Concentration inequalities using the entropy method
Concentration inequalities using the entropy method
复制标题
使用熵法计算浓度不等式
DOI：
10.1214/aop/1055425791
复制
发表时间：
2003
影响因子：
2.3
通讯作者：
P. Massart
中科院分区：
文献类型：
--
作者：
S. Boucheron;G. Lugosi;P. Massart
我们研究了一种新的方法，由Ledoux和Massart提出，用来证明度量集中不等。该方法基于某些修正的对数Sobolev不等式。我们给出了一些非常简单和普遍的现成的不等式。这些不平等中的一个可以被认为是Efron-Stein不等式的指数形式。本文的主要目的是指出该方法的简单性和通用性。我们展示了新方法如何恢复许多TALAGRAND革命性的不等式，并在各种问题中提供了新的应用，包括Rademacher平均、Rademacher混沌、随机图中某些小子图的个数以及在一些统计估计问题中的经验风险最小化问题。
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.