A note on minimal d-separation trees for structural learning

Structural learning of a Bayesian network is often decomposed into problems related to its subgraphs, although many approaches without decomposition were proposed. In 2006, Xie, Geng and Zhao proposed using a d-separation tree to improve the power of conditional independence tests and the efficiency of structural learning. In our research note, we study a minimal d-separation tree under a partial ordering, by which the maximal efficiency can be obtained. Our results demonstrate that a minimal d-separation tree of a directed acyclic graph (DAG) can be constructed by searching for the clique tree of a minimal triangulation of the moral graph for the DAG.