Concentration inequalities : a nonasymptotic theory of independence
 Author/Creator
 Boucheron, Stephane.
 Language
 English.
 Edition
 1st ed.
 Imprint
 Oxford, U.K. : Oxford University Press, 2013.
 Physical description
 x, 481 p. : ill. ; 24 cm.
Access
Contributors
 Contributor
 Lugosi, Gábor.
 Massart, Pascal.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [451]472) and indexes.
 Contents

 Foreword  1. Introduction  2. Basic inequalities  3. Bounding the variance  4. Basic information inequalities  5. Logarithmic Sobolev inequalities  6. The entropy method  7. Concentration and isoperimetry  8. The transportation method  9. Influences and threshold phenomena  10. Isoperimetry on the hypercube and Gaussian spaces  11. The variance of suprema of empirical processes  12. Suprema of empirical processes: exponential inequalities  13. The expected value of suprema of empirical processes  14. PHIentropies  15. Moment inequalities.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 highdimensional 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 selfcontained 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Stéphane Boucheron, Gábor Lugosi, Pascal Massart.
 ISBN
 9780199535255
 0199535256