A doubly sparse approach for group variable selection

Sunghoon Kwon, Jeongyoun Ahn, Woncheol Jang, Sangin Lee and Yongdai Kim ()
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Sunghoon Kwon: Konkuk University
Jeongyoun Ahn: University of Georgia
Woncheol Jang: Seoul National University
Sangin Lee: University of Texas Southwestern Medical Center
Yongdai Kim: Seoul National University

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 5, No 3, 997-1025

Abstract: Abstract We propose a new penalty called the doubly sparse (DS) penalty for variable selection in high-dimensional linear regression models when the covariates are naturally grouped. An advantage of the DS penalty over other penalties is that it provides a clear way of controlling sparsity between and within groups, separately. We prove that there exists a unique global minimizer of the DS penalized sum of squares of residuals and show how the DS penalty selects groups and variables within selected groups, even when the number of groups exceeds the sample size. An efficient optimization algorithm is introduced also. Results from simulation studies and real data analysis show that the DS penalty outperforms other existing penalties with finite samples.

Keywords: Doubly sparse penalty; Group selection; Group selection consistency; Variable selection (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10463-016-0571-z

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