Fast Bayesian High-Dimensional Gaussian Graphical Model Estimation

3881 

Contributed Abstract 

Poster 

Sagnik Bhadury (1), Jeremy Gaskins (2), Riten Mitra (3)

(1) University of Michigan, N/A, (2) University of Louisville, N/A, (3) N/A, N/A

Jeremy Gaskins  
University of Louisville

Riten Mitra  
N/A

Sagnik Bhadury  
University of Michigan

Sagnik Bhadury  
University of Michigan

Gaussian graphical models, essential for depicting relationships among variables via conditional independence, face challenges in high-dimensional spaces where sparse associations are common. Traditional methods struggle with stability, leading to the adoption of sparsity-enhancing techniques. Unlike penalization-based frequentist approaches, our proposed Bayesian method focuses on efficiency and scalability by leveraging parallelizable Bayesian neighborhood regressions. Our method introduces Horseshoe shrinkage prior for sparsity and an innovative variable selection process that leverages the marginal likelihoods from the ranking of predictors. This strategy not only streamlines the estimation of complex relationships but also ensures computational efficacy. By synthesizing regression coefficients into coherent graph and partial correlation matrix estimates, our approach facilitates robust inference. Evaluated through FDR and TPR metrics, it demonstrates superior performance in diverse applications, notably in analyzing genetic expressions in triple-negative breast cancer, showcasing its applicability and effectiveness in real-world scenarios.

Bayesian|Gaussian graphical models| Horseshoe prior|Sparse graph estimation| |