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The Descriptive Complexity of Bayesian Network Specifications

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10369))

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Abstract

We adapt the theory of descriptive complexity to Bayesian networks, by investigating how expressive can be specifications based on predicates and quantifiers. We show that Bayesian network specifications that employ first-order quantification capture the complexity class \(\mathsf {PP}\); that is, any phenomenon that can be simulated with a polynomial time probabilistic Turing machine can be also modeled by such a network. We also show that, by allowing quantification over predicates, the resulting Bayesian network specifications capture the complexity class \(\mathsf {PP}^\mathsf {NP}\), a result that does not seem to have equivalent in the literature.

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Acknowledgements

The first author is partially supported by CNPq, grant 308433/2014-9. This paper was partially funded by FAPESP grant #2015/21880-4 (project Proverbs).

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Authors and Affiliations

  1. Escola Politécnica, Universidade de São Paulo, São Paulo, Brazil

    Fabio G. Cozman

  2. Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brazil

    Denis D. Mauá

Authors
  1. Fabio G. Cozman
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  2. Denis D. Mauá
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Corresponding author

Correspondence to Fabio G. Cozman .

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Editors and Affiliations

  1. IDSIA, Lugano, Switzerland

    Alessandro Antonucci

  2. ONERA, Toulouse, France

    Laurence Cholvy

  3. Aix-Marseille University, Marseille, France

    Odile Papini

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Cozman, F.G., Mauá, D.D. (2017). The Descriptive Complexity of Bayesian Network Specifications. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-61581-3_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61580-6

  • Online ISBN: 978-3-319-61581-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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