عنوان

High-dimensional probability

Terms of Availability and/or Price

9781108231596

(Number (ISBN

9781108415194

Number

E2741

.Language of Text, Soundtrack etc

انگلیسی

Title Proper

High-dimensional probability

General Material Designation

[Electronic book]

Other Title Information

: an introduction with applications in data science

First Statement of Responsibility

/ Roman Vershynin.

Place of Publication, Distribution, etc.

Cambridge, UK

Name of Publisher, Distributor, etc.

: Cambridge University Press

Date of Publication, Distribution, etc.

, 2018.

Series Title

(Cambridge series on statistical and probabilistic mathematics

Volume Designation

; 47)

Text of Note

Includes bibliographical references and index.

Text of Note

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.

0

Text of Note

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

Entry Element

Probabilities

Entry Element

Stochastic processes

Entry Element

Random variables

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a06

a08

Class number

Book number

Vershynin, Roman, 1974-

Country

ایران

Agency

University of Tehran. Library of College of Science

Date and Hour of Consultation and Access

UT_SCI_BL_DB_1002949_0001.pdf

e

BL

278840

1

a

Y