A Bayesian framework with adaptive elastic nets for the inference of Gaussian graphical models

TL;DR

This paper introduces a Bayesian method with adaptive elastic nets for inferring Gaussian graphical models, effectively controlling false discoveries and capturing network heterogeneity.

Contribution

It develops a novel Bayesian framework that incorporates degree heterogeneity and graph topology, improving inference accuracy in high-dimensional data.

Findings

Achieves reliable false discovery rate control in simulations.

Maintains strong power in heterogeneous networks like graphs with hubs.

Produces sparse, interpretable graphs in real data applications.

Abstract

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior accounts for degree heterogeneity edge sparsity, and graph topology the graph. The resulting posterior distribution is incorporated into a multiple testing procedure for graph inference with false discovery rate control. Computation is carried out through a combination of adaptive elastic nets and a variational expectation--maximization algorithm. In simulations, the method achieves reliable false discovery rate control while maintaining strong power, especially in heterogeneous networks such as graphs with hubs, and remains competitive under structural misspecification. Applications to breast cancer gene expression data and financial return networks show that the method yields sparse and interpretable conditional dependence graphs while retaining the most stable interactions detected by competing approaches.