01Statistical Learning Theory - Module OverviewThe mathematical theory of generalization - why ML models work, when they fail, and how to bound their error. Module map and learning objectives for PAC learning, VC dimension, and modern generalization theory.02PAC LearningProbably Approximately Correct framework - sample complexity, consistent learners, finite hypothesis classes, and the formal foundation of why data size matters in ML.03VC DimensionVapnik-Chervonenkis dimension - shattering, VC dimension of common classifiers, the Fundamental Theorem of Statistical Learning, and why model capacity determines generalization.04Bias-Variance TradeoffMathematical decomposition of generalization error into bias, variance, and noise - with formal derivations, practical examples, and the modern double-descent perspective in deep learning.05Rademacher ComplexityRademacher complexity as a data-dependent measure of hypothesis class richness - definition, connection to VC dimension, generalization bounds, and why it gives tighter guarantees for ML.06Regularisation TheoryRegularisation as Occam's razor - Tikhonov regularisation, structural risk minimisation, the connection between dropout and Bayesian inference, and early stopping as regularisation.07Online Learning TheoryThe online learning model, regret bounds, Perceptron algorithm, Follow-The-Leader and Follow-The-Regularised-Leader, Hedge algorithm, and connections to streaming ML and online ad auctions.08Generalisation Bounds in Deep LearningWhy classical theory fails for deep learning - double descent, benign overfitting, implicit regularisation of SGD, neural tangent kernel, and modern PAC-Bayes bounds.
