Strong Completeness and Faithfulness in Bayesian Networks

This addresses the theoretical foundation of Bayesian networks for researchers in probabilistic graphical models, showing that faithfulness is a generic property, which is incremental but clarifies a key assumption.

The paper presents a completeness result for d-separation in discrete Bayesian networks and demonstrates that almost all discrete distributions for a given network structure are faithful, meaning their independence facts exactly match those entailed by the structure.