Stochastic versions of the EM algorithm: An experimental study in the mixture case

Journal of Statistical Computation and Simulation

Volumn 55, Issue 4, 1996, Pages 287-314

  Celeux, Gilles ^a   Chauveau, Didier ^b   Diebolt, Jean ^c  

^a INRIA RHÔNE ALPES   (France)

^b UNIVERSITÉ GUSTAVE EIFFEL   (France)

^c CNRS   (France)

Author keywords

Ergodic markov chain; Incomplete daa; Maximum likelihood estimation; Stochastic iterative algirithms

Indexed keywords

EID: 0030376179     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659608811772     Document Type: Article

References (26)

1. Basford, K. E. and McLachlan, G. J. (1985) Likelikood Estimation with Normal Mixture Models, Applied Statistics, 34, 282-289.
2. Biscarat, J. C. (1994) Almost Sure Convergence of a Class of Stochastic Algorithms, Stochatic Processes and their Applications, 50, 83-99.
3. Broniatowski, M., Celeux, G. and Diebolt, J. (1993) Reconnaissance de Mélanges de Densités par un algorithme d'Apprentissage Probabiliste, Data Analysis and Informatics (Diday E. et al; eds.) 3, 359-374 Amsterdam, North Holland.
4. Celeux, G. and Diebolt, J. (1985) The SEM Algorithm: a Probabilistic Teacher Algorithm Derived from the EM Algorithm for the Mixture Problem, Computational Statistics Quaterly, 2, 73-82.
5. Celeux, G. and Diebolt, J. (1986) Comportement Asymptotique d'un Algorithme d'Apprentissage Probabiliste pour les Mélanges de Lois de Probabilité, Rapport de recherche INRIA, 563.
6. Celeux, G. and Diebolt, J. (1987) A Probabilistic Teacher Algorithm for Iterative Maximum L ikelikood Estimation, Classification and related methods of Data Analysis, (Bock H.H. ed.), 617-623 Amsterdam, North Holland.
7. Celeux, G. and Diebolt, J. (1991) The EM and the SEM algorithms for mixtures: Statistical and numerical aspects, Cahiers du CERO, 32, 135-151.
8. Celeux, G. and Diebolt, J. (1992) A Stochastic Approximation Type EM Algorithm for the Mixture Problem. Stochastics and Stochastics Reports, 41, 119-134.
9. Celeux, G. and Govaert, G. (1993) Comparison of the Mixture and the Classification Maximum Likelihood in Cluster Analysis, Journal of Statis. Comput. simul., 47, 127-146.
10. Chauveau, D. (1992) Algorithmes EM et SEM pour un mélange censuré de distributions de défaillances-Application à la fiabilité, Revue de Statistique Appliquée 40, 67-76.
11. Chaveau, D. (1995) A Stochastic EM Algorithm for Mixtures with Censored Data, J. Statist. Plann. Inference, 46, 1-25.
12. Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977) Maximum L ikelikood from Incomplete Data via the EM Algorithm (with discussion), Journal of the Royal Statistical Society B, 39, 1-38.
13. Diebolt, J. and Celeux, G. (1993) Asymptotic Properties of a Stochastic EM Algorithm for estimating mixture proportions, Stochastic Models, 9, 599-613.
14. Ganesalingam, S. (1989) Classification and Mixture Approach to Clustering via Maximum L ikelihood, Applied Statistics, 38, 455-466.
15. van Laarhoven, P. J. M. and Aarts, E. H. L. (1987) Simulated Annealing: Theory and Applications, Reidel: Dordrecht.
16. Lavielle, M. and Moulines, E. (1995) on a Stochastic Approximation Version of The EM Algorithm, preprint, Université Paris-Sud (submitted to JRSS B).
17. Louis, T. A. (1982) Finding the Observed Information Matrix when Using the EM Algorithm, J. R. Statist. Soc., B44(2) 225-233.
18. McLachlan, G. J. and Basford, K. E. (1989) Mixture models-inference and Applications to Clustering, New York, Marcel Dekker.
19. Qian, W. and Titterington, D. M. (1991) Estimation of parameters in hidden Markov models, Phill. Trans. R. Soc. Lond, A 337, 407-428.
20. Redner, R. A. and Walker, H. F. (1984) Mixtures Densities, Maximum Likelikood and the EM Algorithm, SI AM Review, 26, 195-249.
21. Tanner, M. A. (1991) Tools for Statistical Inference., Lectures Notes in Statistics 67, New York, Springer-Verlag.
22. Tanner, M. A. and Wong, W. H. (1987) The Calculation of Posterior Distribution by Data Augmentation (with discussion), Journal of the American Statistical Association, 82, 528-550.
23. Titterington, D. M. (1990) some Recent Research in the Analysis of Mixture Distribution, Statistics, 21, 619-640.
24. Titterington, D. M., Simth, A. F. M. and Makov, U. E. (1985) Statistical analysis of Finite Mixture Distribution, New York, Wiley.
25. Wei, G. C. G. and Tanner, M. A. (1990) A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms, Journal of the American Statistical Association, 85, 699-704.
26. Wu, C. F. (1993) On the Convergence Properties of the EM Algorithm, Annals of Statistics, 11, 95-103.