Bayesian Covariance Matrix Estimation using a Mixture of Decomposable Graphical Models

TL;DR

This paper introduces a Bayesian method for covariance matrix estimation that uses a mixture prior over decomposable graphical models, improving graph selection and covariance estimation accuracy.

Contribution

It proposes a novel prior that assigns equal probability to graphs of the same size, outperforming uniform graph priors in empirical evaluations.

Findings

Prior with equal probability over graph sizes outperforms uniform graph prior

Improved accuracy in identifying the correct decomposable graph

More efficient covariance matrix estimation

Abstract

A Bayesian approach is used to estimate the covariance matrix of Gaussian data. Ideas from Gaussian graphical models and model selection are used to construct a prior for the covariance matrix that is a mixture over all decomposable graphs. For this prior the probability of each graph size is specified by the user and graphs of equal size are assigned equal probability. Most previous approaches assume that all graphs are equally probable. We show empirically that the prior that assigns equal probability over graph sizes outperforms the prior that assigns equal probability over all graphs, both in identifying the correct decomposable graph and in more efficiently estimating the covariance matrix.