论文信息 - A Transformational Characterization of Markov Equivalence for Directed Acyclic Graphs with Latent Variables

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

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.

Jiji Zhang | Peter Spirtes | P. Spirtes | Jiji Zhang

[1] Judea Pearl,et al. Equivalence and Synthesis of Causal Models , 1990, UAI.

[2] David Maxwell Chickering,et al. Optimal Structure Identification With Greedy Search , 2002, J. Mach. Learn. Res..

[3] D. Madigan,et al. A characterization of Markov equivalence classes for acyclic digraphs , 1997 .

[4] P. Spirtes,et al. Ancestral graph Markov models , 2002 .

[5] Peter Spirtes,et al. A Characterization of Markov Equivalence Classes for Ancestral Graphical Models , 2005 .

[6] T. Richardson,et al. Graphical Answers to Questions about Likelihood Inference for Gaussian Covariance Models , 2004 .

[7] P. Spirtes,et al. A Polynomial Time Algorithm for Determining DAG Equivalence in the Presence of Latent Variables and Selection Bias , 1997, AISTATS.

[8] Thomas S. Richardson,et al. Towards Characterizing Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables , 2005, UAI.

[9] Thomas S. Richardson,et al. Heuristic Greedy Search Algorithms for Latent Variable Models , 1997, AISTATS.

[10] C. Meek,et al. Graphical models: selecting causal and statistical models , 1997 .

[11] David Maxwell Chickering,et al. A Transformational Characterization of Equivalent Bayesian Network Structures , 1995, UAI.