Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
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
Cite
@article{arxiv.1207.1365,
title = {Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables},
author = {Ayesha R. Ali and Thomas S. Richardson and Peter L. Spirtes and Jiji Zhang},
journal= {arXiv preprint arXiv:1207.1365},
year = {2012}
}
Comments
Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005)