Online Expectation Maximization based algorithms for inference in Hidden Markov Models

Electronic Journal of Statistics

Volumn 7, Issue 1, 2013, Pages 763-792

  Le Corff, Sylvain ^a   Fort, Gersende ^a  

^a INSTITUT TELECOM   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84884959903     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-EJS789     Document Type: Article

References (30)

1. Billingsley, P. Probability and Measure. Wiley, New York, 3rd edition, 1995. MR1324786
2. Cappé, O. Online sequential Monte Carlo EM algorithm. In IEEE Workshop on Statistical Signal Processing (SSP), 2009.
3. Cappé, O. Online EM algorithm for Hidden Markov Models. J. Comput. Graph. Statist., 20(3):728-749, 2011. MR2878999
4. Cappé, O. and Moulines, E. Online Expectation Maximization algorithm for latent data models. J. Roy. Statist. Soc. B, 71(3):593-613, 2009. MR2749909
5. Cappé, O., Moulines, E. and Rydén, T. Inference in Hidden Markov Models. Springer, 2005. MR2159833
6. Carlin, B. P., Polson, N. G. and Stoffer, D. S. A Monte Carlo approach to nonnormal and nonlinear state space modeling. Journal of the American Statistical Association, 87:493-500, 1992.
7. Churchill, G. Hidden Markov chains and the analysis of genome structure. Computers & Chemistry, 16(2):107-115, 1992.
8. Davidson, J. Stochastic Limit Theory: An Introduction for Econometricians. Oxford University Press, 1994. MR1430804
9. Del Moral, P. and Guionnet, A. Large deviations for interacting particle systems: applications to non-linear filtering. Stoch. Proc. App., 78:69-95, 1998. MR1653296
10. Del Moral, P., Ledoux, M. and Miclo, L. On contraction properties of Markov kernels. Probab. Theory Related Fields, 126(3):395-420, 2003. MR1992499
11. Del Moral, P., Doucet, A. and Singh, S. S. Forward smoothing using sequential Monte Carlo. arXiv:1012.5390v1, Dec 2010. MR2731399
12. Dempster, A. P., Laird, N. M. and Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B, 39(1):1-38 (with discussion), 1977. MR0501537
13. Douc, R., Moulines, E. and Rydén, T. Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime. Ann. Statist., 32(5):2254-2304, 2004. MR2102510
14. Doucet, A., De Freitas, N. and Gordon, N., editors. Sequential Monte Carlo Methods in Practice. Springer, New York, 2001. MR1847783
15. Dubarry, C. and Le Corff, S. Nonasymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models. Accepted for publication in Bernoulli, arXiv:1012.4183, 2012.
16. Fort, G. and Moulines, E. Convergence of the Monte Carlo Expectation Maximization for curved exponential families. Ann. Statist., 31(4):1220-1259, 2003. MR2001649
17. Hall, P. and Heyde, C. C. Martingale Limit Theory and its Application. Academic Press, New York, London, 1980. MR0624435
18. Juang, B. and Rabiner, L. Hidden Markov models for speech recognition. Technometrics, 33:251-272, 1991. MR1132665
19. Kushner, H. J. and Yin, G. G. Stochastic Approximation Algorithms and Applications. Springer, 1997. MR1453116
20. Le Corff, S. and Fort, G. Supplement paper to "Online Expectation Maximization based algorithms for inference in Hidden Markov Models". Technical report, arXiv:1108.4130, 2011.
21. Le Corff, S. and Fort, G. Convergence of a Particle-Based Approximation of the Block Online Expectation Maximization Algorithm. ACM Trans. Model. Comput. Simul., 23(1):2:1-2:22, 2013.
22. Le Corff, S., Fort, G. and Moulines, E. Online EM algorithm to solve the SLAM problem. In IEEE Workshop on Statistical Signal Processing (SSP), 2011.
23. Le Gland, F. and Mevel, L. Recursive estimation in HMMs. In Proc. IEEE Conf. Decis. Control, pages 3468-3473, 1997.
24. Mamon, R. S. and Elliott, R. J. Hidden Markov Models in Finance, volume 104 of International Series in Operations Research & Management Science. Springer, Berlin, 2007. MR2407726
25. Meyn, S. P. and Tweedie, R. L. Markov Chains and Stochastic Stability. Springer, London, 1993. MR1287609
26. Mongillo, G. and Denève, S. Online learning with hidden Markov models. Neural Computation, 20(7):1706-1716, 2008.. MR2417104
27. Pólya, G. and Szego{double acute}, G. Problems and Theorems in Analysis. Vol. II. Springer, 1976.
28. Polyak, B. T. and Juditsky, A. B. Acceleration of stochastic approximation by averaging. SIAM J. Control Optim., 30(4):838-855, 1992. MR1167814
29. Rio, E. Théorie asymptotique des processus aléatoires faiblement dépendants. Springer, 1990. MR2117923
30. Tadić, V. B. Analyticity, convergence, and convergence rate of recursive maximum-likelihood estimation in hidden Markov models. IEEE Trans. Inf. Theor., 56:6406-6432, December 2010. ISSN 0018-9448. MR2810007