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Identifying functional connectivity biomarkers of major depressive disorder(MDD) patients is essential to advance understanding of the disorder mechanismsand early intervention. However, due to the small sample size and the highdimension of available neuroimaging data, the performance of existing methodsis often limited. Multi-site data could enhance the statistical power andsample size, while they are often subject to inter-site heterogeneity anddata-sharing policies. In this paper, we propose a federated joint estimator,NOTEARS-PFL, for simultaneous learning of multiple Bayesian networks (BNs) withcontinuous optimization, to identify disease-induced alterations in MDDpatients. We incorporate information shared between sites and site-specificinformation into the proposed federated learning framework to learnpersonalized BN structures by introducing the group fused lasso penalty. Wedevelop the alternating direction method of multipliers, where in the localupdate step, the neuroimaging data is processed at each local site. Then thelearned network structures are transmitted to the center for the global update.In particular, we derive a closed-form expression for the local update step anduse the iterative proximal projection method to deal with the group fused lassopenalty in the global update step. We evaluate the performance of the proposedmethod on both synthetic and real-world multi-site rs-fMRI datasets. Theresults suggest that the proposed NOTEARS-PFL yields superior effectiveness andaccuracy than the comparable methods.

Learning Personalized Brain Functional Connectivity of MDD Patients from Multiple Sites via Federated Bayesian Networks