Concentration Inequalities

It was Michel Ledoux (1997) who realized that these ideas may be used as an alternative route to some of Talagrand's exponential concentration inequalities for empirical processes and Rademacher chaos. Ledoux's ideas were taken further ...

Concentration Inequalities

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.

More Books:

Concentration Inequalities
Language: en
Pages: 496
Authors: Stéphane Boucheron, Gábor Lugosi, Pascal Massart
Categories: Mathematics
Type: BOOK - Published: 2013-02-07 - Publisher: OUP Oxford

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
Concentration Inequalities and Model Selection
Language: en
Pages: 343
Authors: Pascal Massart
Categories: Mathematics
Type: BOOK - Published: 2007-04-26 - Publisher: Springer

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
Concentration Inequalities for Sums and Martingales
Language: en
Pages: 120
Authors: Bernard Bercu, Bernard Delyon, Emmanuel Rio
Categories: Mathematics
Type: BOOK - Published: 2015-09-29 - Publisher: Springer

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
Stochastic Inequalities and Applications
Language: en
Pages: 367
Authors: Evariste Giné, Christian Houdré, David Nualart
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Birkhäuser

Concentration inequalities, which express the fact that certain complicated random variables are almost constant, have proven of utmost importance in many areas of probability and statistics. This volume contains refined versions of these inequalities, and their relationship to many applications particularly in stochastic analysis. The broad range and the high
Stochastic Inequalities
Language: en
Pages: 411
Authors: Moshe Shaked
Categories: Mathematics
Type: BOOK - Published: 1992 - Publisher: IMS

Books about Stochastic Inequalities