Title: Bayesian Dirichlet Bayesian network scores and the maximum entropy principle
Authors: Marco Scutari - University of Oxford (United Kingdom) [presenting]
Abstract: A classic approach for learning Bayesian networks from data is to select the maximum a posteriori (MAP) network. In the case of discrete Bayesian networks, the MAP network is selected by maximising one of several possible Bayesian Dirichlet (BD) scores, the most famous of which is the Bayesian Dirichlet equivalent uniform (BDeu) score. Since the number of possible networks to choose from grows more than exponentially in the number of variables, the uniform prior associated with BDeu makes structure learning computationally feasible, and does not require the elicitation of prior knowledge from experts. We will discuss the impact of this uniform prior on structure learning from an information theoretic perspective, showing how BDeu may violate the maximum entropy principle when applied to sparse data. On the other hand, a previous BDs score arises from a piece-wise prior and it does not appear to violate the maximum entropy principle, even though it is asymptotically equivalent to BDeu.