FedGES: A Federated Learning Approach for Bayesian Network Structure Learning

Abstract

Learning the structure of Bayesian Networks (BNs) typically requires centralised access to data, which is often infeasible under privacy or governance constraints. We present Federated Greedy Equivalence Search (FedGES), a federated framework that learns BN structures by exchanging only Directed Acyclic Graphs (DAGs) between clients and a server, never raw data or sufficient statistics. Clients run GES locally with an edge-growth limit, and the server aggregates structures using thresholded consensus fusion or a min-cut-based consensus, iterating until convergence is achieved. With a score-consistent metric, FedGES preserves the theoretical guarantees of centralised GES and ensures finite termination. In experiments on 14 benchmark networks from bnlearn’s repository (20 to 724 nodes) and up to 100 clients, FedGES attains lower Structural Moralized Hamming Distance (SMHD) and competitive or better runtime than state-of-the-art federated baselines. Communication scales with the number of edges rather than data size, improving efficiency. The structure-only protocol is privacy-enhancing by design and is compatible with secure aggregation and edge-level differential privacy to obtain formal guarantees. FedGES provides a scalable and effective solution for discovering BN structures when data cannot be centralised.