Concentration - of - measure inequalities Lecture notes by Gábor Lugosi

Concentration - of - measure inequalities Lecture notes

Moment Inequalities for Functions of Independent Random Variables by Stéphane Boucheron,1 Olivier Bousquet,

A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions [Boucheron, Lugosi and Massart Ann. Probab. 31 (2003) 1583–1614], and is based on a generalized tensorization inequality due to Latała and Oleszkiewicz [Lecture Note...

Concentration inequalities using the entropy method

We investigate a new methodology, worked out by Ledoux and Mas-sart, 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 p...

On concentration of self-bounding functions

We prove some new concentration inequalities for self-bounding functions using the entropy method. As an application, we recover Talagrand’s convex distance inequality. The new Bernstein-like inequalities for self-bounding functions are derived thanks to a careful analysis of the so-called Herbst argument. The latter involves comparison results between solutions of differential inequalities tha...

A sharp concentration inequality with applications

We present a new general concentration-of-measure inequality and illustrate its power by applications in random combinatorics. The results nd direct applications in some problems of learning theory. The work of the second author was supported by DGES grant PB96-0300