Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
This work addresses a foundational problem in causal inference for researchers dealing with latent variables, providing a method to unify causal explanations, though it is incremental as it builds on existing representations like ancestral graphs.
The paper tackles the problem of characterizing Markov equivalence classes for directed acyclic graphs (DAGs) with latent variables, presenting a set of sound and complete orientation rules to construct the equivalence class representative for ancestral graphs, which encode conditional independence relations in such models.
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