Vapnik-Chervonenkis type conditions and uniform Donsker classes of functions

• 成果类型: Article
• 署名作者: Talagrand, M
• 署名单位: Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University System of Ohio; Ohio State University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1055425790
• 发表日期: 2003
• 页码: 1565-1582
• 关键词: glivenko-cantelli problem; entropy

摘要

Given a bounded class of functions, we introduce a combinatorial quantity (related to the idea of Vapnik-Chervonenkis classes) that is much more explicit than the Koltchinskii-Pollard entropy, but is proved to be essentially of the same order.