Foundations of Machine Learning

Why can a learning algorithm make reliable predictions on data it has never seen, even when trained on only finitely many examples? This book explores the mathematical principles that make such generalization possible.

Beginning with the statistical learning model, the book develops the theory systematically through empirical risk minimization, PAC learning, uniform convergence, hypothesis classes, VC dimension, and Rademacher complexity. The discussion culminates in the Fundamental Theorem of Statistical Learning and quantitative generalization bounds that make the conditions for learnability precise.

Every mathematical result is proved in full, with clear and systematic arguments. Numerous exercises with detailed solutions help readers apply the concepts independently and develop a deeper understanding of the theory.

The book provides a rigorous foundation for readers who want to understand what it means for an algorithm to learn, when learning is theoretically possible, and why learned models can generalize to new data. It also prepares readers for further study of machine learning theory and its advanced topics.