ON MARGINAL SLICED INVERSE REGRESSION FOR ULTRAHIGH DIMENSIONAL MODEL-FREE FEATURE SELECTION

• 成果类型: Article
• 署名作者: Yu, Zhou; Dong, Yuexiao; Shao, Jun
• 署名单位: East China Normal University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1424
• 发表日期: 2016
• 页码: 2594-2623
• 关键词: VARIABLE SELECTION; kolmogorov filter; adaptive lasso; reduction; shrinkage

摘要

Model-free variable selection has been implemented under the sufficient dimension reduction framework since the seminal paper of Cook [Ann. Statist. 32 (2004) 1062-1092]. In this paper, we extend the marginal coordinate test for sliced inverse regression (SIR) in Cook (2004) and propose a novel marginal SIR utility for the purpose of ultrahigh dimensional feature selection. Two distinct procedures, Dantzig selector and sparse precision matrix estimation, are incorporated to get two versions of sample level marginal SIR utilities. Both procedures lead to model-free variable selection consistency with predictor dimensionality p diverging at an exponential rate of the sample size n. As a special case of marginal SIR, we ignore the correlation among the predictors and propose marginal independence SIR. Marginal independence SIR is closely related to many existing independence screening procedures in the literature, and achieves model-free screening consistency in the ultrahigh dimensional setting. The finite sample performances of the proposed procedures are studied through synthetic examples and an application to the small round blue cell tumors data.