dataset is available in [this GitHub Repository](https://github.com/CSSEGISandData/COVID-19). ###Code import numpy as np import pandas as pd import matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = (10,3) # make figures larger ###Output _____no_output_____ ###Markdown We can load the most recent data directly from GitHub using `pd.read_csv`. If for some reason the data is not available, you can always use the copy available locally in the `data` folder - just uncomment the line below that defines `base_url`: ###Code base_url = "https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/" # loading from Internet # base_url = "../../data/COVID/" # loading from disk infected_dataset_url = base_url + "time_series_covid19_confirmed_global.csv" recovered_dataset_url = base_url + "time_series_covid19_recovered_global.csv" deaths_dataset_url = base_url + "time_series_covid19_deaths_global.csv" countries_dataset_url = base_url + "../UID_ISO_FIPS_LookUp_Table.csv" ###Output _____no_output_____ ###Markdown Let's now load the data for infected individuals and see how the data looks like: ###Code infected = pd.read_csv(infected_dataset_url) infected.head() ###Output _____no_output_____ ###Markdown We can see that each row of the table defines the number of infected individuals for each country and/or province, and columns correspond to dates. Similar tables can be loaded for other data, such as number of recovered and number of deaths. ###Code recovered = pd.read_csv(recovered_dataset_url) deaths = pd.read_csv(deaths_dataset_url) ###Output _____no_output_____ ###Markdown Making Sense of the Data From the table above the role of province column is not clear. Let's see the different values that are present in `Province/State` column: ###Code infected['Province/State'].value_counts() ###Output _____no_output_____ ###Markdown From the names we can deduce that countries like Australia and China have more detailed breakdown by provinces. Let's look for information on China to see the example: ###Code infected[infected['Country/Region']=='China'] ###Output _____no_output_____ ###Markdown Pre-processing the Data We are not interested in breaking countries down to further territories, thus we would first get rid of this breakdown and add information on all territories together, to get info for the whole country. This can be done using `groupby`: ###Code infected = infected.groupby('Country/Region').sum() recovered = recovered.groupby('Country/Region').sum() deaths = deaths.groupby('Country/Region').sum() infected.head() ###Output _____no_output_____ ###Markdown You can see that due to using `groupby` all DataFrames are now indexed by Country/Region. We can thus access the data for a specific country by using `.loc`:| ###Code infected.loc['US'][2:].plot() recovered.loc['US'][2:].plot() plt.show() ###Output _____no_output_____ ###Markdown > **Note** how we use `[2:]` to remove first two elements of a sequence that contain geolocation of a country. We can also drop those two columns altogether: ###Code infected.drop(columns=['Lat','Long'],inplace=True) recovered.drop(columns=['Lat','Long'],inplace=True) deaths.drop(columns=['Lat','Long'],inplace=True) ###Output _____no_output_____ ###Markdown Investigating the Data Let's now switch to investigating a specific country. Let's create a frame that contains the data on infections indexed by date: ###Code def mkframe(country): df = pd.DataFrame({ 'infected' : infected.loc[country] , 'recovered' : recovered.loc[country], 'deaths' : deaths.loc[country]}) df.index = pd.to_datetime(df.index) return df df = mkframe('US') df df.plot() plt.show() ###Output _____no_output_____ ###Markdown Now let's compute the number of new infected people each day. This will allow us to see the speed at which pandemic progresses. The easiest day to do it is to use `diff`: ###Code df['ninfected'] = df['infected'].diff() df['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown We can see high fluctuations in data. Let's look closer at one of the months: ###Code df[(df.index.year==2020) & (df.index.month==7)]['ninfected'].plot() plt.show() ###Output _____no_output_____ ###Markdown It clearly looks like there are weekly fluctuations in data. Because we want to be able to see the trends, it makes sense to smooth out the curve by computing running average (i.e. for each day we will compute the average value of the previous several days): ###Code df['ninfav'] = df['ninfected'].rolling(window=7).mean() df['ninfav'].plot() plt.show() ###Output _____no_output_____ ###Markdown In order to be able to compare several countries, we might want to take the country's population into account, and compare the percentage of infected individuals with respect to country's population. In order to get country's population, let's load the dataset of countries: ###Code countries = pd.read_csv(countries_dataset_url) countries ###Output _____no_output_____ ###Markdown Because this dataset contains information on both countries and provinces, to get the population of the whole country we need to be a little bit clever: ###Code countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()] pop = countries[(countries['Country_Region']=='US') & countries['Province_State'].isna()]['Population'].iloc[0] df['pinfected'] = df['infected']*100 / pop df['pinfected'].plot(figsize=(10,3)) plt.show() ###Output _____no_output_____ ###Markdown Computing $R_t$ To see how infectuous is the disease, we look at the **basic repoduction number** $R_0$, which indicated the number of people that an infected person would further infect. When $R_0$ is more than 1, the epidemic is likely to spread. $R_0$ is a property of the disease itself, and does not take into account some protective measures that people may take to slow down the pandemic. During the pandemic progression, we can estimate the reproduction number $R_t$ at any given time $t$. It has been shown that this number can be roughly estimated by taking a window of 8 days, and computing $$R_t=\frac{I_{t-7}+I_{t-6}+I_{t-5}+I_{t-4}}{I_{t-3}+I_{t-2}+I_{t-1}+I_t}$$ where $I_t$ is the number of newly infected individuals on day $t$. Let's compute $R_t$ for our pandemic data. To do this, we will take a rolling window of 8 `ninfected` values, and apply the function to compute the ratio above: ###Code df['Rt'] = df['ninfected'].rolling(8).apply(lambda x: x[4:].sum()/x[:4].sum()) df['Rt'].plot() plt.show() ###Output _____no_output_____ ###Markdown You can see that there are some gaps in the graph. Those can be caused by either `NaN`, if `inf` values being present in the dataset. `inf` may be caused by division by 0, and `NaN` can indicate missing data, or no data available to compute the result (like in the very beginning of our frame, where rolling window of width 8 is not yet available). To make the graph nicer, we need to fill those values using `replace` and `fillna` function. Let's further look at the beginning of the pandemic. We will also limit the y-axis values to show only values below 6, in order to see better, and draw horizontal line at 1. ###Code ax = df[df.index<"2020-05-01"]['Rt'].replace(np.inf,np.nan).fillna(method='pad').plot(figsize=(10,3)) ax.set_ylim([0,6]) ax.axhline(1,linestyle='--',color='red') plt.show() ###Output _____no_output_____ ###Markdown Another interesting indicator of the pandemic is the **derivative**, or **daily difference** in new cases. It allows us to see clearly when pandemic is increasing or declining. ###Code df['ninfected'].diff().plot() plt.show() ###Output _____no_output_____ ###Markdown Given the fact that there are a lot of fluctuations in data caused by reporting, it makes sense to smooth the curve by running rolling average to get the overall picture. Let's again focus on the first months of the pandemic: ###Code ax=df[df.index<"2020-06-01"]['ninfected'].diff().rolling(7).mean().plot() ax.axhline(0,linestyle='-.',color='red') plt.show() ###Output _____no_output_____

IL_LTC_Data_Analysis-11-12.ipynb

###Markdown 1 - Pull JSON File from Website ###Code def pull_IL_json_from_web(): ltc_data = getResponse('http://www.dph.illinois.gov/sitefiles/COVIDLTC.json') # Extract Reporting Data reporting_date = '%d-%02d-%02d' %(ltc_data['LastUpdateDate']['year'], ltc_data['LastUpdateDate']['month'], ltc_data['LastUpdateDate']['day']) #Saving a copy of source data ltc_data_json = json.dumps(ltc_data) file = "Source_data/IL_" + reporting_date + "_LTC_data_Source.json" f = open(file, "w") f.write(ltc_data_json) f.close() return file # ltc_data = getResponse('http://www.dph.illinois.gov/sitefiles/COVIDLTC.json') # # Extract Reporting Data # reporting_date = '%d-%02d-%02d' %(ltc_data['LastUpdateDate']['year'], ltc_data['LastUpdateDate']['month'], ltc_data['LastUpdateDate']['day']) # #Saving a copy of source data # ltc_data_json = json.dumps(ltc_data) # f = open("Source_data/IL_" + reporting_date + "_LTC_data_Source.json","w") # f.write(ltc_data_json) # f.close() json_file = pull_IL_json_from_web() with open(json_file) as f: ltc_data = json.load(f) # Extract Reporting Data reporting_date = '%d-%02d-%02d' % (ltc_data['LastUpdateDate']['year'], ltc_data['LastUpdateDate']['month'], ltc_data['LastUpdateDate']['day']) ###Output _____no_output_____ ###Markdown 2 - Put Outbreak data in DataFrame and AugmentData is at the Outbreak level. A Facility can have 1 to Many Outbreaks (not sure about 0) ###Code def outbreak_df_from_file(filename): with open(filename) as f: ltc_data = json.load(f) # Extract Reporting Data reporting_date = '%d-%02d-%02d' %(ltc_data['LastUpdateDate']['year'], ltc_data['LastUpdateDate']['month'], ltc_data['LastUpdateDate']['day']) df = pd.DataFrame(ltc_data['FacilityValues']) df['reporting_date'] = reporting_date df['CFR'] = (df['deaths'] / df['confirmed_cases']) df['outbreaks'] = 1 # to allow counting # of outbreaks by Facility #Save Outbreak data to a file outbreak_file = 'Reporting_data/IL_' + reporting_date + '_Outbreaks_LTC_data_v2.csv' df.to_csv(outbreak_file, index = False) df.sort_values(by='deaths', ascending=False).head(5) ###Output _____no_output_____ ###Markdown 3 - Print Summary Data ###Code # Get summary data from feed - Note this may not match totals - ST-TODO: Check if summary data and totals from raw data match deaths = ltc_data['LTC_Reported_Cases']['deaths'] confirmed_cases = ltc_data['LTC_Reported_Cases']['confirmed_cases'] print ('Date: %s' % reporting_date) print ('Cases: %d' % confirmed_cases) print ('Deaths: %d'% deaths) print ('Outbreaks: %d' % df.reporting_date.value_counts()[0]) print ('Facilities: %d' % len(df.groupby(['County', 'FacilityName']).size().reset_index().rename(columns={0:'count'}).sort_values(by='count', ascending=False))) ###Output Date: 2020-11-06 Cases: 36683 Deaths: 5253 Outbreaks: 1309 Facilities: 1116 ###Markdown 4 - Get Facility Level data, augment and saveFacilities can have multiple outbreaks, need to sum these to get counts at the Facility level ###Code df_facilities = df.groupby(['County', 'FacilityName']).sum() df_facilities['CFR'] = df_facilities['deaths'] / df_facilities['confirmed_cases'] df_facilities.sort_values(by='confirmed_cases', ascending=False).to_csv('Reporting_data/IL_' + reporting_date + '_Facilities_LTC_data_v2.csv') df_facilities.sort_values(by='confirmed_cases', ascending=False).head(10) ###Output _____no_output_____ ###Markdown 4 - County Level Data & Charts ###Code # County Level Data df_county = df.groupby(by=['County']).sum() df_county['CFR'] = (df_county['deaths'] / df_county['confirmed_cases']) df_county.sort_values('deaths', ascending=False).to_csv('Reporting_data/IL_' + reporting_date + '_County_LTC_stats_v2.csv') df_county.sort_values('deaths', ascending=False).head(10) # import altair as alt # df1=df_county.sort_values(by=['deaths'], ascending=False).reset_index() # cols = ['Deaths Non LTC', 'LTC Deaths'] # cols = ['LTC Deaths', 'Deaths Non LTC']23 # chart1 = alt.Chart(df_county.sort_values(by=['deaths'], ascending=False).reset_index()).mark_bar().encode( # x='deaths:Q', # y=alt.Y('County:O', sort='-x'), # tooltip=['County', 'deaths', 'confirmed_cases', 'CFR'] # ) # chart2=chart1.encode(x=alt.X('CFR', axis=alt.Axis(format='%'))) # #chart2=chart1.encode(x=alt.X('CFR')) # chart1 | chart2 # import altair as alt # df1=df_county.sort_values(by=['deaths'], ascending=False).reset_index() # cols = ['Deaths Non LTC', 'LTC Deaths'] # cols = ['LTC Deaths', 'Deaths Non LTC'] # chart1 = alt.Chart(df_county.sort_values(by=['deaths'], ascending=False).reset_index()).mark_bar().encode( # x='deaths:Q', # y=alt.Y('County:O'), # tooltip=['County', 'deaths', 'confirmed_cases', 'CFR'] # ) # chart2=chart1.encode(x=alt.X('CFR', axis=alt.Axis(format='%'))) # #chart2=chart1.encode(x=alt.X('CFR')) # chart1 | chart2 ###Output _____no_output_____