A group bridge approach for variable selection. (English) Zbl 1163.62050

Huang, Jian; Ma, Shuangge; Xie, Huiliang; Zhang, Cun-Hui

Biometrika 96, No. 2, 339-355 (2009).

Summary: 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.

MSC:

62J05	Linear regression; mixed models
62F12	Asymptotic properties of parametric estimators
62-08	Computational methods for problems pertaining to statistics

Keywords:

bridge estimator; iterative lasso; penalized regression; two-level selection; variable-selection consistency