Variable Selection and Estimation in Generalized Linear Models with the Seamless L0 Penalty

• Activity Number: 251
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Zilin Li*+ and Sijian Wang and Xihong Lin
• Companies: Harvard and University of Wisconsin and Harvard School of Public Health
• Keywords: BIC ; Coordinate descent algorithm ; Oracle property ; Penalized likelihood methods ; SELO penalty ; Tuning parameter selection

Abstract

In this paper, we propose variable selection and estimation in generalized linear models using the seamless L0 (SELO) penalized likelihood approach. The SELO penalty is a smooth function that very closely resembles the discontinuous L0 penalty. We develop an efficient algorithm to fit the model, and show that the SELO-GLM procedure has the oracle property in the presence of a diverging number of variables. We propose a Bayesian Information Criterion (BIC) to select the tuning parameter. We show that under some regularity conditions, the proposed SELO-GLM/BIC procedure consistently selects the true model. We perform simulation studies to evaluate the finite sample performance of the proposed methods. Our simulation studies show that the proposed SELO-GLM procedure has a better finite sample performance than several existing methods, especially when the number of variables is large and the signals are weak. We apply the SELO-GLM to analyze a breast cancer genetic dataset to identify the SNPs that are associated with breast cancer risk.