用最小割分析优化贝叶斯网络共识，提升联邦学习中的模型聚合精度。
Bayesian Network Structural Consensus via Greedy Min-Cut Analysis
- 基于最小割分析设计结构评分，动态剪枝弱连接边。
- 在真实数据集上比原始网络和经典融合方法更稀疏且准确。
- 适合分布式场景，无需数据，可后验设定剪枝阈值。
本文提出一种名为最小割贝叶斯网络共识（MCBNC）的贪心算法，用于贝叶斯网络（BN）结构共识，适用于联邦学习与模型聚合。MCBNC通过基于最小割分析的结构评分，从初始无约束融合中剪除弱边，并集成至改进的逆向等价搜索（BES）阶段，该阶段源自贪心等价搜索（GES）算法。该评分量化了边在输入网络中的支持程度，使用最大流计算。与固定树宽限制的方法不同，MCBNC引入一个可后验选择的剪枝阈值θ，仅依赖结构信息。在真实世界贝叶斯网络上的实验表明，MCBNC生成的共识结构更稀疏、更准确，优于标准融合方法及输入网络本身。该方法具有可扩展性、数据无关性，非常适合分布式或联邦环境。
原文摘要 · Abstract (English)
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.
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