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High-Dimensional Probability : An Introduction with Applications in Data Science. 2nd Revised edition.
・ISBN 978-1-009-49064-1 hard GB£ 65.00
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電子版あり 大学・学術機関向け電子ブック（eBook）ISBN 978-1-009-49067-2
| 著者・編者 | Vershynin, Roman, |
|---|---|
| シリーズ | Cambridge Series in Statistical and Probabilistic Mathematics |
| 出版社 | (Cambridge University Press, UK) |
| 出版年月 | 2026 |
| ページ数 | 346 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-18282＞ |
解説
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.