MCMC-Fuzzy: A Fuzzy Metric Applied to Bayesian Network Structure Learning

Abstract

Bayesian network structure learning is considered a complex task as the number of possible structures grows exponentially with the number of variables. Two main methods are used for Bayesian network structure learning: Conditional independence, a method in which a structure is created consistently with independence tests performed on data; and the heuristic search method that explores the structure space. Hybrid algorithms combine both of the aforementioned methods. In this study, we propose the combination of common metrics, used to evaluate Bayesian structures, into a fuzzy system. The idea being that different metrics evaluate different properties of the structure. The proposed fuzzy system is then used as a metric to evaluate Bayesian networks structures in a heuristic search algorithm based on Monte Carlo Markov Chains. The algorithm was evaluated within the context of synthetic databases through comparison with other algorithms and processing time. Results have shown that, despite an increase in processing time, the proposed method improved the structure learning process.