SMOOTHING PROXIMAL GRADIENT METHOD FOR GENERAL STRUCTURED SPARSE REGRESSION
SMOOTHING PROXIMAL GRADIENT METHOD FOR GENERAL STRUCTURED SPARSE REGRESSION
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DOI：
10.1214/11-aoas514
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发表时间：
2012-06-01
影响因子：
1.8
通讯作者：
Xing, Eric P.
中科院分区：
文献类型：
--
作者：
Chen, Xi;Lin, Qihang;Xing, Eric P.
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.
