Conditions Under Which Conditional Independence and Scoring Methods Lead to Identical Selection of Bayesian Network Models
arXiv:1301.2262
Abstract
It is often stated in papers tackling the task of inferring Bayesian network structures from data that there are these two distinct approaches: (i) Apply conditional independence tests when testing for the presence or otherwise of edges; (ii) Search the model space using a scoring metric. Here I argue that for complete data and a given node ordering this division is a myth, by showing that cross entropy methods for checking conditional independence are mathematically identical to methods based upon discriminating between models by their overall goodness-of-fit logarithmic scores.
Appears in Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI2001)