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" High-dimensional probability : "
Roman Vershynin, University of California, Irvine.
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BL
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| Record Number
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839340
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| Main Entry
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Vershynin, Roman,1974-
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| Title & Author
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High-dimensional probability : : an introduction with applications in data science /\ Roman Vershynin, University of California, Irvine.
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| Publication Statement
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Cambridge, United Kingdom ;New York, NY :: Cambridge University Press,, 2018.
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, ©2018
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| Series Statement
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Cambridge series in statistical and probabilistic mathematics ;; 47
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| Page. NO
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1 online resource (xiv, 284 pages) :: illustrations
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| ISBN
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1108231594
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: 9781108231596
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1108415199
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9781108415194
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Preliminaries on random variables -- Concentration of sums of independent random variables -- Random vectors in high dimensions -- Random matrices -- Concentration without independence -- Quadratic forms, symmetrization and contraction -- Random processes -- Chaining -- Deviations of random matrices and geometric consequences -- Sparse recovery -- Dvoretzky-Milman's theorem.
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| Abstract
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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.
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| Subject
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Probabilities.
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Random variables.
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Stochastic processes.
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Probabilities.
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Random variables.
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Stochastic processes.
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| Dewey Classification
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519.2
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| LC Classification
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QA273.V4485 2018
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