Learning Multitask Gaussian Bayesian Networks

Abstract

Major depressive disorder (MDD) requires the study of brain functional connectivity alterations in patients, which can be uncovered by resting-state functional magnetic resonance imaging (rs-fMRI) data. We consider the problem of identifying alterations of the brain functional connectivity for a single MDD patient. This is particularly difficult since the amount of data collected during an fMRI scan is too limited to provide sufficient information for individual analysis. Additionally, rs-fMRI data usually has the characteristics of incompleteness, sparsity, variability, high dimensionality, and high noise.To address the above challenges, we propose a multitask Gaussian Bayesian network (MTGBN) framework to identify disease-induced alterations for a single MDD patient. We assume that such disease-induced alterations show some degree of similarity with the tool to learn such network structures from observations to understand how systems are structured jointly from related tasks. First, we treat each patient in a class of observation as a task and then learn the Gaussian Bayesian networks (GBNs) of this data class by learning from all tasks that share a default covariance matrix that encodes prior knowledge. This setting can help us to learn more information from limited data. Moreover, we derive a closed-form formula of the complete likelihood function and use the Monte-Carlo Expectation-Maximization (MCEM) algorithm to efficiently search for the approximately best Bayesian network structures. Finally, we assess the performance of proposed MTGBN with expensive simulation studies and real-world rs-fMRI datasets.