Properties of Bayesian Dirichlet Scores to Learn Bayesian Network Structures

As we see later, the mathematical derivations are more elaborate A Bayesian network is a probabilistic graphical model that than those recently introduced for BIC and AIC criteria relies on a structured dependency among random variables (de Campos, Zeng, and Ji 2009), and the reduction in the to represent a joint probability distribution in a compact and search space and cache size are less effective when priors efficient manner. It is composed by a directed acyclic graph are strong, but still relevant. This is expected, as the BIC (DAG) where nodes are associated to random variables and score is known to penalize complex graphs more than BD conditional probability distributions are defined for variables scores do. We show that the search space can be reduced given their parents in the graph. Learning the graph (or without losing the global optimality guarantee and that the structure) of these networks from data is one of the most memory requirements are small in many practical cases.