Advertisement

Discrete Exponential Bayesian Networks Structure Learning for Density Estimation

  • Aida Jarraya
  • Philippe Leray
  • Afif Masmoudi
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 304)

Abstract

Our work aims at developing or expliciting bridges between Bayesian Networks and Natural Exponential Families, by proposing discrete exponential Bayesian networks as a generalization of usual discrete ones. In this paper, we illustrate the use of discrete exponential Bayesian networks for Bayesian structure learning and density estimation. Our goal is to empirically determine in which contexts these models can be a good alternative to usual Bayesian networks for density estimation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barndorff-Nielsen, O.: Information and Exponential families in Statistical Theory. John Wiley (1978)Google Scholar
  2. 2.
    Beal, M., Ghahramani, Z.: The Variational Bayesian EM Algorithm for Incomplete Data:with Application to Scoring Graphical Model Structures. Bayesian Statistics 7, 453–464 (2003)MathSciNetGoogle Scholar
  3. 3.
    Chickering, D., Geiger, D., Heckerman, D.: Learning Bayesian Networks: Search Methods and Experimental Results. In: Conference on Artificial Intelligence and Statistics, pp. 112–128 (1995)Google Scholar
  4. 4.
    Consonni, G., Veronese, P.: Conjugate Priors for Exponential Families Having Quadratic Variance Functions. J. Amer. Statist. Assoc. 87, 1123–1127 (1992)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Geiger, D., Heckerman, D., King, H., Meek, C.: Stratified Exponential Families: Graphical Models and Model Selection. Annals of Statistics 29, 505–529 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Jarraya, A., Leray, P., Masmoudi, A.: Discrete Exponential Bayesian Networks: an Ex-tension of Bayesian Networks to Discrete Natural Exponential Families. In: International Conference on Tools with Artificial Intelligence, pp. 205–208 (2011)Google Scholar
  7. 7.
    Lauritzen, S.L., Jensen, F.: Stable Local Computation with Conditional Gaussian Distributions. Statistics and Computing 11(2), 191–203 (2001)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Leray, P., Francois, O.: BNT Structure Learning Package: Documentation and Experi-ments. Tech. rep., Laboratoire PSI (2004)Google Scholar
  9. 9.
    Letac, G.: Lectures on Natural Exponential Families and their Variance Functions. No. 50 in Monograph. Math., Inst. Mat. Pura Aplic. Rio (1992)Google Scholar
  10. 10.
    Murphy, K.: The Bayesnet Toolbox for Matlab. In: Computing Science and Statistics: Proceedings of Interface, vol. 33 (2001)Google Scholar
  11. 11.
    Studeny, M.: Mathematical Aspects of Learning Bayesian Networks: Bayesian Quality Criteria. Research Report 2234, Institute of Information Theory and Automation (2008)Google Scholar
  12. 12.
    Wainwright, M.J., Jordan, M.I.: Graphical models, Exponential Families, and Variational Inference. Foundations and Trends in Machine Learning 1(1-2), 1–305 (2008)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Aida Jarraya
    • 1
    • 2
  • Philippe Leray
    • 2
  • Afif Masmoudi
    • 1
  1. 1.Laboratory of Probability and Statistics, Faculty of Sciences of SfaxUniversity of SfaxTunisia
  2. 2.LINA Computer Science Lab UMR 6241, Knowledge and Decision TeamUniversity of NantesFrance

Personalised recommendations