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Home High-Dimensional Probability (An Introduction with Applications in Data Science)
High-Dimensional Probability (An Introduction with Applications in Data Science)
by Cambridge University Press
Author: Vershynin, Roman
Brand: Cambridge University Press
Details: Product 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. Review 'This is an excellent and very timely text, presenting the modern tools of high-dimensional geometry and probability in a very accessible and applications-oriented manner, with plenty of informative exercises. The book is infused with the author's insights and intuition in this field, and has extensive references to the latest developments in the area. This book will be an extremely useful resource both for newcomers to this subject and for expert researchers.' Terence Tao, University of California, Los Angeles 'Methods of high-dimensional probability have become indispensable in numerous problems of probability theory and its applications in mathematics, statistics, computer science, and electrical engineering. Roman Vershynin's wonderful text fills a major gap in the literature by providing a highly accessible introduction to this area. Starting with no prerequisites beyond a first course in probability and linear algebra, Vershynin takes the reader on a guided tour through the subject and consistently illustrates the utility of the material through modern data science applications. This book should be essential reading for students and researchers in probability theory, data science, and related fields.' Ramon van Handel, Princeton University, New Jersey 'This very welcome contribution to the literature gives a concise introduction to several topics in 'high-dimensional probability' that are of key relevance in contemporary statistical science and machine learning. The author achieves a fine balance between presenting deep theory and maintaining readability for a non-specialist audience - this book is thus highly recommended for graduate students and researchers alike who wish to learn more about this by now indispensable field of modern mathematics.' Richard Nickl, University of Cambridge 'Vershynin is one of the world's leading experts in the area of high-dimensional probability, and his textbook provides a gentle yet thorough treatment of many of the key tools in the area and their applications to the field of data science. The topics covered here are a must-know for anyone looking to do mathematical work in the field, covering subjects important in machine learning, algorithms and theoretical computer science, signal processing, and applied mathematics.' Jelani Nelson, Harvard University, Massachusetts 'High-Dimensional Probability is an excellent treatment of modern methods in probability and data analysis. Vershynin's perspective is unique and insightful, informed by his expertise as both a probabilist and a functional analyst. His treatment of the subject is gentle, thorough and inviting, providing a great resource for both newcomers and those familiar with the subject. I believe, as the author does, that the topics covered in this book are indeed ess
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