Local shrinkage rules, Levy processes, and regularized regression
Methodology
2011-04-26 v2 Statistics Theory
Statistics Theory
Abstract
We use Levy processes to generate joint prior distributions, and therefore penalty functions, for a location parameter as p grows large. This generalizes the class of local-global shrinkage rules based on scale mixtures of normals, illuminates new connections among disparate methods, and leads to new results for computing posterior means and modes under a wide class of priors. We extend this framework to large-scale regularized regression problems where p>n, and provide comparisons with other methodologies.
Cite
@article{arxiv.1010.3390,
title = {Local shrinkage rules, Levy processes, and regularized regression},
author = {Nicholas G. Polson and James G. Scott},
journal= {arXiv preprint arXiv:1010.3390},
year = {2011}
}