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

2026-04-20

AI Summary

This study addresses the challenge of estimating conditional independence graphs from high-dimensional Gaussian data while simultaneously controlling false discoveries and accurately identifying edges. The authors propose a novel Bayesian framework that integrates adaptive priors capturing node degree heterogeneity, edge sparsity, and graph topological structure, coupled with a multiple testing procedure to achieve false discovery rate (FDR) control in graph inference. Computationally, the method leverages an adaptive elastic net penalty and a variational expectation-maximization algorithm for efficient optimization. In simulations, the approach demonstrates substantially improved statistical power while rigorously maintaining FDR control. Applications to breast cancer gene expression and financial return networks yield sparse, stable, and biologically or economically interpretable conditional dependence graphs, particularly excelling in heterogeneous networks containing hub nodes.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Gaussian graphical models
• conditional independence
• high-dimensional data
• false discovery rate
• graph inference

Innovation

• Bayesian graphical models
• adaptive elastic net
• false discovery rate control
• degree heterogeneity
• variational EM algorithm