Prediction risk for global-local shrinkage regression
Year: 2016
Type: preprint
Abstract: Predictive 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 heavy-tailed prior, in combination with a global term providing shrinkage towards zero, can alleviate both these difficulties and consequently, can result in an improved risk for prediction. Demonstration of improved prediction performance over competing approaches in a simulation study and in a pharmacogenomics data set confirms the theoretical findings.
Source: arXiv (Cornell University)
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2401815844