Fast Projections onto ℓ1,q-Norm Balls for Grouped Feature Selection

  • Suvrit Sra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6913)

Abstract

Joint sparsity is widely acknowledged as a powerful structural cue for performing feature selection in setups where variables are expected to demonstrate “grouped” behavior. Such grouped behavior is commonly modeled by Group-Lasso or Multitask Lasso-type problems, where feature selection is effected via ℓ1,q -mixed-norms. Several particular formulations for modeling groupwise sparsity have received substantial attention in the literature; and in some cases, efficient algorithms are also available. Surprisingly, for constrained formulations of fundamental importance (e.g., regression with an ℓ1, ∞ -norm constraint), highly scalable methods seem to be missing. We address this deficiency by presenting a method based on spectral projected-gradient (SPG) that can tackle ℓ1,q -constrained convex regression problems. The most crucial component of our method is an algorithm for projecting onto ℓ1,q -norm balls. We present several numerical results which show that our methods attain up to 30X speedups on large ℓ1, ∞ -multitask lasso problems. Even more dramatic are the gains for just the ℓ1, ∞ -projection subproblem: we observe almost three orders of magnitude speedups compared against the currently standard method.

Keywords

Feature Selection Multiple Kernel Learn Group Lasso Proximity Operator Feature Selection Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Suvrit Sra
    • 1
  1. 1.MPI for Intellingent SystemsTübingenGermany

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