Modeling Unreliable Observations in Bayesian Networks by Credal Networks

  • Alessandro Antonucci
  • Alberto Piatti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5785)

Abstract

Bayesian networks are probabilistic graphical models widely employed in AI for the implementation of knowledge-based systems. Standard inference algorithms can update the beliefs about a variable of interest in the network after the observation of some other variables. This is usually achieved under the assumption that the observations could reveal the actual states of the variables in a fully reliable way. We propose a procedure for a more general modeling of the observations, which allows for updating beliefs in different situations, including various cases of unreliable, incomplete, uncertain and also missing observations. This is achieved by augmenting the original Bayesian network with a number of auxiliary variables corresponding to the observations. For a flexible modeling of the observational process, the quantification of the relations between these auxiliary variables and those of the original Bayesian network is done by credal sets, i.e., convex sets of probability mass functions. Without any lack of generality, we show how this can be done by simply estimating the bounds of likelihoods of the observations for the different values of the observed variables. Overall, the Bayesian network is transformed into a credal network, for which a standard updating problem has to be solved. Finally, a number of transformations that might simplify the updating of the resulting credal network is provided.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Antonucci, A., Zaffalon, M.: Equivalence between bayesian and credal nets on an updating problem. In: Lawry, J., Miranda, E., Bugarin, A., Li, S., Gil, M.A., Grzegorzewski, P., Hryniewicz, O. (eds.) Soft Methods for Integrated Uncertainty Modelling(Proceedings of the third international conference on Soft Methods in Probability and Statistics: SMPS 2006), pp. 223–230. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Antonucci, A., Zaffalon, M.: Decision-theoretic specification of credal networks: A unified language for uncertain modeling with sets of bayesian networks. Int. J. Approx. Reasoning 49(2), 345–361 (2008)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bagozzi, R.P., Phillips, L.W.: Representing and testing organizational theories: A holistic construal. Administrative Science Quarterly 27(3), 459–489 (1982)CrossRefGoogle Scholar
  4. 4.
    Borsboom, D., Mellenbergh, G.J., van Heerden, J.: The theoretical status of latent variables. Psychological Review 110(2), 203–219 (2002)CrossRefGoogle Scholar
  5. 5.
    Cozman, F.G.: Credal networks. Artificial Intelligence 120, 199–233 (2000)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Cozman, F.G.: Graphical models for imprecise probabilities. Int. J. Approx. Reasoning 39(2-3), 167–184 (2005)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    de Campos, C.P., Cozman, F.G.: The inferential complexity of Bayesian and credal networks. In: Proceedings of the International Joint Conference on Artificial Intelligence, Edinburgh, pp. 1313–1318 (2005)Google Scholar
  8. 8.
    de Cooman, G., Zaffalon, M.: Updating beliefs with incomplete observations. Artificial Intelligence 159, 75–125 (2004)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Edwards, J.R., Bagozzi, R.P.: On the nature and direction of relationships between constructs and measures. Psychological Methods 5(2), 155–174 (2000)CrossRefGoogle Scholar
  10. 10.
    Lauritzen, S.L., Spiegelhalter, D.J.: Local computations with probabilities on graphical structures and their application to expert systems. Journal of the Royal Statistical Society (B) 50, 157–224 (1988)MathSciNetMATHGoogle Scholar
  11. 11.
    Levi, I.: The Enterprise of Knowledge. MIT Press, London (1980)Google Scholar
  12. 12.
    Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data. Wiley, New York (1987)MATHGoogle Scholar
  13. 13.
    Mahler, D.A.: Mechanisms and measurement of dyspnea in chronic obstructive pulmonary disease. The Proceedings of the American Thoracic Society 3, 234–238 (2006)CrossRefGoogle Scholar
  14. 14.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)MATHGoogle Scholar
  15. 15.
    Skrondal, A., Rabe-Hesketh, S.: Generalized latent variable modeling: multilevel, longitudinal, and structural equation models. Chapman and Hall/CRC, Boca Raton (2004)CrossRefMATHGoogle Scholar
  16. 16.
    Zaffalon, M.: The naive credal classifier. Journal of Statistical Planning and Inference 105(1), 5–21 (2002)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Zaffalon, M., Miranda, E.: Conservative inference rule for uncertain reasoning under incompleteness. Journal of Artificial Intelligence Research 34, 757–821 (2009)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Alessandro Antonucci
    • 1
  • Alberto Piatti
    • 1
  1. 1.Dalle Molle Institute for Artificial Intelligence (IDSIA)MannoSwitzerland

Personalised recommendations