October 2023 MBR The Mathematics Shelf

The Mathematics Shelf

Mathematical Analysis of Machine Learning Algorithms
Tong Zhang
Cambridge University Press
www.cambridge.org
9781009098380, $54.99, HC, 479pp

https://www.amazon.com/Mathematical-Analysis-Machine-Learning-Algorithms/dp/100909838 1

Synopsis: The mathematical theory of machine learning not only explains the current algorithms but can also motivate principled approaches for the future. "Mathematical Analysis of Machine Learning Algorithms" by Tong Zhang is self-contained textbook that introduces students and researchers of AI to the main mathematical techniques used to analyze machine learning algorithms, with motivations and applications.

The 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 also 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. "Mathematical Analysis of Machine Learning Algorithms" is ideal for anyone who has some background knowledge of basic machine learning methods, but wants to gain sufficient technical knowledge to understand research papers in theoretical machine learning.

Critique: Impressively comprehensive, exceptionally well written, effectively organized and presented, Tong Zhang's "Mathematical Analysis of Machine Learning Algorithms" is an ideal addition to personal, professional, college, and university library Computer Science collections and Programming Algorithms & Pattern Recognition curriculum studies lists. It should be noted for students and academia that "Mathematical Analysis of Machine Learning Algorithms" is also available in a digital book format (Kindle, $52.24).

Editorial Note: Tong Zhang (http://tongzhang-ml.org) 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.'

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