Smoothing Proximal Gradient Method for General Structured Sparse Learning

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, based on the 1/ 2 mixed-norm penalty, and 2) graph-guided fusion penalty. For both types of penalties, due to their non-separability, developing an efficient optimization method has remained a challenging problem. In this paper, we propose a general optimization approach, called smoothing proximal gradient method, which can solve the structured sparse regression problems with a smooth convex loss and a wide spectrum of structured-sparsityinducing penalties. Our approach is based on a general smoothing technique of Nesterov [17]. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used...

• Type: Journal
• Year: 2012
• Where: CORR
• Authors: Xi Chen, Qihang Lin, Seyoung Kim, Jaime G. Carbonell, Eric P. Xing
• Keywords: CORR 2012, Education, Gradient Method, Interior Point Method, Regression Problems