Random Matrix Methods for Machine Learning

Romain / Liao Couillet

450 pages, parution le 20/07/2022

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Résumé

For graduate students, practitioners, and sophisticated users, this book offers a tutorial approach to the foundations of random matrix theory for machine learning and systematic analyses of advanced applications ranging from power detection to deep neural networks. MATLAB and Python code is provided for all concepts and applications.This book presents a unified theory of random matrices for applications in machine learning, offering a large-dimensional data vision that exploits concentration and universality phenomena. This enables a precise understanding, and possible improvements, of the core mechanisms at play in real-world machine learning algorithms. The book opens with a thorough introduction to the theoretical basics of random matrices, which serves as a support to a wide scope of applications ranging from SVMs, through semi-supervised learning, unsupervised spectral clustering, and graph methods, to neural networks and deep learning. For each application, the authors discuss small- versus large-dimensional intuitions of the problem, followed by a systematic random matrix analysis of the resulting performance and possible improvements. All concepts, applications, and variations are illustrated numerically on synthetic as well as real-world data, with MATLAB and Python code provided on the accompanying website.Preface; 1. Introduction; 2. Random matrix theory; 3. Statistical inference in Linear Models; 4. Kernel methods; 5. Large neural networks; 6. Large dimensional convex optimization; 7. Community detection on graphs; 8. Universality and real data; Bibliography; Index.Romain Couillet is a Full Professor at Grenoble-Alpes University, France. Prior to that, he was a Full Professor at CentraleSupelec, University of Paris-Saclay. His research topics are in random matrix theory applied to statistics, machine learning, and signal processing. He is the recipient of the 2021 IEEE/SEE Glavieux prize, of the 2013 CNRS Bronze Medal, and of the 2013 IEEE ComSoc Outstanding Young Researcher Award. Zhenyu Liao is an Associated Professor with Huazhong University of Science and Technology (HUST), China. He is the recipient of the 2021 East Lake Youth Talent Program Fellowship of HUST, the 2019 ED STIC Ph.D. Student Award, and the 2016 Supelec Foundation Ph.D. Fellowship of University of Paris-Saclay, France.

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Romain / Liao Couillet
Parution	20/07/2022
Nb. de pages	450
EAN13	9781009123235

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Random Matrix Methods for Machine Learning

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