Large-scale sparse logistic regression

Jun Liu, Jianhui Chen, Jieping Ye

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

143 Scopus citations

Abstract

Logistic Regression is a well-known classification method that has been used widely in many applications of data mining, machine learning, computer vision, and bioinformatics. Sparse logistic regression embeds feature selection in the classification framework using the l1-norm regularization, and is attractive in many applications involving high-dimensional data. In this paper, we propose Lassplore for solving Large-scale sparse logistic regression. Specifically, we formulate the problem as the l1-ball constrained smooth convex optimization, and propose to solve the problem using the Nesterov's method, an optimal first-order black-box method for smooth convex optimization. One of the critical issues in the use of the Nesterov's method is the estimation of the step size at each of the optimization iterations. Previous approaches either applies the constant step size which assumes that the Lipschitz gradient is known in advance, or requires a sequence of decreasing step size which leads to slow convergence in practice. In this paper, we propose an adaptive line search scheme which allows to tune the step size adaptively and meanwhile guarantees the optimal convergence rate. Empirical comparisons with several state-of-theart algorithms demonstrate the efficiency of the proposed Lassplore algorithm for large-scale problems.

Original languageEnglish (US)
Title of host publicationKDD '09
Subtitle of host publicationProceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Pages547-555
Number of pages9
DOIs
StatePublished - Nov 9 2009
Event15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '09 - Paris, France
Duration: Jun 28 2009Jul 1 2009

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Conference

Conference15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD '09
Country/TerritoryFrance
CityParis
Period6/28/097/1/09

Keywords

  • Adaptive line search
  • L1-ball constraint
  • Logistic regression
  • Nesterov's method
  • Sparse learning

ASJC Scopus subject areas

  • Software
  • Information Systems

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