'High-Dimensional Probability,' winner of the 2019 PROSE Award in Mathematics, offers an accessible and friendly introduction to key probabilistic methods for mathematical data scientists. Streamlined and updated, this second edition integrates theory, core tools, and modern applications. Concentration inequalities are central, including classical results like Hoeffding's and Chernoff's inequalities, and modern ones like the matrix Bernstein inequality. The book also develops methods based on stochastic processes - Slepian's, Sudakov's, and Dudley's inequalities, generic chaining, and VC-based bounds. Applications include covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, and machine learning. New to this edition are 200 additional exercises, alongside extra hints to assist with self-study. Material on analysis, probability, and linear algebra has been reworked and expanded to help bridge the gap from a typical undergraduate background to a second course in probability.

Produktinformation

Utgivningsdatum:2026-02-19
Mått:254 x 29 x 174 mm
Vikt:830 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Series in Statistical and Probabilistic Mathematics
Antal sidor:346
Upplaga:2
Förlag:Cambridge University Press
ISBN:9781009490641

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Roman Vershynin is Professor of Mathematics at the University of California, Irvine. He is an expert on randomness in mathematics and data science, especially in high-dimensional probability, statistics, and machine learning. His influential work has earned numerous honors including an invited ICM lecture, the Bessel Research Award, the IMS Medallion Award, and the 2019 PROSE Award for the first edition of this book.

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'This book is a must-read for anyone interested in high-dimensional probability or its applications to data science. The second edition retains the enlightened selection of topics of the first edition, but with a more streamlined and self-contained exposition. The addition of an introductory chapter that serves as a refresher of basic concepts, and a wealth of new exercises at different levels should make the book appealing to an even broader audience.' Kavita Ramanan, Brown University

Innehållsförteckning

Foreword Sara van de Geer; Preface; Appetizer. Using probability to cover a set; 1. A quick refresher on analysis and probability; 2. Concentration of sums of independent random variables; 3. Random vectors in high dimensions; 4. Random matrices; 5. Concentration without independence; 6. Quadratic forms, symmetrization, and contraction; 7. Random processes; 8. Chaining; 9. Deviations of random matrices on sets; Hints for the exercises; References; Index.