### 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.

Original language | English |
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Title of host publication | Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007) |

Publisher | AUAI Press |

Pages | 450-457 |

Number of pages | 8 |

ISBN (Print) | 974903930 |

Publication status | Published - 1 Jan 2007 |

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## Cite this

ZHANG, J. (2007). A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables. In

*Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007)*(pp. 450-457). AUAI Press.