High-Dimensional Probability

High-Dimensional Probability An Introduction With Applications in Data Science - Cambridge Series in Statistical and Probabilistic Mathematics

Hardback (27 Sep 2018)

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Synopsis

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.

Book information

ISBN: 9781108415194
Publisher: Cambridge University Press
Imprint: Cambridge University Press
Pub date:
DEWEY: 519.2
DEWEY edition: 23
Language: English
Number of pages: xiv, 284
Weight: 748g
Height: 256mm
Width: 189mm
Spine width: 23mm