A group bridge approach for variable selection

By Jian Huang, Shuange Ma, Huiliang Xie, Cun-Hui Zhang. Biometrika, 2009

361 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5d72ad3c372ef741697382b75d0be5e91a73fa3b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistics and Probability

Citations in the corpus

$\ell_{p}-\ell_{q}$ Penalty for Sparse Linear and Sparse Multiple Kernel Multitask Learning (2011, methodology): “... Knight et al. [27] suggested the use of the so-called Bridge penalty, which simply consists in replacing the � 1-norm with a � p pseudonorm with 0 < p < 1. In our MTL framework, this can be naturally generalized by using the regularizer given in (3) with 0 < p < 1. For instance, two very recent ”
On Optimal Treatment Regimes Selection for Mean Survival Time (2014, positive): “The penalty in the preceding equation adopts the weighted group L1 norm, which encourages group selection and also allows the selection of individual covariates within groups, which shares the spirit of the group bridge penalty [30] and the hierarchical group lasso [31].”
Bridge regression: Adaptivity and group selection (2011, background): “Recently Huang et al. (2009) proposed a group bridge approach with 0 < q < 1 that carries out both group variable selection and within-group individual variable levels simultaneously.”
A Selective Review of Group Selection in High-Dimensional Models. (2012, background): “Huang et al. (2009) showed that the global group bridge solution is group selection consistent under certain regularity conditions.”
Causal Interaction in Factorial Experiments: Application to Conjoint Analysis (2018, neutral): “…exist other regularization methods for categorical variables (e.g., Yuan and Lin 2006; Meier, Van De Geer, and Bühlmann 2008; Zhao, Rocha, and Yu 2009; Huang et al. 2009; Huang, Breheny, and Ma 2012; Lim and Hastie 2015), these methods regularize coe ffi cients rather than their di ff erences.”