Random Matrix Methods for Machine Learning

Romain Couillet, Zhenyu Liao

• Publisher: Cambridge University Press
• Year: 2022
• Print ISBN: 9781009123235
• eBook ISBN: 9781009301893
• Topic: Informatica
• Subtopic: Visione artificiale e riconoscimento di schemi

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.

Table of contents

• Cover
• Half-title page
• Title page
• Copyright page
• Contents
• 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