Variable Selection Using Shrinkage Priors

TL;DR

This paper introduces a flexible Bayesian variable selection method using shrinkage priors that is computationally efficient, adaptable to various priors, and effective in high-dimensional, near-collinear data scenarios.

Contribution

It proposes a general, low-tuning-parameter approach for variable selection with shrinkage priors, applicable beyond specific prior types, and provides theoretical and empirical validation.

Findings

Effective in high-dimensional settings

Performs well with near-collinear design matrices

Requires few tuning parameters

Abstract

Variable selection has received widespread attention over the last decade as we routinely encounter high-throughput datasets in complex biological and environment research. Most Bayesian variable selection methods are restricted to mixture priors having separate components for characterizing the signal and the noise. However, such priors encounter computational issues in high dimensions. This has motivated continuous shrinkage priors, resembling the two-component priors facilitating computation and interpretability. While such priors are widely used for estimating high-dimensional sparse vectors, selecting a subset of variables remains a daunting task. In this article, we propose a general approach for variable selection with shrinkage priors. The presence of very few tuning parameters makes our method attractive in comparison to adhoc thresholding approaches. The applicability of the approach is not limited to continuous shrinkage priors, but can be used along with any shrinkage prior. Theoretical properties for near-collinear design matrices are investigated and the method is shown to have good performance in a wide range of synthetic data examples.