On the Equivalence of Causal Models
This work addresses the challenge of extracting causal structures from empirical data for scientists and researchers in fields like statistics and machine learning, providing a theoretical foundation for causal inference, but it is incremental as it builds on existing DAG-based causal modeling frameworks.
The paper tackles the problem of determining when two causal models are indistinguishable by any experiment, presenting a canonical representation that yields an efficient graphical criterion for equivalence and extending it to embedded models with unobservable variables, resulting in an efficient algorithm for determining equivalence based on dependency information.
Scientists often use directed acyclic graphs (days) to model the qualitative structure of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which could distinguish one from the other. A canonical representation for causal models is presented 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 observable. 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.