pages/42_regression.py

import numpy as np
import matplotlib.pyplot as plt
import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.model_selection import train_test_split

# Step 1: Create Synthetic Data
np.random.seed(42)
X = np.linspace(-10, 10, 1000)
y = 2.5 * X + np.random.normal(0, 2, X.shape)  # Linear relation with noise

# Split into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Convert to PyTorch tensors
X_train = torch.tensor(X_train, dtype=torch.float32).view(-1, 1)
y_train = torch.tensor(y_train, dtype=torch.float32).view(-1, 1)
X_test = torch.tensor(X_test, dtype=torch.float32).view(-1, 1)
y_test = torch.tensor(y_test, dtype=torch.float32).view(-1, 1)

# Step 2: Define and Train a Neural Network Model
class SimpleNN(nn.Module):
    def __init__(self):
        super(SimpleNN, self).__init__()
        self.fc1 = nn.Linear(1, 10)
        self.fc2 = nn.Linear(10, 1)

    def forward(self, x):
        x = torch.relu(self.fc1(x))
        x = self.fc2(x)
        return x

# Initialize model, loss function, and optimizer
model = SimpleNN()
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.01)

# Training loop
epochs = 500
losses = []

for epoch in range(epochs):
    model.train()
    optimizer.zero_grad()
    outputs = model(X_train)
    loss = criterion(outputs, y_train)
    loss.backward()
    optimizer.step()
    losses.append(loss.item())
    if (epoch + 1) % 50 == 0:
        print(f'Epoch [{epoch+1}/{epochs}], Loss: {loss.item():.4f}')

# Step 3: Plot the Results
# Plot the synthetic data and the model's predictions
model.eval()
with torch.no_grad():
    predicted = model(X_test).numpy()

plt.figure(figsize=(12, 6))

# Plot data and predictions
plt.subplot(1, 2, 1)
plt.scatter(X_test, y_test, label='Original data', alpha=0.5)
plt.scatter(X_test, predicted, label='Fitted line', alpha=0.5)
plt.title('Regression Results')
plt.xlabel('X')
plt.ylabel('y')
plt.legend()

# Plot training loss
plt.subplot(1, 2, 2)
plt.plot(losses)
plt.title('Training Loss')
plt.xlabel('Epoch')
plt.ylabel('Loss')

plt.tight_layout()
plt.show()