Bayesian joint inference for multiple directed acyclic graphs

TL;DR

This paper introduces a Bayesian joint inference method for estimating multiple directed acyclic graphs simultaneously, improving efficiency and accuracy in understanding complex dependence structures across groups.

Contribution

It presents the first Bayesian approach for joint estimation of multiple DAGs, incorporating a Markov random field prior to promote shared structures across groups.

Findings

Joint inference outperforms separate estimation methods.

The method achieves joint selection consistency in high-dimensional settings.

Application to fMRI data reveals meaningful brain network structures.

Abstract

In many applications, data often arise from multiple groups that may share similar characteristics. A joint estimation method that models several groups simultaneously can be more efficient than estimating parameters in each group separately. We focus on unraveling the dependence structures of data based on directed acyclic graphs and propose a Bayesian joint inference method for multiple graphs. To encourage similar dependence structures across all groups, a Markov random field prior is adopted. We establish the joint selection consistency of the fractional posterior in high dimensions, and benefits of the joint inference are shown under the common support assumption. This is the first Bayesian method for joint estimation of multiple directed acyclic graphs. The performance of the proposed method is demonstrated using simulation studies, and it is shown that our joint inference outperforms other competitors. We apply our method to an fMRI data for simultaneously inferring multiple brain functional networks.