A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables
This work addresses a theoretical gap for researchers in causal inference and graphical models, providing a foundational tool for analyzing and searching models with latent variables.
The paper tackles the lack of a transformational characterization for Markov equivalence in directed maximal ancestral graphs (MAGs) with latent variables, establishing such a characterization to facilitate model search and theoretical proofs.
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Chickering (1995) provided a transformational characterization of Markov equivalence for DAGs (with no latent variables), which is useful in deriving properties shared by Markov equivalent DAGs, and, with certain generalization, is needed to prove the asymptotic correctness of a search procedure over Markov equivalence classes, known as the GES algorithm. For DAG models with latent variables, maximal ancestral graphs (MAGs) provide a neat representation that facilitates model search. However, no transformational characterization -- analogous to Chickering's -- of Markov equivalent MAGs is yet available. This paper establishes such a characterization for directed MAGs, which we expect will have similar uses as it does for DAGs.