PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Concentration inequalities using the entropy method
Stephane Boucheron, Pascal Massart and Gabor LUGOSI
The Annals of Probability Volume 31, Number 3, pp. 1583-1614, 2003. ISSN 0091-1798

Abstract

We investigate a new methodology, worked out by Ledoux and Massart,to prove concentration-of-measure inequalities. The method is based on certain modified logarithmic Sobolev inequalities. We provide some very simple and general ready-to-use inequalities. One of these inequalities may be considered as an exponential version of the Efron-Stein inequality. The main purpose of this paper is to point out the simplicity and the generality of the approach. We show how the new method can recover many of Talagrand's revolutionary inequalities and provide new applications in a variety of problems including Rademacher averages, Rademacher chaos, the number of certain small subgraphs in a random graph, and the minimum of the empirical risk in some statistical estimation problems.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
ID Code:622
Deposited By:Michele Sebag
Deposited On:29 December 2004