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Concentration Inequalities

2013-02-07 Mathematics
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Release : 2013-02-07
Genre : Mathematics
Kind : eBook
Book Rating : 256/5 ( reviews)

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Book Synopsis Concentration Inequalities by : Stéphane Boucheron

Download or read book Concentration Inequalities written by Stéphane Boucheron. This book was released on 2013-02-07. 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.

Concentration Inequalities for Sums and Martingales

2015-09-29 Mathematics
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Release : 2015-09-29
Genre : Mathematics
Kind : eBook
Book Rating : 993/5 ( reviews)

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Book Synopsis Concentration Inequalities for Sums and Martingales by : Bernard Bercu

Download or read book Concentration Inequalities for Sums and Martingales written by Bernard Bercu. This book was released on 2015-09-29. 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.

Concentration Inequalities and Model Selection

2007-04-26 Mathematics
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Release : 2007-04-26
Genre : Mathematics
Kind : eBook
Book Rating : 031/5 ( reviews)

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Book Synopsis Concentration Inequalities and Model Selection by : Pascal Massart

Download or read book Concentration Inequalities and Model Selection written by Pascal Massart. This book was released on 2007-04-26. 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.

Concentration of Measure Inequalities in Information Theory, Communications, and Coding

2014 Computers
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Release : 2014
Genre : Computers
Kind : eBook
Book Rating : 062/5 ( reviews)

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Book Synopsis Concentration of Measure Inequalities in Information Theory, Communications, and Coding by : Maxim Raginsky

Download or read book Concentration of Measure Inequalities in Information Theory, Communications, and Coding written by Maxim Raginsky. This book was released on 2014. 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.

An Introduction to Matrix Concentration Inequalities

2015-05-27 Computers
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Release : 2015-05-27
Genre : Computers
Kind : eBook
Book Rating : 386/5 ( reviews)

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Book Synopsis An Introduction to Matrix Concentration Inequalities by : Joel Tropp

Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Tropp. This book was released on 2015-05-27. 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.

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