A transformational characterization of Markov equivalence for directed acyclic graphs with latent variables

Jiji Zhang; Peter Spirtes

doi:10.48550/arXiv.1207.1419

A transformational characterization of Markov equivalence for directed acyclic graphs with latent variables

Jiji Zhang, Peter Spirtes

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

21 Citations (Scopus)

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (UAI)
Editors	Fahiem Bacchus, Tommi Jaakkola
Publisher	AUAI Press
Pages	667–674
Number of pages	8
ISBN (Print)	9780974903910
DOIs	https://doi.org/10.48550/arXiv.1207.1419
Publication status	Published - Jul 2005
Event	21st Conference on Uncertainty in Artificial Intelligence, UAI 2005 - Edinburgh, United Kingdom Duration: 26 Jul 2005 → 29 Jul 2005 https://www.auai.org/uai2005/ (Conference website) https://dl.acm.org/doi/proceedings/10.5555/3020336 (Conference proceedings)

Conference

Conference	21st Conference on Uncertainty in Artificial Intelligence, UAI 2005
Country/Territory	United Kingdom
City	Edinburgh
Period	26/07/05 → 29/07/05
Internet address	https://www.auai.org/uai2005/ (Conference website) https://dl.acm.org/doi/proceedings/10.5555/3020336 (Conference proceedings)

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title = "A transformational characterization of Markov equivalence 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 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.",

author = "Jiji Zhang and Peter Spirtes",

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doi = "10.48550/arXiv.1207.1419",

language = "English",

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editor = "Fahiem Bacchus and Tommi Jaakkola",

booktitle = "Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (UAI)",

publisher = "AUAI Press",

note = "21st Conference on Uncertainty in Artificial Intelligence, UAI 2005 ; Conference date: 26-07-2005 Through 29-07-2005",

url = "https://www.auai.org/uai2005/, https://dl.acm.org/doi/proceedings/10.5555/3020336",

}

Zhang, J & Spirtes, P 2005, A transformational characterization of Markov equivalence for directed acyclic graphs with latent variables. in F Bacchus & T Jaakkola (eds), Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (UAI). AUAI Press, pp. 667–674, 21st Conference on Uncertainty in Artificial Intelligence, UAI 2005, Edinburgh, United Kingdom, 26/07/05. https://doi.org/10.48550/arXiv.1207.1419

A transformational characterization of Markov equivalence for directed acyclic graphs with latent variables. / Zhang, Jiji; Spirtes, Peter.
Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence (UAI). ed. / Fahiem Bacchus; Tommi Jaakkola. AUAI Press, 2005. p. 667–674.

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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AB - 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.

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A transformational characterization of Markov equivalence for directed acyclic graphs with latent variables

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