A group bridge approach for variable selection

Jian Huang, Shuange Ma, Huiliang Xie, Cun Hui Zhang

Research output: Contribution to journalArticlepeer-review

188 Scopus citations

Abstract

In multiple regression problems when covariates can be naturally grouped, it is important to carry out feature selection at the group and within-group individual variable levels simultaneously. The existing methods, including the lasso and group lasso, are designed for either variable selection or group selection, but not for both. We propose a group bridge approach that is capable of simultaneous selection at both the group and within-group individual variable levels. The proposed approach is a penalized regularization method that uses a specially designed group bridge penalty. It has the oracle group selection property, in that it can correctly select important groups with probability converging to one. In contrast, the group lasso and group least angle regression methods in general do not possess such an oracle property in group selection. Simulation studies indicate that the group bridge has superior performance in group and individual variable selection relative to several existing methods.

Original languageEnglish (US)
Pages (from-to)339-355
Number of pages17
JournalBiometrika
Volume96
Issue number2
DOIs
StatePublished - Jun 2009

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Bridge estimator
  • Iterative lasso
  • Penalized regression
  • Two-level selection
  • Variable-selection consistency

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