Equivalence and Synthesis of Causal Models

Abstract Scientists often use directed acyclic graphs (dags) to model the qualitative struc­ ture of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which could dis­ tinguish one from the other. A canonical representation for causal models is pre­ sented which yields an efficient graphical criterion for deciding equivalence, and provides a theoretical basis for extracting causal structures from empirical data. This representation is then extended to the more general case of an embedded causal model, that is, a dag in which only a subset of the variables are observ­ able. The canonical representation presented here yields an efficient algorithm for determining when two embedded causal models reflect the same dependency information. This algorithm leads to a model theoretic definition of causation in terms of statistical dependencies. Equivalence and Synthesis of Causal Models