SPADES AND MIXTURE MODELS

• 成果类型: Article
• 署名作者: Bunea, Florentina; Tsybakov, Alexandre B.; Wegkamp, Marten H.; Barbu, Adrian
• 署名单位: State University System of Florida; Florida State University; Institut Polytechnique de Paris; ENSAE Paris; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS790
• 发表日期: 2010
• 页码: 2525-2558
• 关键词: VARIABLE SELECTION; DENSITY-ESTIMATION; sparsity; Lasso; aggregation; l(1)

摘要

This paper studies sparse density estimation via l(1) penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a general sparsity oracle inequality that the SPADES estimates satisfy. We offer a data driven method for the choice of the tuning parameter used in the construction of SPADES. The method uses the generalized bisection method first introduced in [10]. The suggested procedure bypasses the need for a grid search and offers substantial computational savings. We complement our theoretical results with a simulation study that employs this method for approximations of one and two-dimensional densities with mixtures. The numerical results strongly support our theoretical findings.