Random Matrix Methods for Machine Learning

Erscheinungsjahr 2022
ISBN: 978-1-009-12323-5
Verlag: Cambridge University Press

Buch, Englisch, 408 Seiten, Format (B × H): 173 mm x 247 mm, Gewicht: 890 g

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.

Autoren/Hrsg.

Couillet, Romain

Liao, Zhenyu

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Automatische Datenerfassung, Datenanalyse
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen

Inhaltsverzeichnis

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.

Über Autor(innen)

Couillet, Romain
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.

Liao, Zhenyu
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.