DETECTION AND FEATURE SELECTION IN SPARSE MIXTURE MODELS

• 成果类型: Article
• 署名作者: Verzelen, Nicolas; Arias-Castro, Ery
• 署名单位: INRAE; University of California System; University of California San Diego
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1513
• 发表日期: 2017
• 页码: 1920-1950
• 关键词: principal-components; variable selection; PCA; CLASSIFICATION; skewness; kurtosis; bounds

摘要

We consider Gaussian mixture models in high dimensions, focusing on the twin tasks of detection and feature selection. Under sparsity assumptions on the difference in means, we derive minimax rates for the problems of testing and of variable selection. We find these rates to depend crucially on the knowledge of the covariance matrices and on whether the mixture is symmetric or not. We establish the performance of various procedures, including the top sparse eigenvalue of the sample covariance matrix ( popular in the context of Sparse PCA), as well as new tests inspired by the normality tests of Malkovich and Afifi [J. Amer. Statist. Assoc. 68 (1973) 176-179].