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
|Title of host publication||Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005)|
|Number of pages||8|
|Publication status||Published - 1 Jan 2005|
ALI, A., RICHARDSON, T., SPIRTES, P., & ZHANG, J. (2005). Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables. In Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005) (pp. 10-17). AUAI Press.