A lower bound based smoothed quasi-Newton algorithm for group bridge penalized regression. Issue 6 (3rd July 2017)

• Record Type: Journal Article
• Authors: Cao, Yongxiu; Huang, Jian; Jiao, Yuling; Liu, Yanyan
• Is Part Of: Communications in statistics. Volume 46:Issue 6(2017)
• Page Start: 4694
• Page End: 4707
• Publication Date: 2017-07-03
• Subjects: Lower bound rule -- Group bridge -- Penalized least squares -- Quasi-Newton algorithm; 65C60 -- 62J05; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2015.1129409
• Languages: English
• ISSNs: 0361-0918

Abstract

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.