Mathematical Analysis of Machine Learning Algorithms

Erscheinungsjahr 2023
ISBN: 978-1-009-09838-0
Verlag: Cambridge University Pr.

Buch, Englisch, 479 Seiten, Format (B × H): 180 mm x 256 mm, Gewicht: 1122 g

The mathematical theory of machine learning not only explains the current algorithms but can also motivate principled approaches for the future. This self-contained textbook introduces students and researchers of AI to the main mathematical techniques used to analyze machine learning algorithms, with motivations and applications. Topics covered include the analysis of supervised learning algorithms in the iid setting, the analysis of neural networks (e.g. neural tangent kernel and mean-field analysis), and the analysis of machine learning algorithms in the sequential decision setting (e.g. online learning, bandit problems, and reinforcement learning). Students will learn the basic mathematical tools used in the theoretical analysis of these machine learning problems and how to apply them to the analysis of various concrete algorithms. This textbook is perfect for readers who have some background knowledge of basic machine learning methods, but want to gain sufficient technical knowledge to understand research papers in theoretical machine learning.

Autoren/Hrsg.

Zhang, Thong

Zhang, Tong

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Mustererkennung, Biometrik

Inhaltsverzeichnis

1. 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.

Über Autor(innen)

Zhang, Tong
Tong Zhang is Chair Professor of Computer Science and Mathematics at the Hong Kong University of Science and Technology, where his research focuses on machine learning, big data, and their applications. A Fellow of the IEEE, the American Statistical Association, and the Institute of Mathematical Statistics, Zhang has served as Chair or Area chair at major machine learning conferences such as NeurIPS, ICML, and COLT, and he has been an associate editor for several top machine learning publications including PAMI, JMLR, and 'Machine Learning.'