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arXiv · 1207.1365

Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables

Ayesha R. Ali·Thomas S. Richardson·Peter L. Spirtes·Jiji Zhang
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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

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Ayesha R. Ali, Thomas S. Richardson, Peter L. Spirtes, Jiji Zhang. 2012-07-04. Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables. https://arxiv.org/abs/1207.1365

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