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

arXiv: https://arxiv.org/abs/2301.02423 · HTML: https://mlsanity.com/paper/2301.02423/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 84 references that are in the map.
- First posted on arXiv 6 Jan 2023.

## Builds on (most cited first, 14 of 14)

- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Multi-site fMRI Analysis Using Privacy-preserving Federated Learning and Domain Adaptation: ABIDE Results](https://mlsanity.com/paper/2001.05647/) (2020)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [HarmoFL: Harmonizing Local and Global Drifts in Federated Learning on Heterogeneous Medical Images](https://mlsanity.com/paper/2112.10775/) (2021)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [A Polynomial-Time Algorithm for Deciding Markov Equivalence of Directed Cyclic Graphical Models](https://mlsanity.com/paper/1302.3600/) (2013)
- [Causal Discovery from Incomplete Data using An Encoder and Reinforcement Learning](https://mlsanity.com/paper/2006.05554/) (2020)
- [Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso](https://mlsanity.com/paper/1512.06171/) (2015)
- [Learning Multitask Gaussian Bayesian Networks](https://mlsanity.com/paper/2205.05343/) (2022)

## Built on by (most cited first, 1 of 1)

- [Discovering Dynamic Effective Connectome of Brain with Bayesian Dynamic DAG Learning](https://mlsanity.com/paper/2309.07080/) (2023)

## Abstract (arXiv)

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