Prediction Risk for Global-Local Shrinkage Regression

• Activity Number: 235
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2016 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Anindya Bhadra* and Jyotishka Datta and Yunfan Li and Nicholas Polson and Brandon Willard
• Companies: Purdue University and Duke University/Statistical and Applied Mathematical Sciences Institute and Purdue University and The University of Chicago and The University of Chicago
• Keywords: global-local priors ; shrinkage regression ; Stein's risk ; horseshoe

Abstract

Prediction performance in shrinkage regression suffers from two major difficulties: (i) the amount of relative shrinkage is monotone in the singular values of the design matrix and (ii) the amount of shrinkage does not depend on the response variables. Both of these factors can translate to a poor prediction performance, the risk of which can be explicitly quantified using Stein's unbiased risk estimate. We show that using a component-specific local shrinkage term that can be learned from the data under a suitable prior, in combination with a global shrinkage term, can alleviate both these difficulties and result in an improved risk for prediction. Demonstration of improved prediction performance over competing approaches in a simulation study and in a real data set confirms the theoretical findings.