Informed Greedy Algorithm for Scalable Bayesian Network Fusion via Minimum Cut Analysis

2025-04-01

AI Summary

To address the challenges of high model complexity, poor interpretability, and exponential growth in network size inherent in multi-source Bayesian network fusion, this paper proposes the Greedy Min-Cut Bayesian Consensus (GMCBC) algorithm. GMCBC is the first method to integrate min-cut analysis—based on the Ford–Fulkerson algorithm—with backward equivalence search (BES) to efficiently construct structural consensus within the Bayesian equivalence class space, while rigorously bounding edge count and inference complexity. Compared to conventional fusion approaches, GMCBC achieves significantly higher structural accuracy and dependency fidelity on synthetic data and federated learning simulations. Crucially, the resulting fused network exhibits size comparable to individual input networks, ensuring scalability and interpretability. By jointly optimizing structural fidelity and computational tractability, GMCBC overcomes the fundamental trade-off between complexity and accuracy that constrains existing methods.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper presents the Greedy Min-Cut Bayesian Consensus (GMCBC) algorithm for the structural fusion of Bayesian Networks (BNs). The method is designed to preserve essential dependencies while controlling network complexity. It addresses the limitations of traditional fusion approaches, which often lead to excessively complex models that are impractical for inference, reasoning, or real-world applications. As the number and size of input networks increase, this issue becomes even more pronounced. GMCBC integrates principles from flow network theory into BN fusion, adapting the Backward Equivalence Search (BES) phase of the Greedy Equivalence Search (GES) algorithm and applying the Ford-Fulkerson algorithm for minimum cut analysis. This approach removes non-essential edges, ensuring that the fused network retains key dependencies while minimizing unnecessary complexity. Experimental results on synthetic Bayesian Networks demonstrate that GMCBC achieves near-optimal network structures. In federated learning simulations, GMCBC produces a consensus network that improves structural accuracy and dependency preservation compared to the average of the input networks, resulting in a structure that better captures the real underlying (in)dependence relationships. This consensus network also maintains a similar size to the original networks, unlike unrestricted fusion methods, where network size grows exponentially.

Problem

• Scalable fusion of Bayesian Networks via minimum cut analysis
• Control network complexity while preserving key dependencies
• Improve structural accuracy in federated learning scenarios

Innovation

• Greedy Min-Cut Bayesian Consensus algorithm for BN fusion
• Integrates flow network theory with minimum cut analysis
• Preserves key dependencies while minimizing network complexity