國立虎尾科技大學 |

High-dimensional probability = an introduction with applications in data science /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	High-dimensional probability/ Roman Vershynin.
Reminder of title:	an introduction with applications in data science /
Author:	Vershynin, Roman.
Published:	Cambridge :Cambridge University Press, : 2018.,
Description:	xiv, 284 p. :ill., digital ; : 24 cm.;
Notes:	Title from publisher's bibliographic system (viewed on 28 Sep 2018).
Subject:	Probabilities. -
Online resource:	https://doi.org/10.1017/9781108231596
ISBN:	9781108231596

High-dimensional probability = an introduction with applications in data science /
Vershynin, Roman.

High-dimensional probabilityan introduction with applications in data science /[electronic resource] :Roman Vershynin. - Cambridge :Cambridge University Press,2018. - xiv, 284 p. :ill., digital ;24 cm. - Cambridge series in statistical and probabilistic mathematics ;47. - Cambridge series in statistical and probabilistic mathematics ;53..

Title from publisher's bibliographic system (viewed on 28 Sep 2018).

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.

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.

ISBN: 9781108231596Subjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273 / .V4485 2018

Dewey Class. No.: 519.2

High-dimensional probability = an introduction with applications in data science /
LDR:02458nam a2200265 a 4500 001 1114155
003 UkCbUP
005 20181002135011.0
006 m d
007 cr nn 008maaau
008 231225s2018 enk o 1 0 eng d
020 $a 9781108231596 $q (electronic bk.)
020 $a 9781108415194 $q (hardback)
035 $a CR9781108231596
040 $a UkCbUP $b eng $c UkCbUP $d GP
050 0 0 $a QA273 $b .V4485 2018
082 0 0 $a 519.2 $2 23
090 $a QA273 $b .V563 2018
100 1 $a Vershynin, Roman. $3 1426864
245 1 0 $a High-dimensional probability $h [electronic resource] : $b an introduction with applications in data science / $c Roman Vershynin.
260 $a Cambridge : $b Cambridge University Press, $c 2018.
300 $a xiv, 284 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge series in statistical and probabilistic mathematics ; $v 47
500 $a Title from publisher's bibliographic system (viewed on 28 Sep 2018).
505 0 $a 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.
520 $a 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.
650 0 $a Probabilities. $3 527847
650 0 $a Stochastic processes. $3 528256
650 0 $a Random variables. $3 598296
830 0 $a Cambridge series in statistical and probabilistic mathematics ; $v 53. $3 1405725
856 4 0 $u https://doi.org/10.1017/9781108231596