Title

Ultrahigh-Dimensional Robust and Efficient Sparse Regression Using Non-Concave Penalized Density Power Divergence

Document Type

Research Article

Publication Title

IEEE Transactions on Information Theory

Abstract

We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression are based on\ell_{1}-penalization, and their theoretical properties are not well-investigated. In contrast, we use a general class of folded concave penalties that ensure sparse recovery and consistent estimation of regression coefficients. We propose an alternating algorithm based on the Concave-Convex procedure to obtain our estimate, and demonstrate its robustness properties using influence function analysis. Under some conditions on the fixed design matrix and penalty function, we prove that this estimator possesses large-sample oracle properties in an ultrahigh-dimensional regime. The performance and effectiveness of our proposed method for parameter estimation and prediction compared to state-of-the-art are demonstrated through simulation studies.

First Page

7812

Last Page

7827

DOI

10.1109/TIT.2020.3013015

Publication Date

12-2020

Comments

Open Access, Green

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