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A doubly sparse approach for group variable selection

Author

Listed:
  • 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)

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.

Suggested Citation

  • Sunghoon Kwon & Jeongyoun Ahn & Woncheol Jang & Sangin Lee & Yongdai Kim, 2017. "A doubly sparse approach for group variable selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 997-1025, October.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0571-z
    DOI: 10.1007/s10463-016-0571-z
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    References listed on IDEAS

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