Description
Book SynopsisThis self-contained textbook introduces students and researchers of AI to the key mathematical concepts and techniques necessary to learn and analyze machine learning algorithms. Readers will gain the technical knowledge needed to understand research papers in theoretical machine learning, without much difficulty.
Trade Review'This graduate-level text gives a thorough, rigorous and up-to-date treatment of the main mathematical tools that have been developed for the analysis and design of machine learning methods. It is ideal for a graduate class, and the exercises at the end of each chapter make it suitable for self-study. An excellent addition to the literature from one of the leading researchers in this area, it is sure to become a classic.' Peter Bartlett, University of California, Berkeley
'This book showcases the breadth and depth of mathematical ideas in learning theory. The author has masterfully synthesized techniques from the many disciplines that have contributed to this subject, and presented them in an accessible format that will be appreciated by both newcomers and experts alike. Readers will learn the tools-of-the-trade needed to make sense of the research literature and to express new ideas with clarity and precision.' Daniel Hsu, Columbia University
'Tong Zhang shares in this book his deep and broad knowledge of machine learning, writing an impressively comprehensive and up-to-date reference text, providing a rigorous and rather advanced treatment of the most important topics and approaches in the mathematical study of machine learning. As an authoritative reference and introduction, his book will be a great asset to the field.' Robert Schapire, Microsoft Research
'This book gives a systematic treatment of the modern mathematical techniques that are commonly used in the design and analysis of machine learning algorithms. Written by a key contributor to the field, it is a unique resource for graduate students and researchers seeking to gain a deep understanding of the theory of machine learning.' Shai Shalev-Shwartz, Hebrew University of Jerusalem
Table of Contents1. Introduction; 2. Basic probability inequalities for sums of independent random variables; 3. Uniform convergence and generalization analysis; 4. Empirical covering number analysis and symmetrization; 5. Covering number estimates; 6. Rademacher complexity and concentration inequalities; 7. Algorithmic stability analysis; 8. Model selection; 9. Analysis of kernel methods; 10. Additive and sparse models; 11. Analysis of neural networks; 12. Lower bounds and minimax analysis; 13. Probability inequalities for sequential random variables; 14. Basic concepts of online learning; 15. Online aggregation and second order algorithms; 16. Multi-armed bandits; 17. Contextual bandits; 18. Reinforcement learning; A. Basics of convex analysis; B. f-Divergence of probability measures; References; Author index; Subject index.
