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Probability-Possibility Transformations: Application to Credal Networks

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Book cover Scalable Uncertainty Management (SUM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9310))

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Abstract

This paper deals with belief graphical models and probability-possibility transformations. It first analyzes some properties of transforming a credal network into a possibilistic one. In particular, we are interested in satisfying some properties of probability-possibility transformations like dominance and order preservation. The second part of the paper deals with using probability-possibility transformations in order to perform MAP inference in credal networks. This problem is known for its high computational complexity in comparison with MAP inference in Bayesian and possibilistic networks. The paper provides preliminary experimental results comparing our approach with both exact and approximate inference in credal networks.

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Notes

  1. 1.

    It is important to note that the number of extreme points can reach N! where N is the number of interpretations [16].

  2. 2.

    http://www.cs.cmu.edu/~javabayes/Home/.

  3. 3.

    Let \(\pi '\) and \(\pi ''\) be two possibility distributions, \(\pi '\) is more specific than \(\pi ''\) iff \(\forall {{\omega }_{i}}{\in }{\varOmega }\), \(\pi '(\omega _{i})\le \pi ''(\omega _{i})\).

  4. 4.

    In the rest of this paper, TR denotes an interval-based probability-possibility transformation satisfying the following principles:

    • Dominance: The possibility distribution \(\pi \) obtained from the IPD IP by TR dominates every probability distribution p compatible with IP, namely \(\forall {\phi } \subseteq \varOmega \), \(\pi (\phi ) \ge p(\phi )\).

    • Order preservation: Given two interpretations \(\omega _i \in {\varOmega }\) and \(\omega _j \in {\varOmega }\), \(\pi (\omega _i) < \pi (\omega _j)\) iff \(\overline{p}(\omega _i) < \underline{p}(\omega _j)\).

  5. 5.

    The permutation property of probability-possibility transformations is discussed in [14].

  6. 6.

    http://ipg.idsia.ch/software/.

  7. 7.

    http://people.idsia.ch/~sun/gl2u-ii.htm.

References

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Acknowledgements

This work is done with the support of a CNRS funded project PEPS FaSciDo 2015 - MAPPOS.

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Authors and Affiliations

  1. Université Lille Nord de France, 59000, Lille, France

    Salem Benferhat, Amélie Levray & Karim Tabia

  2. UArtois, CRIL UMR CNRS 8188, 62300, Lens, France

    Salem Benferhat, Amélie Levray & Karim Tabia

Authors
  1. Salem Benferhat
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  2. Amélie Levray
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  3. Karim Tabia
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Correspondence to Karim Tabia .

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Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, FernUniversität in Hagen, Hagen, Germany

    Christoph Beierle

  2. California Polytechnic State University, SAN LUIS OBISPO, USA

    Alex Dekhtyar

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Benferhat, S., Levray, A., Tabia, K. (2015). Probability-Possibility Transformations: Application to Credal Networks. In: Beierle, C., Dekhtyar, A. (eds) Scalable Uncertainty Management. SUM 2015. Lecture Notes in Computer Science(), vol 9310. Springer, Cham. https://doi.org/10.1007/978-3-319-23540-0_14

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  • DOI: https://doi.org/10.1007/978-3-319-23540-0_14

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