Safe screening with variational inequalities and its application to lasso

Jun Liu, Zheng Zhao, Jie Wang, Jieping Ye

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Scopus citations

Abstract

Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for a certain value of the regularization parameter, is a technique for improving the computational efficiency. Safe screening is gaining increasing attention since 1) solving sparse learning formulations usually has a high computational cost especially when the number of features is large and 2) one needs to try several regularization parameters to select a suitable model. In this paper, we propose an approach called "Sasvi" (Safe screening with variational inequalities). Sasvi makes use of the variational inequality that provides the sufficient and necessary optimality condition for the dual problem. Several existing approaches for Lasso screening can be casted as relaxed versions of the proposed Sasvi, thus Sasvi provides a stronger safe screening rule. We further study the monotone properties of Sasvi for Lasso, based on which a sure removal regularization parameter can be identified for each feature. Experimental results on both synthetic and real data sets are reported to demonstrate the effectiveness of the proposed Sasvi for Lasso screening.

Original languageEnglish (US)
Title of host publication31st International Conference on Machine Learning, ICML 2014
PublisherInternational Machine Learning Society (IMLS)
Pages1556-1571
Number of pages16
ISBN (Electronic)9781634393973
StatePublished - Jan 1 2014
Event31st International Conference on Machine Learning, ICML 2014 - Beijing, China
Duration: Jun 21 2014Jun 26 2014

Publication series

Name31st International Conference on Machine Learning, ICML 2014
Volume2

Other

Other31st International Conference on Machine Learning, ICML 2014
CountryChina
CityBeijing
Period6/21/146/26/14

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ASJC Scopus subject areas

  • Artificial Intelligence
  • Computer Networks and Communications
  • Software

Cite this

Liu, J., Zhao, Z., Wang, J., & Ye, J. (2014). Safe screening with variational inequalities and its application to lasso. In 31st International Conference on Machine Learning, ICML 2014 (pp. 1556-1571). (31st International Conference on Machine Learning, ICML 2014; Vol. 2). International Machine Learning Society (IMLS).