A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional indepen- dence relations among the observed variables. Meek (1995) characterizes Markov equiva- lence classes for DAGs (with no latent vari- ables) by presenting a set of orientation rules that can correctly identify all arrow orienta- tions shared by all DAGs in a Markov equiv- alence class, given a member of that class. For DAG models with latent variables, maxi- mal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to con- struct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is partic- ularly useful for causal inference.
PDF Link: /papers/07/p450-zhang.pdf
AUTHOR = "Jiji Zhang
TITLE = "A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables",
BOOKTITLE = "Proceedings of the Twenty-Third Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-07)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2007",
PAGES = "450--457"