A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables

    Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review

    Abstract

    Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional indepen- dence relations among the observed variables. Meek (1995) characterizes Markov equiva- lence classes for DAGs (with no latent vari- ables) by presenting a set of orientation rules that can correctly identify all arrow orienta- tions shared by all DAGs in a Markov equiv- alence class, given a member of that class. For DAG models with latent variables, maxi- mal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to con- struct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is partic- ularly useful for causal inference.
    Original languageEnglish
    Title of host publicationProceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007)
    PublisherAUAI Press
    Pages450-457
    Number of pages8
    ISBN (Print)974903930
    Publication statusPublished - 1 Jan 2007

    Fingerprint

    Directed Acyclic Graph
    Latent Variables
    Equivalence class
    Graph in graph theory
    Arrowhead
    Sufficient
    Causal Inference
    Conditional Independence
    Graph Model
    Tail
    Class

    Cite this

    ZHANG, J. (2007). A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables. In Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007) (pp. 450-457). AUAI Press.
    ZHANG, Jiji. / A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables. Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007). AUAI Press, 2007. pp. 450-457
    @inproceedings{394fe599aed24f8ab4032e451da3aa1e,
    title = "A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables",
    abstract = "Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional indepen- dence relations among the observed variables. Meek (1995) characterizes Markov equiva- lence classes for DAGs (with no latent vari- ables) by presenting a set of orientation rules that can correctly identify all arrow orienta- tions shared by all DAGs in a Markov equiv- alence class, given a member of that class. For DAG models with latent variables, maxi- mal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to con- struct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is partic- ularly useful for causal inference.",
    author = "Jiji ZHANG",
    year = "2007",
    month = "1",
    day = "1",
    language = "English",
    isbn = "974903930",
    pages = "450--457",
    booktitle = "Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007)",
    publisher = "AUAI Press",

    }

    ZHANG, J 2007, A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables. in Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007). AUAI Press, pp. 450-457.

    A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables. / ZHANG, Jiji.

    Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007). AUAI Press, 2007. p. 450-457.

    Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Researchpeer-review

    TY - GEN

    T1 - A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables

    AU - ZHANG, Jiji

    PY - 2007/1/1

    Y1 - 2007/1/1

    N2 - Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional indepen- dence relations among the observed variables. Meek (1995) characterizes Markov equiva- lence classes for DAGs (with no latent vari- ables) by presenting a set of orientation rules that can correctly identify all arrow orienta- tions shared by all DAGs in a Markov equiv- alence class, given a member of that class. For DAG models with latent variables, maxi- mal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to con- struct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is partic- ularly useful for causal inference.

    AB - Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional indepen- dence relations among the observed variables. Meek (1995) characterizes Markov equiva- lence classes for DAGs (with no latent vari- ables) by presenting a set of orientation rules that can correctly identify all arrow orienta- tions shared by all DAGs in a Markov equiv- alence class, given a member of that class. For DAG models with latent variables, maxi- mal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to con- struct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is partic- ularly useful for causal inference.

    UR - https://dslpitt.org/uai/papers/07/p450-zhang.pdf

    UR - http://commons.ln.edu.hk/sw_master/4381

    M3 - Conference paper (refereed)

    SN - 974903930

    SP - 450

    EP - 457

    BT - Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007)

    PB - AUAI Press

    ER -

    ZHANG J. A characterization of Markov qquivalence classes for directed acyclic graphs with latent variables. In Proceedings of the Twenty-Third Conference Conference on Uncertainty in Artificial Intelligence (2007). AUAI Press. 2007. p. 450-457