Generalized Beta Mixtures of Gaussians

TL;DR

This paper introduces a new class of normal scale mixtures based on a generalized beta distribution, unifying various shrinkage priors and enabling efficient variational Bayes approximations for large-scale regression problems.

Contribution

It proposes a novel generalized beta mixture framework that encompasses many priors and develops scalable variational Bayes methods for massive data analysis.

Findings

Unified framework for shrinkage priors

Efficient variational Bayes algorithms

Potential for improved large-scale regression

Abstract

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. We first propose a new class of normal scale mixtures through a novel generalized beta distribution that encompasses many interesting priors as special cases. This encompassing framework should prove useful in comparing competing priors, considering properties and revealing close connections. We then develop a class of variational Bayes approximations through the new hierarchy presented that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.