Bayesian Covariance Estimation for Multi-group Matrix-variate Data

TL;DR

This paper introduces a hierarchical Bayesian prior for multi-group covariance estimation in matrix-variate data, enabling flexible shrinkage towards shared or group-specific structures, improving accuracy in small sample scenarios.

Contribution

The paper proposes a novel hierarchical prior that combines both across-group and within-group shrinkage, enhancing covariance estimation flexibility and accuracy.

Findings

Improved covariance estimates in speech recognition data

Effective handling of small sample sizes in multi-group settings

Demonstrated utility in chemical exposure data analysis

Abstract

Multi-group covariance estimation for matrix-variate data with small within group sample sizes is a key part of many data analysis tasks in modern applications. To obtain accurate group-specific covariance estimates, shrinkage estimation methods which shrink an unstructured, group-specific covariance either across groups towards a pooled covariance or within each group towards a Kronecker structure have been developed. However, in many applications, it is unclear which approach will result in more accurate covariance estimates. In this article, we present a hierarchical prior distribution which flexibly allows for both types of shrinkage. The prior linearly combines shrinkage across groups towards a shared pooled covariance and shrinkage within groups towards a group-specific Kronecker covariance. We illustrate the utility of the proposed prior in speech recognition and an analysis of chemical exposure data.