Convergence of a particle-based approximation of the block online expectation maximization algorithm

ACM Transactions on Modeling and Computer Simulation

Volumn 23, Issue 1, 2013, Pages

  Corff, Sylvain Le ^a   Fort, Gersende ^a  

^a CNRS   (France)

Author keywords

Expectation maximization; Hidden markov models; Online estimation; Sequential Monte Carlo methods

Indexed keywords

CLOSED FORM; CONVERGENCE PROPERTIES; CONVERGENCE RESULTS; DATA STREAM; EXPECTATION - MAXIMIZATIONS; EXPECTATION-MAXIMIZATION ALGORITHMS; HIDDEN MARKOV; LARGE DATASETS; LATENT MODELS; MONTE CARLO; MONTE CARLO EXPERIMENTS; ON-LINE ESTIMATION; ONLINE EM; ONLINE EXPECTATION MAXIMIZATIONS; PARAMETER INFERENCE; SEQUENTIAL MONTE CARLO METHODS;

HIDDEN MARKOV MODELS; IMAGE SEGMENTATION; INFERENCE ENGINES; MAXIMUM PRINCIPLE; MONTE CARLO METHODS;

ALGORITHMS;

EID: 84873632768     PISSN: 10493301     EISSN: 15581195     Source Type: Journal    
DOI: 10.1145/2414416.2414418     Document Type: Article

References (35)

1. Bailey, T., Nieto, J., Guivant, J., Stevens, M., and Nebot, E. 2006. Consistency of the EKF-SLAM algorithm. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems. IEEE, 3562-3568.
2. Burgard, W., Fox, D., and Thrun, S. 2005. Probabilistic Robotics. MA:MIT Press, Cambridge.
3. Cappé, O. 2009. Online sequential Monte Carlo EM algorithm. In Proceedings of the IEEE Workshop on Statistical Signal Processing (SSP). IEEE, 37-40.
4. Cappé, O. 2011. Online EM algorithm for hidden Markov models. J. Comput. Graph. Statist. 20, 3, 728-749.
5. Cappé, O. and Moulines, E. 2009. Online expectation maximization algorithm for latent data models. J. Roy. Statist. Soc. B 71, 3, 593-613.
6. Cappé, O., Moulines, E., and Rydén, T. 2005. Inference in Hidden Markov Models. Springer, New York.
7. Davidson, J. 1994. Stochastic Limit Theory: An Introduction for Econometricians. Oxford University Press, Oxford.
8. Del Moral, P. 2004. Feynman-Kac Formulae. Genealogical and Interacting Particle Systems with Applications. Springer, New York.
9. Del Moral, P. and Guionnet, A. 1998. Large deviations for interacting particle systems: applications to nonlinear filtering. Stoch. Proc. App. 78, 69-95.
10. Del Moral, P., Ledoux, M., and Miclo, L. 2003. On contraction properties of Markov kernels. Probab. Theory Related Fields 126, 3, 395-420.
11. DelMoral, P., Doucet, A., and Singh, S. 2010a. A backward particle interpretation of Feynman-Kac formulae. ESAIM M2AN 44, 5, 947-975.
12. Del Moral, P., Doucet, A., and Singh, S. 2010b. Forward smoothing using sequential Monte Carlo. Tech. rep., arXiv:1012.5390v1.
13. Delyon, B., Lavielle, M., and Moulines, E. 1999. Convergence of a stochastic approximation version of the EM algorithm. Ann. Stat. 27, 1, 94-128.
14. Dempster, A. P., Laird, N. M., and Rubin, D. B. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. B 39, 1, 1-38 (with discussion).
15. Douc, R., Fort, G., Moulines, E., and Priouret, P. 2009. Forgetting the initial distribution for hidden Markov models. Stoch. Proc. Their Appl. 119, 4, 1235-1256.
16. Douc, R., Garivier, A., Moulines, E., and Olsson, J. 2011. Sequential Monte Carlo smoothing for general state space hidden Markov models. Ann. Appl. Probab. 21, 6, 2109-2145.
17. Doucet, A., De Freitas, N., and Gordon, N. 2001. Sequential Monte Carlo Methods in Practice. Springer, New York.
18. Doucet, A., Poyiadjis, G., and Singh, S. 2010. Particle approximations of the score and observed information matrix in state-space models with application to parameter estimation. Biometrika 98, 1, 65-80.
19. Dubarry, C. and Le Corff, S. 2011. Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models. Tech. rep., arXiv:1012.4183v1.
20. Fort, G. and Moulines, E. 2003. Convergence of the Monte Carlo Expectation Maximization for curved exponential families. Ann. Statist. 31, 4, 1220-1259.
21. Le Corff, S. and Fort, G. 2011a. Convergence of a particle-based approximation of the Block Online Expectation Maximization algorithm. Tech. rep., arXiv.
22. Le Corff, S. and Fort, G. 2011b. Online expectation maximization based algorithms for inference in Hidden Markov Models. Tech. rep., arXiv:1108.3968v1.
23. Le Corff, S. and Fort, G. 2011c. Supplement paper to "Online Expectation Maximization based algorithms for inference in Hidden Markov Models". Tech. rep., arXiv:1108.4130v1.
24. Le Corff, S., Fort, G., and Moulines, E. 2011. Online EM algorithm to solve the SLAM problem. in Proceedings of the IEEE Workshop on Statistical Signal Processing (SSP). IEEE, Nice.
25. Le Gland, F. and Mevel, L. 1997. Recursive estimation in HMMs. in Proceedings of the IEEE Conference on Decision Control. IEEE, 3468-3473.
26. Liu, J. 2001. Monte Carlo Strategies in Scientific Computing. Springer, New York.
27. Martinez-Cantin, R. 2008. Active map learning for robots: Insights into statistical consistency. Ph.D. dissertation, University of Zaragoza.
28. McLachlan, G. J. and Krishnan, T. 1997. the EM Algorithm and Extensions. Wiley, New York.
29. McLachlan, G. J. and Ng, S. K. 2003. On the choice of the number of blocks with the incremental EM algorithm for the fitting of normal mixtures. Stat. Comput. 13, 1, 45-55.
30. Meyn, S. P. and Tweedie, R. L. 1993. Markov Chains and Stochastic Stability. Springer, London.
31. Montemerlo, M., Thrun, S., Koller, D., and Wegbreit, B. 2003. FastSLAM 2.0: An improved particle filtering algorithm for simultaneous localization and mapping that provably converges. in Proceedings of the 16th Annual International Joint Conferences on Artificial Intelligence (IJCAI). AAAI Press, Mexico.
32. Polyak, B. T. 1990. a new method of stochastic approximation type. Autom. Remote Control 51, 98-107.
33. Tadić, V. B. 2010. Analyticity, convergence, and convergence rate of recursive maximum-likelihood estimation in hidden Markov models. IEEE Trans. Inf. Theor. 56, 6406-6432.
34. Titterington, D. M. 1984. Recursive parameter estimation using incomplete data. J. Roy. Statist. Soc. B 46, 2, 257-267.
35. Wu, C. F. J. 1983. On the convergence properties of the EM algorithm. Ann. Statist. 11, 95-103.