Genetic Algorithms for Tractable Bayesian Network Fusion via Pre-Fusion Edge Pruning

Structural fusion of Bayesian Networks (BNs) is essential for aggregating knowledge from multiple sources, but traditional methods often produce overly dense graphs with high treewidth, rendering them computationally intractable for inference. This paper addresses the challenge of creating a consensus BN that is both structurally representative of the input models and computationally efficient by enforcing a strict treewidth limit.

The authors introduce a consensus framework that moves away from the traditional 'all-or-nothing' fusion approach. Instead of merging all dependencies, the proposed method uses a genetic algorithm to selectively prune edges from the input networks before fusion. The researchers define two distinct search strategies: one where edge removal decisions are applied globally to identical edges across all input networks, and another where edges are treated as unique elements, allowing for network-specific pruning. The fitness function is specifically designed to minimize the structural distance to the input networks while penalizing any violation of the target treewidth.

Experiments on both synthetic and real-world datasets demonstrate that the proposed genetic algorithms significantly outperform existing greedy baselines and adapted versions of prior fusion methods. By pruning edges directly in the input networks, the framework produces consensus models that are not only more tractable but also more robust against noisy or spurious dependencies that often corrupt unrestricted fusion results. The results confirm that the genetic approach effectively navigates the trade-off between structural fidelity and computational scalability.

As distributed and federated learning become more prevalent, the ability to aggregate local probabilistic models into a single, efficient, and interpretable consensus structure is critical. This research provides a practical, automated tool for practitioners to maintain the utility of BNs in large-scale applications where inference speed and model transparency are paramount.