Concentration Inequalities

A Nonasymptotic Theory of Independence

Nonfiction, Science & Nature, Mathematics, Statistics, Computers, General Computing
Cover of the book Concentration Inequalities by Pascal Massart, Stéphane Boucheron, Gábor Lugosi, OUP Oxford
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Pascal Massart, Stéphane Boucheron, Gábor Lugosi ISBN: 9780191655517
Publisher: OUP Oxford Publication: February 7, 2013
Imprint: OUP Oxford Language: English
Author: Pascal Massart, Stéphane Boucheron, Gábor Lugosi
ISBN: 9780191655517
Publisher: OUP Oxford
Publication: February 7, 2013
Imprint: OUP Oxford
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 from OUP Oxford

Cover of the book The Physiology of the Novel by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book French Philosophy, 1572-1675 by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Arbitration of Trust Disputes by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book The Oxford Handbook of the Eighteenth-Century Novel by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Rebel Barons by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Measuring Poverty and Wellbeing in Developing Countries by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Reference by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book The Future of the Professions by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Law and Childhood Studies by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Gender and Green Governance by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Remedies in International Human Rights Law by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Testosterone by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book A Cosmopolitan Legal Order by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Normativity and Power by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
Cover of the book Emergencies in Critical Care by Pascal Massart, Stéphane Boucheron, Gábor Lugosi
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy