Selective factor extraction in high dimensions

• 成果类型: Article
• 署名作者: She, Yiyuan
• 署名单位: State University System of Florida; Florida State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw059
• 发表日期: 2017
• 页码: 97110
• 关键词: Principal component analysis; Oracle Inequalities; variable selection; face recognition; SPARSE; regression

摘要

This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset of input features. The proposed estimators enjoy sharp oracle inequalities, and with a predictive information criterion for model selection, they adapt to unknown sparsity by controlling both rank and row support of the coefficient matrix. A class of algorithms is developed that can accommodate various convex and nonconvex sparsity-inducing penalties, and can be used for rank-constrained variable screening in high-dimensional multivariate data. The paper also showcases applications in macroeconomics and computer vision to demonstrate how low-dimensional data structures can be effectively captured by joint variable selection and projection.