formalStatistics

The probability and statistics foundations behind modern machine learning.

Deep-dive explainers combining rigorous mathematics, interactive visualizations, and working code. The bridge between formalCalculus and formalML.

formalCalculus formalStatistics formalML

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foundational 40 min read

Sample Spaces, Events & Axioms

The Kolmogorov axioms, sigma-algebras, combinatorial probability, and the union bound that powers PAC learning.

8 Tracks · 32 Topics

Track 1

Foundations of Probability

Kolmogorov axioms, conditional probability, random variables, expectation

4 topics
Track 2

Core Distributions & Families

Discrete and continuous distributions, exponential families, multivariate distributions

4 topics
Track 3

Convergence & Limit Theorems

Modes of convergence, law of large numbers, central limit theorem, tail bounds

4 topics
Track 4

Statistical Estimation

Bias-variance, maximum likelihood, method of moments, sufficiency

4 topics
Track 5

Hypothesis Testing & Confidence

Neyman-Pearson paradigm, likelihood ratio tests, confidence intervals, multiple testing

4 topics
Track 6

Regression & Linear Models

Least squares, generalized linear models, regularization, model selection

4 topics
Track 7

Bayesian Statistics

Prior selection, MCMC computation, model comparison, hierarchical models

4 topics
Track 8

High-Dimensional & Nonparametric

Order statistics, kernel density estimation, bootstrap, empirical processes

4 topics