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High-Dimensional Probability: An Introduction with Applications in Data Science
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High-Dimensional Probability: An Introduction with Applications in Data Science Hardback - 2018

by Roman Vershynin

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From the publisher

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.

Details

  • Title High-Dimensional Probability: An Introduction with Applications in Data Science
  • Author Roman Vershynin
  • Binding Hardback
  • Pages 296
  • Volumes 1
  • Language ENG
  • Publisher Cambridge University Press
  • Publication date 2018-09-27
  • Features Bibliography, Index
  • ISBN 9781108415194 / 1108415199
  • Weight 1.56 lbs (0.71 kg)
  • Dimensions 10.3 x 7.38 x 0.9 in (26.16 x 18.75 x 2.29 cm)
  • Category Mathematics
  • Library of Congress subjects Stochastic processes, Probabilities
  • Library of Congress Catalogue Number 2018016910
  • Dewey Decimal Code 519.2
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