Recursive computation of the score and observed information matrix in hidden Markov models

IEEE Workshop on Statistical Signal Processing Proceedings

Volumn 2005, Issue , 2005, Pages 703-707

  Cappé, Olivier ^a   Moulines, Eric ^a  

^a TELECOM PARISTECH   (France)

Author keywords

Hidden Markov models; Information matrix; Recursive computation; Score; Smoothing

Indexed keywords

HIDDEN MARKOV MODELS; MATHEMATICAL MODELS; MONTE CARLO METHODS; RECURSIVE FUNCTIONS; STATE SPACE METHODS;

INFORMATION MATRIX; RECURSIVE COMPUTATION; SENSITIVITY EQUATIONS; SMOOTHING;

INFORMATION ANALYSIS;

EID: 33947138238     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ssp.2005.1628685     Document Type: Conference Paper

References (18)

1. L. E. Baum, T. P. Petrie, G. Soules, and N. Weiss, "A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains," Ann. Math. Statist., vol. 41, no. 1, pp. 164-171, 1970.
2. R. E. Kalman and R. Bucy, "New results in linear filtering and prediction theory," J. Basic Eng., Trans. ASME, Series D, vol. 83, no. 3, pp. 95-108, 1961.
3. A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. Roy. Statist. Soc. Ser. B, vol. 39, no. 1, pp. 1-38 (with discussion), 1977.
4. A. Doucet, N. De Freitas, and N. Gordon, Eds., Sequential Monte Carlo Methods in Practice, Springer, 2001.
5. O. Cappé, E. Moulines, and T. Rydén, Inference in Hidden Markov Models, Springer, 2005.
6. A. Doucet, S. Godsill, and C. Andrieu, "On sequential Monte-Carlo sampling methods for Bayesian filtering," Stat. Comput., vol. 10, pp. 197-208, 2000.
7. F. Campillo and F. Le Gland, "MLE for patially observed diffusions: Direct maximization vs. the EM algorithm," Stoch. Proc. App., vol. 33, pp. 245-274, 1989.
8. N. Gupta and R. Mehra, "Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations," IEEE Trans. Automat. Control, vol. 19, no. 6, pp. 774-783, 1974.
9. F. Le Gland and L. Mevel, "Recursive estimation in HMMs," in Proc. IEEE Conf. Decis. Control, 1997, pp. 3468-3473.
10. O. Cappé, V. Buchoux, and E. Moulines, "Quasi-Newton method for maximum likelihood estimation of hidden Markov models," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 1998, vol. 4, pp. 2265-2268.
11. I. B. Collings and T. Rydén, "A new maximum likelihood gradient algorithm for on-line hidden Markov model identification," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 1998, vol. 4, pp. 2261-2264.
12. M. Segal and E. Weinstein, "A new method for evaluating the log-likelihood gradient, the Hessian, and the Fisher information matrix for linear dynamic systems," IEEE Trans. Inform. Theory, vol. 35, pp. 682-687, 1989.
13. T. A. Louis, "Finding the observed information matrix when using the EM algorithm," J. Roy. Statist. Soc. Ser. B, vol. 44, pp. 226-233, 1982.
14. O. Zeitouni and A. Dembo, "Exact filters for the estimation of the number of transitions of finite-state continuous-time Markov processes," IEEE Trans. Inform. Theory, vol. 34, no. 4, July 1988.
15. R. J. Elliott, L. Aggoun, and J. B. Moore, Hidden Markov models: Estimation and Control, Springer, 1995.
16. O. Cappé, "Recursive computation of smoothed functionals of hidden Markovian processes using a particle approximation," Monte Carlo Methods Appl., vol. 7, no. 1-2, pp. 81-92, 2001.
17. J. Fichou, F. Le Gland, and L. Mevel, "Particle based methods for parameter estimation and tracking : Numerical experiments," Tech. Rep. PI-1604, INRIA, 2004.
18. A. Doucet and V. B. Tadić, "Parameter estimation in general state-space models using particle methods," Ann. Inst. Statist. Math., vol. 55, no. 2, pp. 409-422, 2003.