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European Workshop on Probabilistic Graphical Models

PGM 2014: Probabilistic Graphical Models pp 458–470Cite as

On Expressiveness of the AMP Chain Graph Interpretation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8754))

Abstract

In this paper we study the expressiveness of the Andersson-Madigan-Perlman interpretation of chain graphs. It is well known that all independence models that can be represented by Bayesian networks also can be perfectly represented by chain graphs of the Andersson-Madigan-Perlman interpretation but it has so far not been studied how much more expressive this second class of models is. In this paper we calculate the exact number of representable independence models for the two classes, and the ratio between them, for up to five nodes. For more than five nodes the explosive growth of chain graph models does however make such enumeration infeasible. Hence we instead present, and prove the correctness of, a Markov chain Monte Carlo approach for sampling chain graph models uniformly for the Andersson-Madigan-Perlman interpretation. This allows us to approximate the ratio between the numbers of independence models representable by the two classes as well as the average number of chain graphs per chain graph model for up to 20 nodes. The results show that the ratio between the numbers of representable independence models for the two classes grows exponentially as the number of nodes increases. This indicates that only a very small fraction of all independence models representable by chain graphs of the Andersson-Madigan-Perlman interpretation also can be represented by Bayesian networks.

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Author information

Authors and Affiliations

  1. ADIT, IDA, Linköping University, Sweden

    Dag Sonntag

Authors
  1. Dag Sonntag
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Editors and Affiliations

  1. Utrecht University, Faculty of Science, Department of Information and Computing Sciences, Princetonplein 5, 3584 CC Utrecht, The Netherlands

    Linda C. van der Gaag

  2. Utrecht University, Faculty of Science, Department of Information and Computing Sciences, Princetonplein 5, 3584 CC Utrecht,, The Netherlands

    Ad J. Feelders

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© 2014 Springer International Publishing Switzerland

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Sonntag, D. (2014). On Expressiveness of the AMP Chain Graph Interpretation. In: van der Gaag, L.C., Feelders, A.J. (eds) Probabilistic Graphical Models. PGM 2014. Lecture Notes in Computer Science(), vol 8754. Springer, Cham. https://doi.org/10.1007/978-3-319-11433-0_30

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  • DOI: https://doi.org/10.1007/978-3-319-11433-0_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11432-3

  • Online ISBN: 978-3-319-11433-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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