DOI QR코드

DOI QR Code

Online Parameter Estimation and Convergence Property of Dynamic Bayesian Networks

  • Published : 2007.12.01

Abstract

In this paper, we investigate a novel online estimation algorithm for dynamic Bayesian network(DBN) parameters, given as conditional probabilities. We sequentially update the parameter adjustment rule based on observation data. We apply our algorithm to two well known representations of DBNs: to a first-order Markov Chain(MC) model and to a Hidden Markov Model(HMM). A sliding window allows efficient adaptive computation in real time. We also examine the stochastic convergence and stability of the learning algorithm.

Keywords

References

  1. K. Murphy, 'Dynamic Bayesian networks: Representation, Inference and Learning.' Ph. D. Dissertation, UC Berkeley, 2002
  2. J. M. Mendel, Lessons in estimation theory for signal processing, communications, and control, Prentice Hall, 1995
  3. T. K. Moon, 'The expectation-maximization algorithm,' IEEE Signal Processing Magazine, vol. 13, no. 6, pp. 47-60, 1996 https://doi.org/10.1109/79.543975
  4. X. Huang, A. Acero, and H.-W. Hon, Spoken language processing, Prentice Hall, 2001
  5. J. Ying, T. Kirubarajan, K. R. Pattipati, A. Patterson-Hine, 'A hidden Markov model-based algorithm for fault diagnosis with partial and imperfect tests,' IEEE Trans. on Systems, Man and Cybernetics, vol. 30, no. 4, pp. 463-473, 2000 https://doi.org/10.1109/5326.897073
  6. D. Hernandez-Hernandez, S. I. Marcus, and P. J. Fard, 'Analysis of a risk-sensitive control problem for hidden Markov chains,' IEEE Trans. on Automatic Control, vol. 44, no. 5, pp. 1093-1100, 1999 https://doi.org/10.1109/9.763237
  7. H. C. Cho, S. M. Fadali, and K. S. Lee, 'Estimation of non-Gaussian probability density by dynamic Bayesian networks,' Int. Conf on Control, Automation, and Systems, pp. 408-413, 2005
  8. P. Baldi and Y. Chauvin, 'Smooth on-line learning algorithm for hidden Markov models,' Neural Computation, vol. 6, no. 2, pp. 307-318, 1994 https://doi.org/10.1162/neco.1994.6.2.307
  9. J. J. Ford and J. B. Moore, 'Adaptive estimation of HMM transition probabilities,' IEEE Trans. on Signal Processing, vol. 46, no. 5, pp. 1374-1385, 1998 https://doi.org/10.1109/78.668799
  10. J. C. Stiller and G. Radons, 'Online estimation of hidden Markov models,' IEEE Signal Processing Letters, vol. 6, no. 8,pp.213-215, 1999 https://doi.org/10.1109/97.774870
  11. I. Cohen and A. Bronstein, 'Adaptive online learning of Bayesian network parameters,' http://www.hpl.hp.com /techreports /2001/HPL-2001-156.pdf, 2001
  12. S.-Z. Zhang, H. Yu, N-H. Yang, and X.-K Wang, 'An application of online learning algorithm for Bayesian network parameter,' Proc. of the Second International Conf. on Machine Learning and Cybernetics, pp. 153-156, 2003
  13. E. Parzen, 'On estimation of a probability density function and mode,' Annals of Mathematical Statistics, vol. 33, no. 3, pp. 1065-1076, 1962 https://doi.org/10.1214/aoms/1177704472
  14. B. W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman & Hall/CRC, 1986
  15. V. Krishnamurthy, J. B. Moore, and S.-H. Chung, 'Hidden Markov model signal processing in presence of unknown deterministic inferences,' IEEE Transaction on Automatic Control, vol. 38, no. 1, pp. 146-152,1993 https://doi.org/10.1109/9.186328
  16. R. J. Serfling, Approximation theorems of mathematical statistics, Wiley, 1980
  17. W. J. Rugh, Linear system theory, Prentice Hall, 1996. 2004

Cited by

  1. Probabilistic Modeling of Photovoltaic Power Systems with Big Learning Data Sets vol.23, pp.5, 2013, https://doi.org/10.5391/JKIIS.2013.23.5.412