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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 for Sums and Martingales

2017-02-22
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Release : 2017-02-22
Genre :
Kind : eBook
Book Rating : 793/5 ( reviews)

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Book Synopsis Concentration Inequalities for Sums and Martingales by : Jacob Tyler

Download or read book Concentration Inequalities for Sums and Martingales written by Jacob Tyler. This book was released on 2017-02-22. 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.

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.

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.

Probabilistic Methods for Algorithmic Discrete Mathematics

2013-03-14 Mathematics
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Release : 2013-03-14
Genre : Mathematics
Kind : eBook
Book Rating : 881/5 ( reviews)

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Book Synopsis Probabilistic Methods for Algorithmic Discrete Mathematics by : Michel Habib

Download or read book Probabilistic Methods for Algorithmic Discrete Mathematics written by Michel Habib. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: Leave nothing to chance. This cliche embodies the common belief that ran domness has no place in carefully planned methodologies, every step should be spelled out, each i dotted and each t crossed. In discrete mathematics at least, nothing could be further from the truth. Introducing random choices into algorithms can improve their performance. The application of proba bilistic tools has led to the resolution of combinatorial problems which had resisted attack for decades. The chapters in this volume explore and celebrate this fact. Our intention was to bring together, for the first time, accessible discus sions of the disparate ways in which probabilistic ideas are enriching discrete mathematics. These discussions are aimed at mathematicians with a good combinatorial background but require only a passing acquaintance with the basic definitions in probability (e.g. expected value, conditional probability). A reader who already has a firm grasp on the area will be interested in the original research, novel syntheses, and discussions of ongoing developments scattered throughout the book. Some of the most convincing demonstrations of the power of these tech niques are randomized algorithms for estimating quantities which are hard to compute exactly. One example is the randomized algorithm of Dyer, Frieze and Kannan for estimating the volume of a polyhedron. To illustrate these techniques, we consider a simple related problem. Suppose S is some region of the unit square defined by a system of polynomial inequalities: Pi (x. y) ~ o.

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