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Smoothing Proximal Gradient Method for General Structured Sparse Learning
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Smoothing Proximal Gradient Method for General Structured Sparse Learning

Xi Chen, Qihang Lin, Seyoung Kim, Jaime Carbonell and Eric Xing
arXiv.org
Cornell University Library, arXiv.org
02/14/2012
DOI: 10.48550/arXiv.1202.3708
url
https://doi.org/10.48550/arXiv.1202.3708View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

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.
 Optimization Fines & penalties Nonlinear programming Regression models Smoothing Sparsity

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