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Physics, Poetry, Mathematics, Humanity, Thermodynamics.
Once upon a time, there was a book Let’s say a novel, no gobbledygook An epic tale, told masterfully Of characters wholesome and silly Page after page of insightful prose But, between these pages a dispute arose Page thirty-nine was unhappy with its neighbors; Page hundred-one, untouched by
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impatient readers, Envied page one which was in turn tired Of its well-worn visage; it felt ill attired Overthrowing their bindings, the pages set free Page thirty-nine was dancing with glee When a fight broke out amongst its words Lacking vocabulary, they fought with fists and swords They revolted
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against the author-imposed order A free-for-all tussle, ‘a’s and ‘the’s hugged the border ‘Incomprehensible’ and ‘argumentative’ dominated a while Till everyone renounced their domicile The sweet taste of freedom ‘incomprehensible’ could comprehend You can probably guess how its story will end Yup,
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its letters degenerated into an incomprehensible heap To picture the author’s bewilderment requires no leap Of imagination — she searched for her characters In the disordered pages, words, and letters Crawling on her hands and knees, she looked everywhere With her eyes, with her soul for characters
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that weren’t there Her body got way more tired than it ought That’s when her hands, knees, and eyes had a thought… — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — This poem can be read at face value, just for absurd hilarity and entertainment. There are other layers to it though —
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we’ll explore some below. I am curious to know how you interpreted it - please do share your thoughts if you can! “Once upon a time, there was a book Let’s say a novel, no gobbledygook An epic tale, told masterfully Of characters wholesome and silly” There was no need for any explicit second law
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‘gobbledygook’ — even a novel is a highly ordered system, sufficient to make my point. I’m also playing on the concept of emergent properties — when does paper cut into rectangles to form pages, with ink dots assembled to make up letters and words, turn into ‘wholesome and silly characters’? “Page
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after page of insightful prose But, between these pages a dispute arose Page thirty-nine was unhappy with its neighbors; Page hundred-one, untouched by impatient readers, Envied page one which was in turn tired Of its well-worn visage; it felt ill attired” At all levels, like entities find reasons
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to compare, to envy, and to fight — why should pages of a novel be any exception?! Here is a thread of thought layered in — it feels rather sad that we human beings bicker with each other, nations of this world bicker with each other, when really we are all pages of the same novel, so to say.
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“Overthrowing their bindings, the pages set free Page thirty-nine was dancing with glee When a fight broke out amongst its words Lacking vocabulary, they fought with fists and swords” We do feel the need to throw our bindings and assert our individuality, and we all have perhaps experienced a
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flavor of the glee that page thirty-nine felt. However, we will end up with chaos and disorder if we take the ‘freedom above everything else’ stance to the extreme. Have you seen examples where a faction separated from the whole asserting its individual identity, and soon disintegrated into its own
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fractions? ‘Use your words’ being the trite mantra for a civil discourse, I got a kick out of thinking of words fighting with fists and swords because they ‘lacked vocabulary’! “They revolted against the author-imposed order A free-for-all tussle, ‘a’s and ‘the’s hugged the border
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‘Incomprehensible’ and ‘argumentative’ dominated a while Till everyone renounced their domicile” Here, ‘a’s and ‘the’s might be the small nations of the world, or kids on a playground, trying to stay out of the way while the bullies throw their weight around. Classrooms, the United Nations, novels,
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us — all are composite systems with a high degree of order. An effort is needed to create and maintain that order in all contexts. “The sweet taste of freedom ‘incomprehensible’ could comprehend You can probably guess how its story will end Yup, its letters degenerated into an incomprehensible heap
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To picture the author’s bewilderment requires no leap Of imagination — she searched for her characters In the disordered pages, words, and letters” What happens when the omnipresent tussle between components succeeds in breaking up the systems? This is the direction of the change favored by the
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second law — even the stars and planets and galaxies will turn to photon dust eventually. “Crawling on her hands and knees, she looked everywhere With her eyes, with her soul for characters that weren’t there Her body got way more tired than it ought That’s when her hands, knees, and eyes had a
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thought…” I wonder if just like the author who is worried about her lost characters while her own life is in danger with her limbs ‘having a thought’ (this is meant to be absurd like Mrs. Potatohead breaking up), we may be having this virtual conversation while our very existence is at risk. Is
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humanity united enough to successfully navigate climate change, future pandemics, and our own inventions like nuclear power and artificial intelligence? I hope we are, for something beautiful can be lost when the whole is broken up into parts. Just like a good novel with its memorable characters is
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so much more than the sum total of the pages and words and characters, what humanity as a whole can achieve is so much more than the sum total of the nations and states and individuals. The device you are reading this on was only possible through collaboration, and the physical device itself is
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Space, Astronomy, Technology, Data Science, Science.
A real photograph of Elon Musk’s Tesla Roadster, with Earth in the background. The camera was mounted on the external boom. (Image credit: SpaceX) A reporter brought to my attention a compilation of recent statements from Elon Musk on the subject of aliens. They included a social media post : “I
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have seen no evidence for aliens and, with about 6000 satellites orbiting Earth, I think I would know.” In an interview, Musk explained: “A lot of people ask me where are the aliens, and I think if anyone would know about aliens on Earth, it would probably be me.” More recently, Musk elaborated on
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the same theme in a panel discussion : “SpaceX, with the Starlink constellation, has roughly 6,000 satellites, and not once have we had to maneuver around a UFO… Never. So, I’m like, okay, I don’t see any evidence of aliens.” Musk also said: “If somebody has evidence of aliens, you know, that’s not
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just a fuzzy blob, then I’d love to see it, love to hear about it, but I don’t think there is.” He then concluded: “We should really think of human civilization as being like a tiny candle in a vast darkness.” This last sentence is premature based on the standards of science. Keep in mind that the
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volume occupied by the disk of stars in our Milky-Way galaxy is 41 orders of magnitude (1 followed by 41 zeros) larger than the volume surveyed by the Starlink satellites and the Milky-Way history is measured in billions of years. But even near Earth, the chance of a meter-size object to collide
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with a Starlink satellite in one orbit at an altitude of order 550 kilometers is a part in 10 million. It would take a thousand years for a collision to occur. But even if there were many meter-size UFOs near Earth, most of them might spend most of their time at a lower altitude. Putting aside the
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negligible chance for a direct collision, Starlink satellites are not equipped with cameras and sensors needed to detect objects that arrive near Earth from interstellar space. The relevant instruments were assembled recently in the Harvard Observatory of the Galileo Project that I am leading.
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Astronomers never constructed an observatory to survey the entire sky at all times for nearby, fast moving objects. In recent months we used our optical, infrared and audio sensors to detect nearly a million objects in the sky. We did not find a UFO as of yet. But even if one in a billion objects
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will be found to have originated from outside the Solar system, this discovery will be big news for humanity. The government’s day job is national security and we should not ask it to tell us what lies outside the Solar system. This is my day job as an astrophysicist. The Galileo Project is in the
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process of constructing two copies of the Harvard Observatory in Colorado and Pennsylvania, at a cost of half a million dollars per observatory. With the investment of ten million dollars, we could build twenty observatories in different locations and get to the bottom of the mysterious nature of
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the Unidentified Anomalous Phenomena (UAPs) reported by the Director of National Intelligence to the U.S. Congress in recent years. If Elon Musk is genuinely curious on whether interstellar objects orbit near Earth, the Galileo Project team can build the needed observatories for him. But there is
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another path for collecting related scientific evidence. A year ago, I led a Pacific Ocean expedition to retrieve materials from the crash site of the 2014 interstellar meteor discovered by U.S. government satellites. We are now planning the next expedition in search of bigger pieces from this
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wreckage. Here again, Elon Musk can promote the collection of new data by funding this new expedition. We will be delighted to have him on our research team or report directly to him in real time from the Pacific Ocean, in case he wishes to fund our next expedition. There are hundreds of billions
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of stars which are older than the Sun by billions of years in the Milky Way galaxy alone. Even with conventional chemical propulsion, as used by SpaceX, it takes less than a billion years to traverse the Milky Way disk from one side to the other. It would be arrogant to think that we are alone
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without checking our back yard for interstellar technological space trash. Consider the Tesla Roadster car launched as a dummy payload by SpaceX in 2018. It is now in an elliptic orbit around the Sun but cannot be seen by our survey telescopes because its small size does not reflect enough
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sunlight. However, the car would be easily detected by the U.S. Government satellites when it collides with Earth in tens of millions of years, through the fireball that it will generate as a result of its friction with air. I wonder how many dummy payloads similar to the Tesla Roadster car are out
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there, constituting interstellar space trash. Every now and then, one of them may collide with Earth, and we could retrieve its defunct engine from the wreckage on the ocean floor. When people say: “extraordinary claims require extraordinary evidence,” they are not seeking the evidence. In
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response, I say: “extraordinary evidence requires extraordinary funding and proper instruments.” In order to discover the Higgs boson, we had to invest ten billion dollars in the Large Hadron Collider. New scientific knowledge does not fall into our lap; it requires a dedicated effort. Elon Musk’s
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uncertainty about aliens can be resolved by using the scientific method. I am as curious as he is about aliens and will be delighted to do the scientific search in collaboration with him. The path not taken is straightforward: he can easily reach me by email or phone. In 2012, Elon and I were
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featured on the same page in Scientific American’s list of “The 25 Most Influential People in Space.” ABOUT THE AUTHOR Image credit: Chris Michel (October 2023) Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute
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for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and
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Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. His new book, titled “Interstellar”, was published in August 2023.
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Logistic Regression, Generalized Linear Model, Machine Learning, Data Science, Statistical Learning.
Revisiting Logistic Regression — A Gentle Introduction to Generalized Linear Models All models are wrong, but some are useful The two fundamental pillars of supervised statistical learning — Regression and Classification. Simple Linear Regression and Logistic Regression is how many of us have
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started our journey in Statistics and Data Science. A long-standing debate still prevails on why is Logistic Regression a Classification Model instead of a Regression Model? Here we revisit Logistic Regression from an intuitive perspective along with statistical rigor. We will briefly touch up on
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the concepts behind Generalized Linear Model along with an optional section on Iterative Re-weighted Least Squares (IRLS) to fit these models. Introduction Statisticians love Linear Models, trust me when I say that. They can go howsoever far possible to impose linearity. Let me give you a instance
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when I was particularly shocked in my Linear Statistical Model classes where we were learning about ANOVA models. My professor said when we fit this model taking into account the possibility of interaction between two factors, if there is no statistically significant interaction we would proceed
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further (i.e. to analyze the breakdown of sum of square errors by ignoring the interaction term which destroys linearity) but if there is a significant interaction then we can’t proceed further and our analysis halts there. But why do they love linearity so much? The key is interpretability where
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we can work out the influence on response variable due to each particular input factor or covariate seperately. The more non-linear model we choose, the more flexible these models will get and fit our data better at the cost of interpretability. This is often desired to model many real-life
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situations and keep into account the interpretability-flexibility tradeoff or Bias-Variance tradeoff. Here we will learn about an extension of the linear model, popularly know as Generalized Linear Models. Let’s get started… Logistic Regression I will walk you through the intuition behind the
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Logistic Regression in this section. Consider a classic scenario where you have the following data X is a collection of input r.v. and y is the response r.v. where X is the explanatory variable, let’s say the amount of poisonous gas released in a closed chamber and y is the binary r.v. indicating
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whether the cat in the chamber is dead or alive. I think the situation must be very familiar. Assume that the cat dies instantly when X amount of gas is administered in the chamber. Why can’t we model this situation with a simple linear regression? Suppose, Linear Regression of alive status of cat
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to amount of poisonous gas If we fit the above model, we will end up with the following Simple Linear Regression fit to the above described data Inspecting the point X = 10 i.e. 10 units of poisonous gas administered will let to the alive status of the cat to be 1/2. Wola! Schrodinger’s Cat in
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superposition. Unfortunately, even if that might be possible in Quantum World, in the classical world that’s impossible and absurd. We need a fix. The problems above are we are modelling the alive status of the cat which is discrete and binary with a linear regression which doesn’t account for
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cases like higher amounts of poisonous gas (see from the above diagram it will result in negative alive status). So, we can instead model a continuous response like probability of the cat being alive. Probability is continuous but bounded Will that do? Realize that the input variable can be any
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non-negative value so this will lead to response probability predictions to be below 0(And the Statistician’s life will be a lie). Thus we need a unbounded response variable to be modeled which has the good property of being continuous and convey the similar meaning as the probability of being
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alive. That’s where we get odds, Odds are unbounded above and continuous but the linear model can predict negative values too Everything is almost perfect above, except we have unboundedness in only one direction but the linear model can very well predict negative values as can be seen from the
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diagram. So, we have logarithm to our rescue which takes any real value taking into account positive values. log odds is also called logit and this is now possessing all the desired properties Thus, it makes sense to model logit of the cat’s alive status with a linear model which we know as
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Logistic Regression. This is our Logistic Regression Model Just to pump you up about one of the major building blocks of modern AI revolution. I will re-write the above expression and present the basic unit of highly flexible Neural Network models, a neuron. The last line sigma stands for the
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sigmoid function The sigmoid function looks like this which has a support of entire real line and outputs a value between 0 and 1. Exactly what we want! The sigmoid function Now, a pictoral depiction of the above expression gives us the world’s smallest Neural Network, a single Neuron (Millions,
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Billions and even trillions of these chain together to form a Deep Model — RIP Interpretability) A Neuron a.k.a. Logistic Regression, note here p is the probability of not being alive though by symmetry we can take it to be probability of being alive by interchanging the labels Our Logistic
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Regression model is ready! But how do we estimate the parameters. We will look into it near the end. Let’s see Generalized Linear Models in the next section and its connection with Logistic Regression. Generalized Linear Model If we break down what we did above in Logistic Regression is the
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following The explanatory variables (X) are assumed to be given, so we model expected response y given X. Why do we model expected value? Since, we assume the actual response to be a noisy version of actual underlying response where the error/noise can not be modeled. In Logistic Regression the
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following was the choice of g, Logistic Regression as Generalized Linear Model Here, the linear predictor is the input to the inverse function of g, which is usually denoted by eta. The g function is know as Link Function in GLM Literature. The Linear Predictor For Logistic Regression the
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distribution of y|X was Bernoulli. We can have an arsenal of various link functions and response distributions which fit in together to account for wide range of real-life data. Ideally, the distribution should be from Exponential Family. Table from Wikipedia A common misconception is why do we
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call this Generalized Linear Model, even when we are applying non-linearity. This is because the model is still linear but not with the mean of the dependent variable rather some function of it is linearly related. We assume that the input variables influence only via a linear function i.e. eta,
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the linear predictor. In fact Linear Regression is also a Generalized Linear Model, which is the first example in the table above with normal response distribution and identity link function. Why Particular Link Function are desired? (Optional) The response variable y are believed to be from an
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exponential family with density The Exponential Family where, The parameters and functions involved in the expression for the Exponential Family Above theta is also known as natural or canonical parameter and phi is viewed as a nuisance. It is pretty straightforward to show, This connects the
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natural parameter with the mean Now, the mean, as mentioned in the starting of GLM section, is seen as an invertible and smooth function of the linear predictor i.e. The GLM Equation The link function which is usually preferred is the canonical link function given by Canonical Link Function The
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canonical link function has several desired statistical properties: It makes X’y the sufficient statistic for the parameters to be estimated. The Newton Method and Fisher Scoring Method for finding MLE coincide. It simplifies derivation of MLE. It ensures some properties in the Linear Regression
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like sum of residuals being 0 and ensures that mu stays within the range of outcome variable. One thing to keep in mind is we use this model when the effects can be approximated as additive on the scale given by the canonical or any other link function. The following diagram allows to easily go
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from one direction to the other The connection between Natural Parameter, Mean and Linear Predictor With the canonical link function we have, Canonical Link Function simplifies the relation between natural parameter and linear predictor Gamma function is known as the cumulant moment generating
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function. The link function relates the linear predictor to the mean and is required to be monotone, increasing, continuously differentiable and invertible. Now we will see in the next section how to fit a Logistic Regression Model. Fitting Logistic Regression We will start by finding the
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Likelihood Expression for the data under the Logistic Regression Model, which is given by, Likelihood of the data where the expression inside the product is the Bernoulli density The probabilities (pi terms) involved in the above expression is given by the Logistic Regression Model as The
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probability of the ith observation’s response to be 1 Now, to simplify the likelihood we take logarithm and arrive at the following expression for Log-Likelihood, The Log Likelihood of the data for Logistic Regression Model The above Log-Likelihood function needs to be maximized w.r.t. beta.
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Sometime it is framed as a problem where the negative of the above log-likelihood needs to be minimized and is known as Binary Cross Entropy (BCE) Loss. The above function needs to be maximized and we can adopt one of the many strategies available to us, Newton-Raphson Method Fisher Scoring Method
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Iterative Re-weighted Least Square (IRLS) Method Gradient Descent on BCE Loss Generalized Linear Models are usually fit using a technique called Fisher Scoring Method by iterating something of the form, The Fisher Scoring Method to fit GLM Here 𝐽(𝑚) will be either the observed or expected Hessian
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of the log likelihood at the mth step. Calculating the derivative of the log likehood we get the following where, X is the design matrix with rows as observations and columns as explanatory variables. Similarly, we can calculate the second derivative as follows, which can be written in a
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consolidated way, Hessian Matrix Creating a intermediate response variable z, allows us to frame the Fisher Scoring Method as IRLS as shown below, Intermediate Response Variable used for framing IRLS This let’s us right the derivative in this way which results in the Fisher Scoring Method to be
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written like this Iterated Reweighted Least Squares Update Comments on convergence Finally, a few quick comments on convergence. Even though theoretically each 𝐽(𝑚) is negative definite, bad initial conditions can still prevent this algorithm from converging. If we're using the canonical link in
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the algorithm we won't ever be dividing by 𝑦̂ 𝑖(1−𝑦̂ 𝑖) to get undefined weights, but if we've got a situation where some 𝑦̂ 𝑖 are approaching 0 or 1, such as in the case of perfect separation, then we'll still get non-convergence as the gradient dies without us reaching anything. Application
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Logistic Regression has various applications in the real world. One of the most appealing use cases is in medical studies where interpretability is desired w.r.t. some explanatory variables and the status of disease in a person. It can also be used to predict the chances of a person having the
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disease. I worked on one such problem of Alzheimer’s Disease Prediction and finding key explanatory variables. Check out the Alzheimer’s Disease Report here and find the code in the repository here. Logistic Regression Performance in predicting AD Status
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Pandas.
Developed by Wes McKinney in 2008, Pandas has become one of the most widely used tools in data science, enabling users to handle data in various forms such as CSV files, SQL databases, Excel spreadsheets, and more. Def: Pandas is a Python library that offers flexible and expressive data structures,
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such as dataframes and series, designed for data manipulation. Background: Pandas offers the ability to read and write data from various sources, including CSV files, Excel spreadsheets, SQL databases, HDFS, and more.It offers functionalities to add, update, and delete columns, merge or divide
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dataframes/series, manage datetime objects, impute missing values, process time series data, and convert to and from numpy arrays, among other capabilities. Pandas operates in-memory, as it loads the entire dataset into the local memory of the machine it is running on. This limits its ability to
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handle large datasets. With cuDF’s pandas accelerator you can now bring accelerated computing to pandas workflows. Also their cuDF library will automatically know if you’re running on GPU or CPU and speed up your processing. RAPIDS cuDF is now integrated directly into Google Colab. Sections Why
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Pandas.
Built-in functions to help in Exploratory Data Analysis Built-in support for CSV, SQL, HTML, JSON, pickle, excel, clipboard and a lot more and a lot more Section 2- Advantages Remarkably user-friendly and requiring minimal effort to master, this tool simplifies the management of tabular data. An
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(employs matplotlib to generate various visualizations behind the scenes). Section 3- Downsides Using it is easy, but it uses more memory. Pandas makes a bunch of extra objects that can slow things down when you’re trying to work with them easily. Inability to utilize distributed infrastructure,
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though pandas can work with formats like HDFS files, It can’t use a distributed system setup to make things run faster. Section 4- Features: The central feature of Pandas lies in its diverse data structures, which enable users to carry out a wide range of analytical operations. Pandas offers a
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range of modules for data manipulation, such as reshaping, joining, merging, and pivoting. Pandas possesses capabilities for data visualization. Built on Top of NumPy Users have the ability to execute mathematical operations, encompassing calculus and statistics, without the need for external
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libraries. It includes modules that assist in managing missing data. There are many built-in functions available for Exploratory Data Analysis. Section 5- Installing Pandas If you’re using Anaconda, pandas should already be included. However, if it’s not installed for some reason, you can simply
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run the following command to install it.conda install pandas. conda install pandas If you’re not utilizing Anaconda, you can install the package using pip by following the appropriate command. pip install pandas Importing numpy alongside pandas is beneficial as it provides access to a broader range
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of numpy features, which are useful in Exploratory Data Analysis (EDA). Section 6- Importing To import pandas, use import pandas as pd import numpy as np Please Follow and 👏 Clap for the story courses teach to see latest updates on this story 🚀 Elevate Your Data Skills with Coursesteach! 🚀 Ready to
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dive into Python, Machine Learning, Data Science, Statistics, Linear Algebra, Computer Vision, and Research? Coursesteach has you covered! 🔍 Python, 🤖 ML, 📊 Stats, ➕ Linear Algebra, 👁️🗨️ Computer Vision, 🔬 Research — all in one place! Don’t Miss Out on This Exclusive Opportunity to Enhance Your
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Skill Set! Enroll Today 🌟 at Machine Learning libraries Course 🔍 Explore Tools, Python libraries for ML, Slides, Source Code, Free online Courses and More! Stay tuned for our upcoming articles because we reach end to end ,where we will explore specific topics related to Machine Learning libraries
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in more detail! Remember, learning is a continuous process. So keep learning and keep creating and Sharing with others!💻✌️ 📚GitHub Repository Ready to dive into data science and AI but unsure how to start? I’m here to help! Offering personalized research supervision and long-term mentoring. Let’s
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chat on Skype: themushtaq48 or email me at [email protected]. Let’s kickstart your journey together! Contribution: We would love your help in making coursesteach community even better! If you want to contribute in some courses , or if you have any suggestions for improvement in any coursesteach
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Astronomy, Space, Space Exploration, Universe, Aliens.
Edwin Hubble way back in 1931 using Doppler effect found out that universe is actually expanding, using same principle of sound of car passing by next to you. This idea was used in process of describing light waves. When a galaxy is moving away, the colour of the light shifts toward the red end of
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Astronomy, Space, Space Exploration, Universe, Aliens.
the spectrum. For every theory we need infinite number of proofs and only one exception to declare it false. So for every galaxy he found out the colour of the light shifts toward the red end of spectrum. And actually, more surprisingly he noticed the redshifting was more severe the further away
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Astronomy, Space, Space Exploration, Universe, Aliens.
the galaxy was, which meant universe is accelerating. So next question arises, is universe infinite or finite?? The most accepted idea nowadays is idea of flat or partially flat universe. Flat follows Euclidian geometry meaning parallel lines never intersect, and the angles of a triangle always add
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up to 180 degrees. The best demonstration is using ‘infinite’ sheet of paper, flat universe is expressed through piece of paper while partially flat can be shown if we take that piece of paper and roll it into a cylinder, then roll it again into a torus. But even if universe is not infinite
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