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

TL;DR

This paper demonstrates that, under certain conditions, conditional independence tests and scoring methods for Bayesian network structure learning are mathematically equivalent, challenging the common distinction between these approaches.

Contribution

It proves that for complete data and a fixed node ordering, conditional independence tests and scoring methods are fundamentally identical in Bayesian network model selection.

Findings

Conditional independence tests and scoring methods are mathematically identical under specific conditions.

The equivalence holds for complete data and a fixed node ordering.

This challenges the traditional separation of these approaches in Bayesian network inference.

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.