Grouping Variable Selection by Weight Fused Elastic Net for Multi-Collinear Data

Abstract

In this article, we consider the problem of variable selection and estimation with the strongly correlated multi-collinear data by using grouping variable selection techniques. A new grouping variable selection method, called weight-fused elastic net(WFEN), is proposed to deal with the high dimensional collinear data. The proposed model, combined two different grouping effect mechanisms induced by the elastic net and weight-fused LASSO, respectively, can be easily unified in the frame of LASSO and computed efficiently. The performance with the simulation and real data sets shows that our method is competitive with other related methods, especially when the data present high multi-collinearity.

Keywords:

• Elastic net
• Grouping variable selection
• LASSO
• Multi-collinearity
• Weight fused LASSO
• WFEN

Mathematics Subject Classification:

• Primary 62H86
• Secondary 62-07

Acknowledgment

The author would like to express my gratitude to Dr. Zhongyin John Daye for his help on this article. This work is financially supported by the National Natural Science Foundation of P. R. China (Grants No. 10771217). The studies meet with the approval of the university's review board.