Bayesian Network Structural Consensus via Greedy Min-Cut Analysis

This paper presents the Min-Cut Bayesian Network Consensus (MCBNC) algorithm, a greedy method for structural consensus of Bayesian Networks (BNs), with applications in federated learning and model aggregation. MCBNC prunes weak edges from an initial unrestricted fusion using a structural score based on min-cut analysis, integrated into a modified Backward Equivalence Search (BES) phase of the Greedy Equivalence Search (GES) algorithm. The score quantifies edge support across input networks and is computed using max-flow. Unlike methods with fixed treewidth bounds, MCBNC introduces a pruning threshold θ that can be selected post hoc using only structural information. Experiments on real-world BNs show that MCBNC yields sparser, more accurate consensus structures than both canonical fusion and the input networks. The method is scalable, data-agnostic, and well-suited for distributed or federated structural learning of BNs or causal discovery.

Authors

• Pablo Torrijos Instituto de Investigación en Informática de Albacete (I3A), Universidad de Castilla-La Mancha, Albacete, Spain Departamento de Sistemas Informáticos, Universidad de Castilla-La Mancha, Albacete, Spain
• Jose M. Puerta Instituto de Investigación en Informática de Albacete (I3A), Universidad de Castilla-La Mancha, Albacete, Spain Departamento de Sistemas Informáticos, Universidad de Castilla-La Mancha, Albacete, Spain
• Juan A. Aledo Instituto de Investigación en Informática de Albacete (I3A), Universidad de Castilla-La Mancha, Albacete, Spain Departamento de Matemáticas, Universidad de Castilla-La Mancha, Albacete, Spain
• José A. Gámez Instituto de Investigación en Informática de Albacete (I3A), Universidad de Castilla-La Mancha, Albacete, Spain Departamento de Sistemas Informáticos, Universidad de Castilla-La Mancha, Albacete, Spain

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