Reciprocal Regularization for High-Dimensional Regression

• Activity Number: 695
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Qifan Song* and Faming Liang
• Companies: Purdue University and University of Florida
• Keywords: High Dimensional ; Lasso ; variable selection

Abstract

Penalized likelihood methods have been widely used in variable selection problems, where the penalty functions are typically symmetric about 0, continuous and nondecreasing. We propose a new penalized likelihood method, reciprocal Lasso (or in short, rLasso), based on a new class of penalty functions which are decreasing, discontinuous at 0, and converge to infinity when the coefficients approach zero. The new penalty functions give nearly zero coefficients infinity penalties; This distinguishing feature makes rLasso very attractive for variable selection: It can effectively avoid to select overly dense models. We establish the consistency of the rLasso for variable selection and coefficient estimation under both the low and high dimensional settings.