A theoretical study of Y structures for causal discovery
Mani S, Cooper GF, Spirtes P. A theoretical study of Y structures for causal discovery. In: Proceedings of the Conference on Uncertainty in Artificial Intelligence (2006).
Causal discovery from observational data in the presence of unobserved variables is challenging. Identiﬁcation of so-called Y substructures is a suﬃcient condition for ascertaining some causal relations in the large sample limit, without the assumption of no hidden common causes. An example of a Y substructure is A → C, B → C, C → D. This paper describes the ﬁrst asymptotically reliable and computationally feasible scorebased search for discrete Y structures that doesnotassumethattherearenounobserved common causes. For any parameterization of a directed acyclic graph (DAG) that has scores with the property that any DAG that canrepresentthedistributionbeatsanyDAG that can’t, and for two DAGs that represent the distribution, if one has fewer parameters than the other, the one with the fewest parameter wins. In this framework there is no need to assign scores to causal structures with unobserved common causes. The paper also describes how the existence of a Y structure shows the presence of an unconfounded causal relation, without assuming that there are no hidden common causes.