Possibilistic MDL: A New Possibilistic Likelihood Based Score Function for Imprecise Data

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)

Abstract

Recent years have seen a surge of interest in methods for representing and reasoning with imprecise data. In this paper, we propose a new possibilistic likelihood function handling this particular form of data based on the interpretation of a possibility distribution as a contour function of a random set. The proposed function can serve as the foundation for inferring several possibilistic models. In this paper, we apply it to define a new scoring function to learn possibilistic network structure. Experimental study showing the efficiency of the proposed score is also presented.

References

  1. 1.
    Ben Amor, N., Benferhat, S.: Graphoid properties of qualitative possibilistic independence relations. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst. 13(01), 59–96 (2005)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Borgelt, C., Kruse, R.: Operations and evaluation measures for learning possibilistic graphical models. Artif. Intell. 148(1), 385–418 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Trans. Inf. Theory 14(3), 462–467 (1968)CrossRefMATHGoogle Scholar
  4. 4.
    Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Mach. Learn. 9(4), 309–347 (1992)MATHGoogle Scholar
  5. 5.
    Couso, I., Dubois, D.: Maximum likelihood under incomplete information: toward a comparison of criteria. In: Ferraro, M.B., Giordani, P., Vantaggi, B., Gagolewski, M., Gil, M.Á., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Data Science. AISC, vol. 456, pp. 141–148. Springer, Cham (2017). doi:10.1007/978-3-319-42972-4_18 CrossRefGoogle Scholar
  6. 6.
    Denoeux, T.: Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Trans. knowl. data Eng. 25(1), 119–130 (2013)CrossRefGoogle Scholar
  7. 7.
    Dubois, D., Prade, H.: Possibility Theory. Springer, Berlin (1988)CrossRefMATHGoogle Scholar
  8. 8.
    Fonck, P.: Propagating uncertainty in a directed acyclic graph. In: Proceedings of the Fourth Information Processing and Management of Uncertainty Conference, 92, 17–20 (1992)Google Scholar
  9. 9.
    Grünwald, P.D.: Theory and applications: advances in minimum description length, Mdl tutorial (2005)Google Scholar
  10. 10.
    Haddad, M., Leray, P., Amor, N.B.: Evaluating product-based possibilistic networks learning algorithms. In: Proceedings of Symbolic and Quantitative Approaches to Reasoning with Uncertainty, pp. 312–321 (2015)Google Scholar
  11. 11.
    Haddad, M., Leray, P., Amor, N.B.: Learning possibilistic networks from data : a survey. In: 16th World Congress of the International Fuzzy Systems Association and the 9th Conference of the European Society for Fuzzy Logic and Technology, pp. 194–201 (2015)Google Scholar
  12. 12.
    Haddad, M., Leray, P., Levray, A., Tabia, K.: Possibilistic networks parameter learning: Preliminary empirical comparison. In: 8èmes journées francophones de réseaux bayésiens (JFRB 2016), (2016)Google Scholar
  13. 13.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Francisco (1988)MATHGoogle Scholar
  14. 14.
    Rissanen, J.: Modeling by shortest data description. Automatica 14(5), 465–471 (1978)CrossRefMATHGoogle Scholar
  15. 15.
    Sangüesa, R., Cabós, J., Cortes, U.: Possibilistic conditional independence: A similarity-based measure and its application to causal network learning. Int. J. Approximate Reasoning 18(1), 145–167 (1998)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Serrurier, M., Prade, H.: An informational distance for estimating the faithfulness of a possibility distribution, viewed as a family of probability distributions, with respect to data. Int. J. Approximate Reasoning 54(7), 919–933 (2013)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Shafer, G.: A mathematical Theory of Evidence, vol. 1. Princeton University Press, Princeton (1976)MATHGoogle Scholar
  18. 18.
    Shapiro, L.G., Haralick, R.M.: A metric for comparing relational descriptions. IEEE Trans. Pattern Anal. Mach. Intell. 1(1), 90–94 (1985)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Maroua Haddad
    • 1
    • 2
  • Philippe Leray
    • 2
  • Nahla Ben Amor
    • 1
  1. 1.LARODEC Laboratory ISGUniversité de TunisTunisTunisia
  2. 2.LINA-UMR CNRS 6241Université de NantesNantesFrance

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