Square root penalty: Adaptation to the margin in classification and in edge estimation

• 成果类型: Article
• 署名作者: Tsybakov, AB; van de Geer, SA
• 署名单位: Sorbonne Universite; Universite Paris Cite; Leiden University; Leiden University - Excl LUMC
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000001066
• 发表日期: 2005
• 页码: 1203-1224
• 关键词: Complexity

摘要

We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the excess risk, that is, rates that can be faster than n(-1/2), where n is the sample size. We show that our method also gives adaptive estimators for the problem of edge estimation.