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It is often stated in papers tackling the task of inferring Bayesian networkstructures from data that there are these two distinct approaches: (i) Applyconditional independence tests when testing for the presence or otherwise ofedges; (ii) Search the model space using a scoring metric. Here I argue thatfor complete data and a given node ordering this division is a myth, by showingthat cross entropy methods for checking conditional independence aremathematically identical to methods based upon discriminating between models bytheir overall goodness-of-fit logarithmic scores.

Conditions Under Which Conditional Independence and Scoring Methods Lead to Identical Selection of Bayesian Network Models