Skip to main content

Parametric simplex method for sparse learning

Author(s): Pang, H; Vanderbei, Robert; Liu, H; Zhao, T

To refer to this page use:
Abstract: © 2017 Neural information processing systems foundation. All rights reserved. High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a regularization factor, and solve them by the parametric simplex method (PSM). Our parametric simplex method offers significant advantages over other competing methods: (1) PSM naturally obtains the complete solution path for all values of the regularization parameter; (2) PSM provides a high precision dual certificate stopping criterion; (3) PSM yields sparse solutions through very few iterations, and the solution sparsity significantly reduces the computational cost per iteration. Particularly, we demonstrate the superiority of PSM over various sparse learning approaches, including Dantzig selector for sparse linear regression, LAD-Lasso for sparse robust linear regression, CLIME for sparse precision matrix estimation, sparse differential network estimation, and sparse Linear Programming Discriminant (LPD) analysis. We then provide sufficient conditions under which PSM always outputs sparse solutions such that its computational performance can be significantly boosted. Thorough numerical experiments are provided to demonstrate the outstanding performance of the PSM method.
Publication Date: 1-Jan-2017
Citation: Pang, H, Vanderbei, R, Liu, H, Zhao, T. (2017). Parametric simplex method for sparse learning. Advances in Neural Information Processing Systems, 2017-December (188 - 197
ISSN: 1049-5258
Pages: 188 - 197
Type of Material: Journal Article
Journal/Proceeding Title: Advances in Neural Information Processing Systems
Version: Author's manuscript

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.