Uncertainty in Artificial Intelligence
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Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
Ayesha Ali, Thomas Richardson, Peter Spirtes, Jiji Zhang
Abstract:
It is well known that there may be many causal explanations that are consistent with a given set of data. Recent work has been done to represent the common aspects of these explanations into one representation. In this paper, we address what is less well known: how do the relationships common to every causal explanation among the observed variables of some DAG process change in the presence of latent variables? Ancestral graphs provide a class of graphs that can encode conditional independence relations that arise in DAG models with latent and selection variables. In this paper we present a set of orientation rules that construct the Markov equivalence class representative for ancestral graphs, given a member of the equivalence class. These rules are sound and complete. We also show that when the equivalence class includes a DAG, the equivalence class representative is the essential graph for the said DAG
Keywords:
Pages: 10-17
PS Link:
PDF Link: /papers/05/p10-ali.pdf
BibTex:
@INPROCEEDINGS{Ali05,
AUTHOR = "Ayesha Ali and Thomas Richardson and Peter Spirtes and Jiji Zhang",
TITLE = "Towards Characterizing Markov Equivalence Classes 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 = "10--17"
}


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