Advertisement

Computational Statistics

, Volume 16, Issue 1, pp 173–194 | Cite as

Selecting dynamic graphical models with hidden variables from data

  • Beatriz Lacruz
  • Pilar Lasala
  • Alberto Lekuona
Article

Summary

Selecting graphical models for a set of variables from data consists of finding the graphical structure and its associated probability distribution which best fit the data. In this paper we propose a new method for selecting Markovian dynamic graphical models from data and, in particular, we develop a new Bayesian technique for selecting graphical hidden Markov models, depicted by a chain graph, from an incomplete data set where values corresponding to hidden or latent variables are not present in data. The proposed method is illustrated by a case study.

Keywords

Graphical Models Hidden Markov Models Bayesian Learning 

References

  1. Castillo, E.; Gutiérrez, J.M. & Hadi, A.S. (1997), Expert systems and probabilistic network models. Springer.Google Scholar
  2. Dawid, A.P. & Lauritzen, S.L. (1993), ‘Hyper Markov laws in the statistical analysis of decomposable models’, The Annals of Statistics, 21(3), 1272–1317.MathSciNetCrossRefGoogle Scholar
  3. Geiger, D. & Heckerman, D. (1994), ‘Learning Gaussian networks’, in ‘Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence (UAI-94)’, Standford University, 29–31th July, 235–243.Google Scholar
  4. Heckerman, D. (1995), A tutorial on learning with Bayesian networks. Technical Report MSR-TR-95-06. ftp://ftp.research.microsoft.com/pub/techreports/winter94-95/tr-95-06.ps.
  5. Heckerman, D. & Geiger, D. (1995), ‘Learning Bayesian networks: A unification for discrete and Gaussian domains’, in ‘Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence (UAI-95)’, MCGill University, Montreal, Quebec, Canada, 18–20th August, 274–284.Google Scholar
  6. Heckerman, D.; Geiger, D. & Chickering, D.M. (1995), ‘Learning Bayesian networks: the combination of knowledge and statistical data’, Machine Learning 20, 197–243.zbMATHGoogle Scholar
  7. Kong, A.; Liu, J.S. & Wong, W.H. (1994), ‘Sequential imputations and Bayesian missing data problems’, Journal of the American Statistical Association 89(425), Theory and Methods, 278–288.CrossRefGoogle Scholar
  8. Lacruz, B. (1998), Procedimientos secuenciales de modelización gráfica, inferencia y aprendizaje de un sistema dinámico parcialmente observado. PhD Thesis, University of Zaragoza, Spain.Google Scholar
  9. Lacruz, B.; Lasala, P. & Lekuona, A. (2000), ‘Dynamic graphical models and nonhomogeneous hidden Markov models’, Statistics and Probability Letters (in press).Google Scholar
  10. Lauritzen, S.L. (1996), Graphical models. Clarendon Press, Oxford.zbMATHGoogle Scholar
  11. Spiegelhalter, D. J. & Lauritzen, S. L. (1990), ‘Sequential updating of conditional probabilities on directed graphical structures’, Networks, 20, 579–605.MathSciNetCrossRefGoogle Scholar

Copyright information

© Physica-Verlag 2001

Authors and Affiliations

  • Beatriz Lacruz
    • 1
  • Pilar Lasala
    • 1
  • Alberto Lekuona
    • 1
  1. 1.Departamento de Métodos EstadísticosUniversidad de ZaragozaZaragozaSpain

Personalised recommendations