Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables
Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005)
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
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ISBN of the source publication: 0974903914
Ali, A., Richardson, T., Spirtes, P., & Zhang, J. (2015). Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables. In F. Bacchus & T. Jaakkola (Eds.), Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005) (pp.10-17). Arlington, Virginia: AUAI Press. Retrieved from https://dslpitt.org/uai/papers/05/p10-ali.pdf