High-dimensional probability :
Vershynin, Roman, 1974-
High-dimensional probability : an introduction with applications in data science / Roman Vershynin. - Cambridge : Cambridge University Press, 2018. - 1 online resource (xiv, 284 pages) : digital, PDF file(s). - Cambridge series in statistical and probabilistic mathematics ; 47 . - Cambridge series in statistical and probabilistic mathematics ; 47. .
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.
9781108231596 (ebook)
Probabilities.
Stochastic processes.
Random variables.
QA273 / .V4485 2018
519.2
High-dimensional probability : an introduction with applications in data science / Roman Vershynin. - Cambridge : Cambridge University Press, 2018. - 1 online resource (xiv, 284 pages) : digital, PDF file(s). - Cambridge series in statistical and probabilistic mathematics ; 47 . - Cambridge series in statistical and probabilistic mathematics ; 47. .
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.
9781108231596 (ebook)
Probabilities.
Stochastic processes.
Random variables.
QA273 / .V4485 2018
519.2