“High-Dimensional Probability — An Introduction with Applications in Data Science”, by Roman Vershynin

UPDATED 341-page PDF 2nd Edition — download from the author’s website: https://math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.html…

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High-Dimensional Probability

Source: https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.html

Who is this book for?

This textbook is aimed at doctoral students, advanced master’s students, and beginning researchers in mathematics, statistics, computer science, electrical engineering, and related fields who seek a deeper understanding of probabilistic methods used in modern data science research. It can be used for self-study or as a textbook for a second probability course.

Why this book?

Data science evolves rapidly, and probabilistic methods are central to these advances. A traditional graduate probability course often does not provide the mathematical sophistication required for modern research in data science. This book fills that gap.

Are you ready?

You should know probability theory at the master’s or doctoral level, strong undergraduate linear algebra, and basic metric, normed, and Hilbert spaces. Measure theory is not required.

Quick intro

February 19, 2026 -- Second edition published September 30, 2018 -- First edition published