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High-Dimensional Probability - pr_130640

High-Dimensional Probability

An Introduction with Applications in Data Science



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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.

Product code: 9781108415194

ISBN 9781108415194
Dimensions (HxWxD in mm) H260xW183xS22
No. Of Pages 296
Publisher Cambridge University Press
Series Cambridge Series in Statistical and Probabilistic Mathematics
The data sciences are moving fast, and probabilistic methods are both the foundation and a driver. This highly motivated text brings beginners up to speed quickly and provides working data scientists with powerful new tools. Ideal for a basic second course in probability with a view to data science applications, it is also suitable for self-study.