In Posts 11 through 13 we built classifiers that draw boundaries directly, fitting logistic curves and trees to the Adult Census Income data. This post takes the opposite route and then the long way around: we start with generative classifiers that model how each income class produces its features, pivot
In the last few posts we built up the machinery of supervised learning from first principles, from nearest neighbors through decision trees and ensemble methods. Now we turn to the oldest and most enduring family in the toolbox: linear models. By the end of this post we will have fitted
In Post 11 we learned to interpret our models and engineer features, but we left a nagging question on the table: how do we know the numbers we report are trustworthy? This post answers that question with the Adult Census Income dataset, and by the end we land a random
In Post 10 we learned how to split data into training, validation, and test sets, and in Posts 3 and 4 we built our first regression models and baselines. Now we take the next step: training our first real classifiers on the UCI Adult Census Income dataset, where we predict
In the last few posts we built regression models from raw features and learned how to inspect what drives them, but every one of those models assumed a table that was already tidy. This post takes the opposite starting point: we begin with the raw New York City Airbnb listings,
In Post 8 we built the optimization toolkit that turns a problem into a solvable form, learning how gradients and convexity give us a path to good answers. Now we face the harder truth: some problems resist every clever trick we know, and the only honest response is to understand
In Post 6 we learned to clean tabular data until it told a coherent story. This post takes that same discipline and applies it to a different kind of structure: the directed, weighted graph of the world's flight network. We build a graph from raw OpenFlights data, then
In Post 6 we built recursion and divide-and-conquer from first principles, learning to split problems into independent halves and combine the answers. This post takes those tools and points them at a harder class of problems: ones where the subproblems overlap, where strings refuse to be split cleanly,
In Post 2 we built the foundations with Python lists, dicts, sets, and recursion, learning how the language's core containers behave under load. Now we put those tools through their paces on a real dataset: 370,103 English words, one per line, drawn from the dwyl/english-words
In Posts 3 and 4 we built the probabilistic foundations and learned how to update beliefs with Bayes' rule. Now we put that machinery to work on a concrete question: how much information is actually in a piece of text? This post measures that quantity on WikiText-2, a
In Post 3 we explored the Adult Census Income dataset through distributions, correlations, and outlier fences, learning to let the data speak before we model it. Now we put that exploratory foundation to work and ask the question every data scientist eventually faces: is the pattern we see real, or
In the last post we wrangled the Adult Census Income dataset into a clean, analysis-ready form. Now we turn that clean data into a laboratory for the core ideas of probability and estimation: Bayes' theorem, the distributions that describe real populations, the limit theorems that justify our confidence,
Stochastic Blog
Last time we built our first Python pipeline and learned to load, inspect, and manipulate data. Now we take the next step: every machine learning model, from linear regression to deep neural networks, rests on three pillars: linear algebra, calculus, and convex optimization. We'll build each one from
Stochastic Blog
Every machine learning project, no matter how sophisticated, rests on a handful of foundational ideas. In this post we build them from scratch using the UCI Adult Census Income dataset, a classic binary classification task where we predict whether someone earns more than $50,000 per year. By the time