Description: High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.
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EAN: 9781108415194
UPC: 9781108415194
ISBN: 9781108415194
MPN: N/A
Book Title: High-Dimensional Probability: An Introduction with
Number of Pages: 296 Pages
Language: English
Publication Name: High-Dimensional Probability : an Introduction with Applications in Data Science
Publisher: Cambridge University Press
Subject: Probability & Statistics / Stochastic Processes, Probability & Statistics / General
Publication Year: 2018
Item Height: 0.9 in
Item Weight: 25.2 Oz
Type: Textbook
Author: Roman Vershynin
Subject Area: Mathematics
Item Length: 10.2 in
Series: Cambridge Series in Statistical and Probabilistic Mathematics Ser.
Item Width: 7.2 in
Format: Hardcover
