A lower bound based smoothed quasi-Newton algorithm for group bridge penalized regression

Yongxiu Cao, Jian Huang, Yuling Jiao, Yanyan Liu

Research output: Journal article publicationReview articleAcademic researchpeer-review

Abstract

In this paper, we propose a lower bound based smoothed quasi-Newton algorithm for computing the solution paths of the group bridge estimator in linear regression models. Our method is based on the quasi-Newton algorithm with a smoothed group bridge penalty in combination with a novel data-driven thresholding rule for the regression coefficients. This rule is derived based on a necessary KKT condition of the group bridge optimization problem. It is easy to implement and can be used to eliminate groups with zero coefficients. Thus, it reduces the dimension of the optimization problem. The proposed algorithm removes the restriction of groupwise orthogonal condition needed in coordinate descent and LARS algorithms for group variable selection. Numerical results show that the proposed algorithm outperforms the coordinate descent based algorithms in both efficiency and accuracy.

Original languageEnglish
Pages (from-to)4694-4707
Number of pages14
JournalCommunications in Statistics: Simulation and Computation
Volume46
Issue number6
DOIs
Publication statusPublished - 3 Jul 2017
Externally publishedYes

Keywords

  • Group bridge
  • Lower bound rule
  • Penalized least squares
  • Quasi-Newton algorithm

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation

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