Theoretical Analysis and Verification of Loop Cutsets in Bayesian Network Inference

Bayesian networks are widely used in probabilistic graphical modeling, but inference in multiply connected networks remains computationally challenging due to loop structures. The loop cutset, a critical component of Pearl’s conditioning method, directly determines inference complexity. This paper presents a systematic theoretical analysis of loop cutsets and develops a Bayesian estimation framework that quantifies the probability of nodes and node pairs being included in the minimal loop cutset. By incorporating structural features such as node degree and shared nodes into a posterior probability model, we provide a unified statistical framework for interpreting cutset membership. Experiments on synthetic and real-world networks validate the proposed approach, demonstrating that Bayesian estimation effectively captures the influence of structural metrics and achieves better predictive accuracy and stability than classical heuristic and randomized algorithms. The findings offer new insights and practical strategies for optimizing loop cutset computation, thereby improving the efficiency and reliability of Bayesian network inference.