Learning the Bayesian Network Structure: Dirichlet Prior versus Data

In the Bayesian approach to structure learning of graphical models, the equivalent sample size (ESS) in the Dirichlet prior over the model parameters was recently shown to have an important effect on the maximum-a-posteriori estimate of the Bayesian network structure. In the first contribution, authors theoretically analyze the case of large ESS-values, which complements previous work: among other results, authors find that the presence of an edge in a Bayesian network is favoured over its absence even if both the Dirichlet prior and the data imply independence, as long as the conditional empirical distribution is notably different from uniform.