An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation

In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence informa­ tion, where a causal influence was defined as the existence of a directed arc in all mini­ mal causal models consistent with the data. In this paper we address the question of de­ ciding whether there exists a causal model that explains ALL the observed dependencies and independencies. Formally, given a list M of conditional independence statements, it is required to decide whether there exists a directed acyclic graph ( dag) D that is per­ fectly consistent with M, namely, every state­ ment in M, and no other, is reflected via d­ separation in D. We present and analyze an effective algorithm that tests for the existence of such a dag, and produces one, if it exists.