Risk bounds for statistical learning

• 成果类型: Article
• 署名作者: Massart, Pascal; Nedelec, Elodie
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000786
• 发表日期: 2006
• 页码: 2326-2366
• 关键词: Concentration Inequalities; Empirical Processes; CONVERGENCE; rates

摘要

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM). We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type conditions by using concentration inequalities for conveniently weighted empirical processes. This allows us to deal with ways of measuring the size of a class of classifiers other than entropy with bracketing as in Tsybakov's work. In particular, we derive new risk bounds for the ERM when the classification rules belong to some VC-class under margin conditions and discuss the optimality of these bounds in a minimax sense.