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High-Dimensional Probability
Contributor(s): Vershynin, Roman (Author)

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 ISBN: 1108415199     ISBN-13: 9781108415194
Publisher: Cambridge University Press
OUR PRICE: $73.14  

Binding Type: Hardcover - See All Available Formats & Editions
Published: September 2018
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Additional Information
BISAC Categories:
- Mathematics | Probability & Statistics - General
Dewey: 519.2
LCCN: 2018016910
Series: Cambridge Statistical and Probabilistic Mathematics
Physical Information: 0.9" H x 7.38" W x 10.3" L (1.56 lbs) 296 pages
Features: Bibliography, Index, Price on Product
 
Descriptions, Reviews, Etc.
Publisher Description:
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.

Contributor Bio(s): Vershynin, Roman: - Roman Vershynin is Professor of Mathematics at the University of California, Irvine. He studies random geometric structures across mathematics and data sciences, in particular in random matrix theory, geometric functional analysis, convex and discrete geometry, geometric combinatorics, high-dimensional statistics, information theory, machine learning, signal processing, and numerical analysis. His honors include an Alfred Sloan Research Fellowship in 2005, an invited talk at the International Congress of Mathematicians in Hyderabad in 2010, and a Bessel Research Award from the Humboldt Foundation in 2013. His 'Introduction to the Non-Asymptotic Analysis of Random Matrices' has become a popular educational resource for many new researchers in probability and data science.
 
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