Selective factor extraction in high dimensions

Yiyuan She

Biometrika, 2017, vol. 104, issue 1, 97-110

Abstract: SUMMARY 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.

Keywords: Information criterion; Nonconvex optimization; Oracle inequality; Principal component analysis; Reduced rank regression; Variable screening. (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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