Bayesian Inference of Multiple Gaussian Graphical Models

TLDR

The study proposes a Bayesian method for inferring multiple Gaussian graphical models, allowing some networks to be unrelated while others share common structure. The method uses a Markov random field prior with spike‑and‑slab parameters and edge‑specific informative priors to encourage shared edges and learn which groups share a graph structure. The approach improves network estimation accuracy, provides measures of relative similarity across groups, and successfully infers protein networks for cancer subtypes.

Abstract

In this paper, we propose a Bayesian approach to inference on multiple Gaussian graphical models. Specifically, we address the problem of inferring multiple undirected networks in situations where some of the networks may be unrelated, while others share common features. We link the estimation of the graph structures via a Markov random field (MRF) prior which encourages common edges. We learn which sample groups have a shared graph structure by placing a spike-and-slab prior on the parameters that measure network relatedness. This approach allows us to share information between sample groups, when appropriate, as well as to obtain a measure of relative network similarity across groups. Our modeling framework incorporates relevant prior knowledge through an edge-specific informative prior and can encourage similarity to an established network. Through simulations, we demonstrate the utility of our method in summarizing relative network similarity and compare its performance against related methods. We find improved accuracy of network estimation, particularly when the sample sizes within each subgroup are moderate. We also illustrate the application of our model to infer protein networks for various cancer subtypes and under different experimental conditions.