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Imputation of Possibilistic Data for Structural Learning of Directed Acyclic Graphs

  • Maroua Haddad
  • Nahla Ben Amor
  • Philippe Leray
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8256)

Abstract

One recent focus of research in graphical models is how to learn them from imperfect data. Most of existing works address the case of missing data. In this paper, we are interested by a more general form of imperfection i.e. related to possibilistic datasets where some attributes are characterized by possibility distributions. We propose a structural learning method of Directed Acyclic Graphs (DAGs), which form the qualitative component of several graphical models, from possibilistic datasets. Experimental results show the efficiency of the proposed method even in the particular case of missing data regarding the state of the art Closure under tuple intersection (CUTS) method [1].

Keywords

Bayesian Network Directed Acyclic Graph Maximum Frequency Possibility Distribution Possibility Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Borgelt, C., Steinbrecher, M., Kruse, R.: Graphical models: representations for learning, reasoning and data mining, vol. 704. Wiley (2009)Google Scholar
  2. 2.
    Pearl, J.: Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann (1988)Google Scholar
  3. 3.
    Lauritzen, S.: The EM algorithm for graphical association models with missing data. Computational Statistics & Data Analysis 19(2), 191–201 (1995)CrossRefzbMATHGoogle Scholar
  4. 4.
    Haouari, B., Ben Amor, N., Elouedi, Z., Mellouli, K.: Naïve possibilistic network classifiers. Fuzzy Sets and Systems 160(22), 3224–3238 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bounhas, M., Mellouli, K., Prade, H., Serrurier, M.: From Bayesian classifiers to possibilistic classifiers for numerical data. In: Deshpande, A., Hunter, A. (eds.) SUM 2010. LNCS, vol. 6379, pp. 112–125. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Jenhani, I., Amor, N., Elouedi, Z.: Decision trees as possibilistic classifiers. International Journal of Approximate Reasoning 48(3), 784–807 (2008)CrossRefGoogle Scholar
  7. 7.
    Ammar, A., Elouedi, Z., Lingras, P.: K-modes clustering using possibilistic membership. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part III. CCIS, vol. 299, pp. 596–605. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Fonck, P.: Propagating uncertainty in a directed acyclic graph. In: IPMU, vol. 92, pp. 17–20 (1992)Google Scholar
  9. 9.
    Ayachi, R., Ben Amor, N., Benferhat, S., Haenni, R.: Compiling possibilistic networks: Alternative approaches to possibilistic inference. In: Proceedings of the Twenty-Sixth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI 2010), Corvallis, Oregon, pp. 40–47. AUAI Press (2010)Google Scholar
  10. 10.
    Dubois, D., Prade, H., Harding, E.: Possibility theory: an approach to computerized processing of uncertainty, vol. 2. Plenum Press, New York (1988)CrossRefzbMATHGoogle Scholar
  11. 11.
    Chow, C., Liu, C.: Approximating discrete probability distributions with dependence trees. IEEE Transactions on Information Theory 14(3), 462–467 (1968)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Cooper, G., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9(4), 309–347 (1992)zbMATHGoogle Scholar
  13. 13.
    Shannon, E.: A mathematical theory of evidence: Bellsyt. Techn. Journal 27, 379–423 (1948)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Chernoff, H., Lehmann, E.: The use of maximum likelihood estimates in χ 2 tests for goodness of fit. The Annals of Mathematical Statistics 25(3), 579–586 (1954)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Maroua Haddad
    • 1
  • Nahla Ben Amor
    • 1
  • Philippe Leray
    • 2
  1. 1.LARODEC Laboratory ISGUniversity of TunisTunisia
  2. 2.LINA Laboratory UMR 6241PolytechNantesFrance

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