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.
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook Mathematical Analysis of Machine Learning Algorithms for free.
- Title
- Mathematical Analysis of Machine Learning Algorithms
- Publisher
- Cambridge University Press
- Author(s)
- Tong Zhang
- Published
- 2023-08-10
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 479
- Language
- English
- ISBN-10
- 1009098381
- ISBN-13
- 9781009098380
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Chapter 1: Introduction Chapter 2: Basic Probability Inequalities Chapter 3: Uniform Convergence Chapter 4: Empirical Covering Number Analysis and Symmetrization Chapter 5: Covering Number Estimates Chapter 6: Rademacher Complexity and Concentration Inequalities Chapter 7: Algorithmic Stability Analysis Chapter 8: Model Selection Chapter 9: Analysis of Kernel Methods Chapter 10: Additive and Sparse Models Chapter 11: Analysis of Neural Networks Chapter 12: Lower Bounds and Minimax Analysis Chapter 13: Probability Inequalities for Sequential Random Variables Chapter 14: Basic Concepts of Online Learning Chapter 15: Online Aggregation and Second Order Algorithms Chapter 16: Multi-armed Bandits Chapter 17: Contextual Bandits Chapter 18: Reinforcement Learning