Aggregation via empirical risk minimization

• 成果类型: Article
• 署名作者: Lecue, Guillaume; Mendelson, Shahar
• 署名单位: Australian National University; Technion Israel Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0180-8
• 发表日期: 2009
• 页码: 591-613
• 关键词: convexity; bounds

摘要

Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F. It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show that this conjecture is false. Despite that, we prove that empirical minimization in the convex hull of a well chosen, empirically determined subset of F is an optimal aggregation method.