Random Matrix Methods for Machine Learning

Inbunden, Engelska, 2022

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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.

Produktinformation

Utgivningsdatum2022-07-21
Mått174 x 251 x 23 mm
Vikt870 g
FormatInbunden
SpråkEngelska
Antal sidor408
FörlagCambridge University Press
ISBN9781009123235

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Romain Couillet is a Full Professor at Grenoble-Alpes University, France. Prior to that, he was a Full Professor at CentraleSupélec, 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 Supélec Foundation Ph.D. Fellowship of University of Paris-Saclay, France.

'Roman Couillet's book is unique among books on random matrix theory in that it provides a solid yet accessible introduction to the theory and its transformative potential in applications. After presenting a coherent and uncluttered introduction of the theory, several chapters illustrate how it applies to important problems, including, high dimensional statistical inference, neural networks, random graphs, and convex optimization. Written in a self-contained and exceptionally clear style this book will be of great utility to researchers in machine learning, statistics and signal processing who want to learn about how random matrix theory can be applied.' Alfred Hero, University of Michigan