Non-Informative Dirichlet Score for learning Bayesian networks

Learning Bayesian networks is known to be highly sensitive to the chosen equivalent sample size (ESS) in the Bayesian Dirichlet equivalence uniform (BDeu). This sensitivity often engenders unstable or undesired results because the prior of BDeu does not represent ignorance of prior knowledge, but rather a user’s prior belief in the uniformity of the conditional distribution. This paper presents a proposal for a noninformative Dirichlet score by marginalizing the possible hypothetical structures as the user’s prior belief. Some numerical experiments demonstrate that the proposed score improves learning accuracy. The results also suggest that the proposed score might be effective especially for small samples.