Technology Category
Reasoning under Uncertainty: Graphical ModelsMachine Learning: Graph-based Machine LearningData Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
A Bayesian framework with adaptive elastic nets for the inference of Gaussian graphical models
🤖 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.
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Application Category
📝 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
Research questions and friction points this paper is trying to address.
Gaussian graphical models
conditional independence
high-dimensional data
false discovery rate
graph inference
Innovation
Methods, ideas, or system contributions that make the work stand out.
Bayesian graphical models
adaptive elastic net
false discovery rate control
degree heterogeneity
variational EM algorithm
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