Abstract
Bayesian Network (BN) structure learning traditionally centralizes data, raising privacy concerns when data is distributed across multiple entities. This research introduces Federated GES (FedGES), a novel Federated Learning approach tailored for BN structure learning in decentralized settings using the Greedy Equivalence Search (GES) algorithm. FedGES uniquely addresses privacy and security challenges by exchanging only evolving network structures, not parameters or data. It performs collaborative model development, using structural fusion to combine the limited models generated by each client in successive iterations. A controlled structural fusion is also proposed to enhance client consensus when adding any edge. Experimental results on various BNs from bnlearn’s BN Repository validate the effectiveness of FedGES, particularly in high-dimensional (a large number of variables) and sparse data scenarios, offering a practical and privacy-preserving solution for real-world BN structure learning.
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Notes
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Horizontal partitioning divides data instances across clients, where each client possesses complete records but for different samples or segments. In contrast, vertical partitioning splits data attributes across clients, with each retaining all instances but only for specific attributes or features.
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The minimal DAG \(\mathcal {G}^{\sigma }\) that being compatible with \(\sigma \) preserves as much as possible of the conditional independences in \(\mathcal {G}\), although the number of arcs considerably increases.
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It is essential to highlight that, despite the terminology referring to structure learning of Causal Networks, in the three aforementioned contributions, we can use this term interchangeably with Bayesian Networks. This is attributed to their exploration of the space of Markov equivalence classes rather than the space of DAGs, highlighting their emphasis on equivalent causal structures.
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With five clients, C25 and Union fusion are equivalent (\(\lfloor 5 \cdot 0.25\rfloor = \lfloor 1.25\rfloor = 1\)), involving the addition of all edges present in the DAGs.
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Acknowledgements
The following projects have funded this work: TED2021-131291B-I00 (MICIU/AEI/10.13039/501100011033 and European Union NextGenerationEU/PRTR), SBPLY/21/180225/000062 (Junta de Comunidades de Castilla-La Mancha and ERDF A way of making Europe), PID2022-139293NB-C32 (MICIU/AEI/10.13039/501100011033 and ERDF, EU), FPU21/01074 (MICIU/AEI/10.13039/501100011033 and ESF+); 2022-GRIN-34437 (Universidad de Castilla-La Mancha and ERDF A way of making Europe).
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Torrijos, P., Gámez, J.A., Puerta, J.M. (2025). FedGES: A Federated Learning Approach for Bayesian Network Structure Learning. In: Pedreschi, D., Monreale, A., Guidotti, R., Pellungrini, R., Naretto, F. (eds) Discovery Science. DS 2024. Lecture Notes in Computer Science(), vol 15244. Springer, Cham. https://doi.org/10.1007/978-3-031-78980-9_6
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