Open Access
Translator Disclaimer
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

Abstract

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.

Citation

Download Citation

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. https://doi.org/10.1214/11-AOAS514

Information

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

JOURNAL ARTICLE
34 PAGES


SHARE
Vol.6 • No. 2 • June 2012
Back to Top