Sparse optimization for nonconvex group penalized estimation

제목
Sparse optimization for nonconvex group penalized estimation
저자

Sangin Lee; Oh, Miae; Yongdai Kim

키워드
concave convex procedure; group LASSO; nonconvex penalty; variable selection
발행연도
2015-03-30
발행기관
Taylor & Francis
Series
Journal of Statistical Computation and Simulation, vol. 86, no. 3, pp. 597 - 610
Journal Title
Journal of Statistical Computation and Simulation
초록
We consider a linear regression model where there are group structures in covariates. The group LASSO has been proposed for group variable selections. Many nonconvex penalties such as smoothly clipped absolute deviation and minimax concave penalty were extended to group variable selection problems. The group coordinate descent (GCD) algorithm is used popularly for fitting these models. However, the GCD algorithms are hard to be applied to nonconvex group penalties due to computational complexity unless the design matrix is orthogonal. In this paper, we propose an efficient optimization algorithm for nonconvex group penalties by combining the concave convex procedure and the group LASSO algorithm. We also extend the proposed algorithm for generalized linear models. We evaluate numerical efficiency of the proposed algorithm compared to existing GCD algorithms through simulated data and real data sets.
ISSN
0094-9655
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