10.1184/R1/6476330.v1 Xi Chen Xi Chen Qihang Lin Qihang Lin Seyoung Kim Seyoung Kim Jaime G. Carbonell Jaime G. Carbonell Eric P Xing Eric P Xing Smoothing Proximal Gradient Method for General Structured Sparse Learning Carnegie Mellon University 2011 Machine Learning 2011-07-01 00:00:00 Journal contribution https://kilthub.cmu.edu/articles/journal_contribution/Smoothing_Proximal_Gradient_Method_for_General_Structured_Sparse_Learning/6476330 <p>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 l1/l2 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-sparsity-inducing penalties. Our approach is based on a general smoothing technique of Nesterov. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used interior-point method. Numerical results are reported to demonstrate the efficiency and scalability of the proposed method.</p>