Concentration Inequalities

Author : Stéphane Boucheron
Publisher : Oxford University Press
ISBN 13 : 0199535256
Total Pages : 492 pages
Book Rating : 4.55/5 ( download)

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Download or read book Concentration Inequalities written by Stéphane Boucheron and published by Oxford University Press. This book was released on 2013-02-07 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented.

Author : Joel Tropp
Publisher :
ISBN 13 : 9781601988386
Total Pages : 256 pages
Book Rating : 4.89/5 ( download)

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Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Tropp and published by . This book was released on 2015-05-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.

Author : Bernard Bercu
Publisher : Springer
ISBN 13 : 3319220993
Total Pages : 120 pages
Book Rating : 4.94/5 ( download)

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Download or read book Concentration Inequalities for Sums and Martingales written by Bernard Bercu and published by Springer. This book was released on 2015-09-29 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.

Author : Pascal Massart
Publisher : Springer
ISBN 13 : 3540485031
Total Pages : 343 pages
Book Rating : 4.32/5 ( download)

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Download or read book Concentration Inequalities and Model Selection written by Pascal Massart and published by Springer. This book was released on 2007-04-26 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration inequalities have been recognized as fundamental tools in several domains such as geometry of Banach spaces or random combinatorics. They also turn to be essential tools to develop a non asymptotic theory in statistics. This volume provides an overview of a non asymptotic theory for model selection. It also discusses some selected applications to variable selection, change points detection and statistical learning.

Author : Maxim Raginsky
Publisher :
ISBN 13 : 9781601989062
Total Pages : 256 pages
Book Rating : 4.67/5 ( download)

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Download or read book Concentration of Measure Inequalities in Information Theory, Communications, and Coding written by Maxim Raginsky and published by . This book was released on 2014 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration of Measure Inequalities in Information Theory, Communications, and Coding focuses on some of the key modern mathematical tools that are used for the derivation of concentration inequalities, on their links to information theory, and on their various applications to communications and coding.

Author : Stéphane Boucheron
Publisher : OUP Oxford
ISBN 13 : 0191655503
Total Pages : 496 pages
Book Rating : 4.00/5 ( download)

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Download or read book Concentration Inequalities written by Stéphane Boucheron and published by OUP Oxford. This book was released on 2013-02-08 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in an accessible way by covering the key developments and applications in the field. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented. A self-contained introduction to concentration inequalities, it includes a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes. Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.94/5 ( download)

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Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Author : Michel Ledoux
Publisher : American Mathematical Soc.
ISBN 13 : 0821837923
Total Pages : 194 pages
Book Rating : 4.24/5 ( download)

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Download or read book The Concentration of Measure Phenomenon written by Michel Ledoux and published by American Mathematical Soc.. This book was released on 2001 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. This book offers the basic techniques and examples of the concentration of measure phenomenon. It presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications and product measures.

Author : Devdatt P. Dubhashi
Publisher : Cambridge University Press
ISBN 13 : 0521884276
Total Pages : 213 pages
Book Rating : 4.73/5 ( download)

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Download or read book Concentration of Measure for the Analysis of Randomized Algorithms written by Devdatt P. Dubhashi and published by Cambridge University Press. This book was released on 2009-06-15 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent and unified account of classical and more advanced techniques for analyzing the performance of randomized algorithms.

Author : Olivier Bousquet
Publisher : Springer
ISBN 13 : 3540286500
Total Pages : 246 pages
Book Rating : 4.09/5 ( download)

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Download or read book Advanced Lectures on Machine Learning written by Olivier Bousquet and published by Springer. This book was released on 2011-03-22 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine Learning has become a key enabling technology for many engineering applications, investigating scientific questions and theoretical problems alike. To stimulate discussions and to disseminate new results, a summer school series was started in February 2002, the documentation of which is published as LNAI 2600. This book presents revised lectures of two subsequent summer schools held in 2003 in Canberra, Australia, and in Tübingen, Germany. The tutorial lectures included are devoted to statistical learning theory, unsupervised learning, Bayesian inference, and applications in pattern recognition; they provide in-depth overviews of exciting new developments and contain a large number of references. Graduate students, lecturers, researchers and professionals alike will find this book a useful resource in learning and teaching machine learning.