Fitting probabilistic automata VIA the EM algorithm

Communications in Statistics. Part C: Stochastic Models

Volumn 12, Issue 3, 1996, Pages 405-424

  Turin, William ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

EM algorithm; Hidden Markov models; Markov modulated Bernoulli processes; Markov modulated Poisson processes; Markovian arrival; Model fitting; Phase type distributions; Probabilistic automata

Indexed keywords

BERNOULLI PROCESS; EM ALGORITHM; KULLBACK LEIBLER INFORMATION; MAXIMUM LIKELIHOOD; OPTIMIZATION METHOD; POISSON PROCESS; PROBABILISTIC AUTOMATON;

MARKOV PROCESSES; SEQUENTIAL MACHINES;

RANDOM PROCESSES;

EID: 0030360328     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1080/15326349608807392     Document Type: Article

References (30)

1. Abate J. and Whitt W., (1992) "The Fourier-series method for inverting transforms of probability distributions," Queueing Syst. 10, 5-88.
2. Asmussen, S. and Nerman, O. (1991) "Fitting phase-type distributions via the EM algorithm," Symposium i Anvendt Statistik, Copenhagen, 335-346.
3. Bacon, G. C. (1964) "Minimal-state stochastic finite state systems," IEEE Trans. on Circuit Theory, CT-11, 307-308.
4. Baum L. E. and Eagon, J. A. (1967) "An inequality with applications to statistical estimation for probabilistic functions of Markov processes ant to a model of ecology," Bull. Amer. Math. Soc. 73, 360-363.
5. Baum, L. E. Petrie, T. Soules, G. and Weiss, N. (1970) "A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains," Ann. Math. Statist. 41, 164-171.
6. Carlyle, J. W. (1963) "Reduced forms for stochastic sequential machines," J. Math. Anal. and Appl., 7, No. 2, 167-175.
7. Dempster, A. P. Laird, N. M. and Rubin, D. B. (1977) "Maximum likelihood from incomplete data via the EM algorithm," J. R. Statist. Ass.,76, 341-353.
8. Ephraim, Y. Dembo, A. and Rabiner, L. (1989) "A minimum discrimination information approach for hidden Markov modeling," IEEE Trans. Inf. Theor., 35, No. 5, 1001-1013.
9. Even, S. (1965) "Comments on the minimization of stochastic machines," IEEE Trans. on Electron. Comp., EC-14, No. 4, 634-637.
10. Gantmacher, F. R. (1977) The Theory of Matrices,Chelsea, New York.
11. Juang, B. H. and Rabiner, L. R. (1985) "A probabilistic distance measure for hidden Markov models," AT&T Tech. J., 64 (2), 391-408.
12. Kantorovich L. V. and Akilov, G. P. (1964) Functional Analysis in Normed Spaces, MacMillan, New York.
13. Kemeny, J. G. and Snell, J. L. (1960) Finite Markov Chains, Van Nostrand, Princeton, NJ.
14. Kullback, S. (1959) Information Theory and Statistics, John Wiley & Sons, New York.
15. Leroux, B. G. (1992) "Maximum-likelihood estimation for hidden Markov models," Stock. Proc. Appl.,40, 127-143.
16. Louis, T. A. (1982) "Finding the observed information matrix when using the EM algorithm," J. R. Statist. Soc., 44, 226-233.
17. Meier-Hellstern, K. S. (1987) "A fitting algorithm for Markov-modulated Poisson processes having two arrival rates," Eur. J. Op. Res.,29, 370-377.
18. Meilijson, I (1989) "A fast improvement of the EM algorithm on its own terms," J. R. Statist. Soc.,51, 127-138.
19. Moler C. and Van Loan C. (1978) "Nineteen dubious ways to compute the exponential of a matrix," SIAM Review 20, 801-836.
20. Neuts, M. F. (1981) Matrix-Geometric Solutions in Stochastic Models, John Hopkinks, Baltimore.
21. Paz, A. (1971) Introduction to Probabilistic Automata, Academic Press, New York.
22. Rabiner, L. and Juang, B.-H. (1993) Fundamentals of Speech Recognition, Prentice Hall, Englewood Cliffs, New Jersey.
23. Redner, R. A. and Walker, H. F. (1984) "Mixture densities, maximum likelihood and the EM algorithm," SIAM Review, 26, 195-239.
24. Ryden, T (1993) An EM algorithm for multiple state MMPP parameter estimation, Dept. of Math. Statist., Lund Institute of Technology.
25. Turin, W. (1990) Performance Analysis of Digital Transmission Systems, Computer Science Press, New York.
26. Turin, W. and Sondhi, M. M. (1993) "Modeling error sources in digital channels," IEEE Journ. Sel. Areas in Commun.,11, No. 3, 340-347.
27. Turin, W. (1995) "Minimum Divergence Solutions for Positive Inverse Problems," submitted for publication.
28. Vardi, Y. and Lee, D. (1993) "From image deblurring to optimal investments: maximum likelihood solutions for positive linear inverse problems," J. R. Statist. Soc.,55, 569-612.
29. Wu, C. F. J. (1983) "On the convergence properties of the EM algorithm," Ann. Statist. 11, 95-103.
30. Zangwill, W. I. (1969) Nonlinear Programming: A Unified Approach, Prentice Hall, Englewood Cliffs, NJ.