Learning incoherent sparse and low-rank patterns from multiple tasks

Jianhui Chen, Liu Ji, Jieping Ye

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

42 Scopus citations

Abstract

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. In addition, we present two projected gradient algorithms and discuss their rates of convergence. Experimental results on benchmark data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

Original languageEnglish (US)
Title of host publicationKDD'10 - Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data
Pages1179-1187
Number of pages9
DOIs
StatePublished - 2010
Event16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD-2010 - Washington, DC, United States
Duration: Jul 25 2010Jul 28 2010

Publication series

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

Other

Other16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD-2010
CountryUnited States
CityWashington, DC
Period7/25/107/28/10

Keywords

  • Multi-task learning
  • Sparse and low-rank patterns
  • Trace norm

ASJC Scopus subject areas

  • Software
  • Information Systems

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