Bayesian Network Structural Consensus via Greedy Min-Cut Analysis
This addresses the need for efficient model aggregation in distributed or federated learning scenarios, though it is incremental as it builds on existing GES and consensus techniques.
The paper tackles the problem of structural consensus for Bayesian Networks in federated learning by proposing the MCBNC algorithm, which prunes weak edges using min-cut analysis and a modified GES algorithm, resulting in sparser and more accurate consensus structures than existing methods in experiments on real-world BNs.
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 scenarios.