Comparison of score metrics for Bayesian network learning

Recently, researchers have paid significant attention to the topic of learning Bayesian networks from data. One of the approaches is to construct Bayesian networks from a database by defining a score metric and employing a search strategy to identify the network with maximum score. In this paper, we compare the performance of four score metrics: UPSM, CUPSM, DPSM, and BDe, resulting from four different assumptions: uniform prior, conditional uniform prior, Dirichlet prior and likelihood equivalence. Simple simulation experiments show that when they are applied to identify the true network structures from several candidates, the 10th order DPSM yields the best discriminant score, the CUPSM often performs better than UPSM, and BDe may fail to identify the true network if the equivalent sample size is not set properly. Experiments also show that the higher order DPSM performs better if a network's joint probability is more evenly distributed. These results suggest that using the higher order DPSM in an induction algorithm, such as K2, would result in a more reliable solution.