Federated Bayesian network learning from multi-site data

Objective: Identifying functional connectivity biomarkers of major depressive disorder (MDD) patients is essential to advance the understanding of disorder mechanisms and early intervention. Multi-site data arise naturally which could enhance the statistical power of single-site-based methods. However, the main concern is the inter-site heterogeneity and data sharing barriers between different sites. Our objective is to overcome these barriers to learn multiple Bayesian networks (BNs) from rs-fMRI data. Methods: We propose a federated joint estimator and the corresponding optimization algorithm, called NOTEARS-PFL. Specifically, we incorporate both shared and site-specific information into NOTEARS-PFL by utilizing the sparse group lasso penalty. Addressing data-sharing constraint, we develop the alternating direction method of multipliers for the optimization of NOTEARS-PFL. This entails processing neuroimaging data locally at each site, followed by the transmission of the learned network structures for central global updates. Results: The effectiveness and accuracy of the NOTEARS-PFL method are validated through its application on both synthetic and real-world multi-site resting-state functional magnetic resonance imaging (rs-fMRI) datasets. This demonstrates its superior efficiency and precision in comparison to alternative approaches. Conclusion: We proposed a toolbox called NOTEARS-PFL to learn the heterogeneous brain functional connectivity in MDD patients using multi-site data efficiently and with the data sharing constraint. The comprehensive experiments on both synthetic data and real-world multi-site rs-fMRI datasets with MDD highlight the excellent efficacy of our proposed method.