Learning the structure of a Bayesian network:: An application of information geometry and the minimum description length principle

The present paper addresses the issue of learning the underlying structure of a discrete binary Bayesian network, expressed as a directed acyclic graph, which includes the specification of the conditional independence assumptions among the attributes of the model; and given the model, the conditional probability distributions that quantify those dependencies. The approach followed in this work heuristically searches the space of network structures using a scoring function based on the Minimum Description Length Principle, that takes into account the volume of the model manifold [1] [2]. Empirical results on synthetic datasets are presented, that analyse the underlying properties and relative effectiveness of this information geometric score, when varying the size and complexity of a Bayesian network.