Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables

Ayesha ALI, Thomas RICHARDSON, Peter SPIRTES, Jiji ZHANG

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

    17 Citations (Scopus)

    Abstract

    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
    Original languageEnglish
    Title of host publicationProceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005)
    PublisherAUAI Press
    Pages10-17
    Number of pages8
    ISBN (Print)974903914
    Publication statusPublished - 1 Jan 2005

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    Directed Acyclic Graph
    Latent Variables
    Equivalence class
    Graph in graph theory
    Conditional Independence
    Model

    Cite this

    ALI, A., RICHARDSON, T., SPIRTES, P., & ZHANG, J. (2005). Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables. In Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005) (pp. 10-17). AUAI Press.
    ALI, Ayesha ; RICHARDSON, Thomas ; SPIRTES, Peter ; ZHANG, Jiji. / Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables. Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005). AUAI Press, 2005. pp. 10-17
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    title = "Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables",
    abstract = "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",
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    ALI, A, RICHARDSON, T, SPIRTES, P & ZHANG, J 2005, Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables. in Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005). AUAI Press, pp. 10-17.

    Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables. / ALI, Ayesha; RICHARDSON, Thomas; SPIRTES, Peter; ZHANG, Jiji.

    Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005). AUAI Press, 2005. p. 10-17.

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

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    AB - 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

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    ALI A, RICHARDSON T, SPIRTES P, ZHANG J. Towards characterizing Markov equivalence classes for directed acyclic graphs with latent variables. In Proceedings of the Twenty-First Conference Conference on Uncertainty in Artificial Intelligence (2005). AUAI Press. 2005. p. 10-17