A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables
Jiji Zhang, Peter Spirtes
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Chickering (1995) provided a transformational characterization of Markov equivalence for DAGs (with no latent variables), which is useful in deriving properties shared by Markov equivalent DAGs, and, with certain generalization, is needed to prove the asymptotic correctness of a search procedure over Markov equivalence classes, known as the GES algorithm. For DAG models with latent variables, maximal ancestral graphs (MAGs) provide a neat representation that facilitates model search. However, no transformational characterization -- analogous to Chickering's -- of Markov equivalent MAGs is yet available. This paper establishes such a characterization for directed MAGs, which we expect will have similar uses as it does for DAGs.
PDF Link: /papers/05/p667-zhang.pdf
AUTHOR = "Jiji Zhang
and Peter Spirtes",
TITLE = "A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables",
BOOKTITLE = "Proceedings of the Twenty-First Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-05)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2005",
PAGES = "667--674"