Bringing order into bayesian-network construction

ABSTRACT

Among the tasks involved in building a Bayesian network, obtaining the required probabilities is generally considered the most daunting. Available data collections are often too small to allow for estimating reliable probabilities. Most domain experts, on the other hand, consider assessing the numbers to be quite demanding. Qualitative probabilistic knowledge, however, is provided more easily by experts. We propose a method for obtaining probabilities, that uses qualitative expert knowledge to constrain the probabilities learned from a small data collection. A dedicated elicitation technique is designed to support the acquisition of the qualitative knowledge required for this purpose. We demonstrate the application of our method by quantifying part of a network in the field of classical swine fever.

REFERENCES

• 1: Brunk H.D. Maximum likelihood estimates of monotone parameters. Annals of Mathematical Statistics, 1955, 26:607--616.
• 2: Druzdzel M.J., van der Gaag L.C. Elicitation of probabilities for belief networks: combining qualitative and quantitative information. In: Besnard P., Hanks S. (Eds.). Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann Publishers, San Francisco, California, 1995, 141--148.
• 3: Feelders A., van der Gaag L.C. Learning Bayesian network parameters under order constraints. In: Lucas P. (Ed.). Proceedings of the Second European Workshop on Probabilistic Graphical Models (PGM'04). Leiden, 2004, 73--80.
• 4: Gigerenzer G., Hoffrage U. How to improve Bayesian reasoning without instruction: frequency formats. Psychological Review, 1995, 102:684--704.
• 5: Helsper E.M., van der Gaag L.C. Building Bayesian networks through ontologies. In: van Harmelen F. (Ed.). Proceedings of the 15th European Conference on Artificial Intelligence. IOS Press, Amsterdam, 2002, 680--684.
• 6: Helsper E.M., van der Gaag L.C., Groenendaal F. Designing a procedure for the acquisition of probability constraints for Bayesian networks. In: Motta E., Shadbolt N.R., Stutt A., Gibbins N. (Eds.). Engineering Knowledge in the Age of the Semantic Web: 14th International Conference, EKAW 2004. Springer-Verlag, Heidelberg, 2004, 280--292.
• 7: Finn V. Jensen, Bayesian Networks and Decision Graphs, Springer-Verlag New York, Inc., Secaucus, NJ, 2001
• 8: Kahneman D., Slovic P., Tversky A. Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, Cambridge, 1982.
• 9: Eliciting and analyzing expert judgment: a practical guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2001
• 10: Miller G.A. The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review, 1956, 63:81--97.
• 11: Morgan M.G., Henrion M. Uncertainty, a Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press, Cambridge, 1990.
• 12: Robertson T., Wright F., Dykstra R.L. Order Restricted Statistical Inference. Wiley, New York, 1988.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning
          Subjects: Knowledge acquisition

Additional Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning
          Subjects: Parameter learning

General Terms:
Design

Keywords:
bayesian networks, interview techniques, probability estimation, uncertainty