High-Dimensional Probability

'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.

• The most accessible book on the subject, designed so that students who finish basic undergraduate courses can jump right to this material
• Updated with 200 new exercises to assist with course design, and extra hints added to help with self-study
• Selects the core ideas and methods and presents them systematically with modern motivating applications to bring readers quickly up to speed