Symmetrization approach to concentration inequalities for empirical processes
成果类型：
Article
署名作者：
Panchenko, D
署名单位：
Massachusetts Institute of Technology (MIT)
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1068646378
发表日期：
2003
页码：
2068-2081
关键词：
摘要：
We introduce a symmetrization technique that allows us to translate a problem of controlling the deviation of some functionals on a product space from their mean into a problem of controlling the deviation between two independent copies of the functional. As an application we give a new easy proof of Talagrand's concentration inequality for empirical processes, where besides symmetrization we use only Talagrand's concentration inequality on the discrete cube {0, 1}(n). As another application of this technique we prove new Vapnik-Chervonenkis type inequalities. For example, for VC-classes of functions we prove a classical inequality of Vapnik and Chervonenkis only with normalization by the sum of variance and sample variance.