High-Dimensional Probability
An Introduction with Applications in Data Science
2nd Edition
Will be published approx. on 31. March 2026
Book
Hardback
346 pages
978-1-009-49064-1 (ISBN)
Description
'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.
More details
Series
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Edition type
Revised edition
Illustrations
Worked examples or Exercises
Dimensions
Height: 260 mm
Width: 183 mm
Thickness: 23 mm
Weight
846 gr
ISBN-13
978-1-009-49064-1 (9781009490641)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Previous edition
Book
09/2018
Cambridge University Press
€83.40
Shipment within 15-20 days
Person
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.
Content
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.