A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables

Understand

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.