Open Access
June 2012 Smoothing proximal gradient method for general structured sparse regression
Xi Chen, Qihang Lin, Seyoung Kim, Jaime G. Carbonell, Eric P. Xing
Ann. Appl. Stat. 6(2): 719-752 (June 2012). DOI: 10.1214/11-AOAS514


We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlapping-group-lasso penalty, generalized from the group-lasso penalty; and (2) the graph-guided-fused-lasso penalty, generalized from the fused-lasso penalty. For both types of penalties, due to their nonseparability and nonsmoothness, developing an efficient optimization method remains a challenging problem. In this paper we propose a general optimization approach, the smoothing proximal gradient (SPG) method, which can solve structured sparse regression problems with any smooth convex loss under a wide spectrum of structured sparsity-inducing penalties. Our approach combines a smoothing technique with an effective proximal gradient method. It achieves a convergence rate significantly faster than the standard first-order methods, subgradient methods, and is much more scalable than the most widely used interior-point methods. The efficiency and scalability of our method are demonstrated on both simulation experiments and real genetic data sets.


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Xi Chen. Qihang Lin. Seyoung Kim. Jaime G. Carbonell. Eric P. Xing. "Smoothing proximal gradient method for general structured sparse regression." Ann. Appl. Stat. 6 (2) 719 - 752, June 2012.


Published: June 2012
First available in Project Euclid: 11 June 2012

zbMATH: 1243.62100
MathSciNet: MR2976489
Digital Object Identifier: 10.1214/11-AOAS514

Keywords: optimization , proximal gradient , smoothing , Sparse regression , structured sparsity

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.6 • No. 2 • June 2012
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