Comparison of score metrics for Bayesian network learning

In order to induct a Bayesian network from data, researchers proposed a variety of score metrics based on different assumptions. The score metric that performs best is of interest. In this paper, we compared the performance of five score metrics: uniform prior score metric (UPSM), conditional uniform prior score metric (CUPSM), Dirichlet prior score metric (DPSM), likelihood-equivalence Bayesian Dirichlet score metric (BDe), and minimum description length (MDL); resulting from five different assumptions: uniform prior, conditional uniform prior, Dirichlet prior, likelihood equivalence, and MDL. We used a three-node net, a five-node net, and the ALARM net to conduct several comparison experiments. The experimental results show that when they are applied to identify the true network structures, the DPSM yields the best discrimination score and BDe may fail to identify the true network if the equivalent sample size is not set properly. When they are applied to learn a network from data using the K2-like greedy search and the maximum likelihood (ML) parameter estimation, the network inducted by the K2D10, corresponding to the tenth-order DPSM, is most similar to the true network based on the cross-entropy criterion. It is concluded that the tenth-order DPSM is the best score metric and the corresponding K2D10 is the most reliable network learning algorithm.