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High-Dimensional Probability: An Introduction with Applications in Data

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

Item Length: 26.2 cm

Number of Pages: 296 Pages

Language: English

Publication Name: High-Dimensional Probability: an Introduction with Applications in Data Science

Publisher: Cambridge University Press

Publication Year: 2018

Subject: Economics, Computer Science, Mathematics

Item Height: 260 mm

Item Weight: 710 g

Type: Textbook

Author: Roman Vershynin

Subject Area: Data Analysis

Item Width: 183 mm

Format: Hardcover

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