Pick a goal - foundations, supervised methods, or modern AI - and get this site’s own ordered plan for reaching it: which learning path to take at each stage, what to read alongside it, and how long the lessons run.
Start from probability and finish able to state precisely what a model is estimating, why it cannot be perfect, and how to measure its error honestly.
Stage 1
Sample spaces, the two axioms, and the addition and multiplication rules, then reversing a conditional with Bayes and seeing how badly base rates fool intuition.
Learning path: Probability and Statistical Foundations · 130 min of lessons
Reading: probability from zero, bayes theorem and belief updating
ProbabilityMathematics
Stage 2
What an estimate does and does not say about the population behind it: bias against variance, what a confidence interval promises about the procedure rather than about your interval, and what a p-value is a probability of.
Learning path: Statistical Inference · 85 min of lessons
Reading: what a sample can and cannot tell you
StatisticsProbability
Stage 3
What breaks when rows are not independent: a regression that finds a relationship between two unrelated series, a standard error too narrow by a computable factor, and the validation split that measures interpolation instead of forecasting.
Learning path: Time Series · 85 min of lessons
Reading: the regression that finds a relationship that is not there
StatisticsMachine Learning
Stage 4
Why a comparison between the treated and the untreated can carry the wrong sign, what randomisation buys that adjustment cannot, and the rule for which variables to control - including the ones that manufacture bias.
Learning path: Causal Inference · 80 min of lessons
Reading: the treatment that helps everyone and harms the average
StatisticsMachine Learning
Stage 5
What a training score actually reports, the capacity measure that survives an infinite hypothesis class, and the averaging theorem that prices the assumptions every learner must make.
Learning path: Statistical Learning Theory · 85 min of lessons
Reading: why learning from data works at all
Machine LearningMathematics
Stage 6
Sizing a test before it starts, the exaggeration an underpowered one reports, the false winners produced by extra looks, metrics and segments, and turning a measured effect into a decision.
Learning path: Experimentation and A/B Testing · 85 min of lessons
Reading: the experiment that was going to win anyway
StatisticsMachine Learning
Stage 7
Entropy as the shortest a code can be rather than a summary, the surcharge for the wrong distribution that turns out to be the loss you already minimise, and the ceiling mutual information puts on everything downstream of a feature.
Learning path: Information Theory · 85 min of lessons
Reading: the bound that is actually reached
MathematicsMachine Learning
Stage 8
The Y = f(X) + e setup, the split between reducible and irreducible error, and deciding whether you are doing prediction or inference.
Reading: what is statistical learning
StatisticsMachine Learning
Stage 9
The exact bias-variance decomposition, and using k-fold cross-validation to estimate test error from the data you already have.
Reading: the bias variance tradeoff, cross validation and resampling
StatisticsMachine Learning
Study plans are this site’s own ordering of its material, not an official syllabus of any institution.
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The setup behind every predictive model: estimating an unknown function f from data, the split between reducible and irreducible error, and why prediction and inference pull in different directions.
Build probability from the ground up: possible worlds, the sample space, the two basic axioms, and the addition and multiplication rules, each derived rather than asserted, with worked numeric examples.