Uncertainty in Artificial Intelligence
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A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
Jiji Zhang
Abstract:
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.
Keywords:
Pages: 450-457
PS Link:
PDF Link: /papers/07/p450-zhang.pdf
BibTex:
@INPROCEEDINGS{Zhang07,
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"
}


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