Abstract: The joint estimation of multiple graphical models from high-dimensional data has been studied in the statistics and machine learning literature, owing to its importance in diverse fields including molecular biology, neuroscience, and the social sciences. We propose a Bayesian approach that decomposes the model parameters across multiple graphical models into shared components across subsets of models and edges, and idiosyncratic components. This approach leverages a novel multivariate prior distribution, coupled with a jointly convex regression-based pseudo-likelihood that enables fast computation using a robust and efficient Gibbs sampling scheme. We establish strong posterior consistency for model selection under high-dimensional scaling, with the number of variables growing exponentially as a function of the sample size. Lastly, we demonstrate the efficiency of the proposed approach in borrowing strength across models to identify shared edges using both synthetic and real data.

Key words and phrases: Gibbs sampling, Omics data, posterior consistency, Pseudo-likelihood.