LEARNING BY MIRROR AVERAGING

• 成果类型: Article
• 署名作者: Juditsky, A.; Rigollet, P.; Tsybakov, A. B.
• 署名单位: Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria; University System of Georgia; Georgia Institute of Technology; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS546
• 发表日期: 2008
• 页码: 2183-2206
• 关键词: model selection; aggregation; prediction

摘要

Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion. We define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original nonlinear one and constitutes a special case of the mirror averaging algorithm. We show that the aggregate satisfies sharp oracle inequalities under some general assumptions. The results are applied to several problems including regression, classification and density estimation.