Selecting hidden Markov model state number with cross-validated likelihood

Computational Statistics

Volumn 23, Issue 4, 2008, Pages 541-564

  Celeux, Gilles ^a   Durand, Jean Baptiste ^b  

^a INRIA   (France)

^b UNIV GRENOBLE ALPES   (France)

Author keywords

Cross validation; EM algorithm; Hidden Markov models; Missing values at random; Model selection

Indexed keywords

EID: 53549114249     PISSN: 09434062     EISSN: 16139658     Source Type: Journal    
DOI: 10.1007/s00180-007-0097-1     Document Type: Article

References (32)

1. Akaike H (1973). Information theory as an extension of the maximum likelihood theory. In: Petrov, BN and Csaki, F (eds) Second International Symposium on Information Theory, pp 267-281. Akademiai Kiado, Budapest
2. LE Baum T Petrie G Soules N Weiss 1970 A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains Ann Math Stat 41 1 164 171
3. Bernardo JM and Smith AFM (1994). Bayesian theory. Wiley, Chichester
4. C Biernacki G Celeux G Govaert 2001 Assessing a mixture model for clustering with the integrated completed likelihood IEEE Trans Pattern Anal Mach Intel 22 7 719 725
5. C Biernacki G Celeux G Govaert 2003 Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models Comput Stat Data Anal 41 3-4 561 575
6. Boucheron S, Gassiat E (2005) Inference in hidden Markov models, chapter order estimation. In: Cappé O, Moulines E, Rydén T (eds) Springer, Heidelberg
7. Celeux G, Clairambault J (1992) Estimation de chaînes de Markov cachées:méthodes et problèmes. In: Actes des journées thématiques Approches markoviennes en signal et images. GDR signal-images CNRS, pp 5-20
8. GA Churchill 1989 Stochastic models for heterogeneous DNA sequences Bull Math Biol 51 79 94
9. J Clairambault L Curzi-Dascalova F Kauffmann C Médigue C Leffler 1992 Heart rate variability in normal sleeping full-term and preterm neonates Early Human Dev 28 169 183
10. AP Dempster NM Laird DB Rubin 1977 Maximum likelihood from incomplete data via the EM Algorithm J R Stat Soc Ser B 39 1 38
11. PA Devijver 1985 Baum's forward-backward Algorithm revisited Pattern Recogn Lett 3 369 373
12. Durand J-B (2003) Modèles à structure cachée: inférence, séction de modèles et applications (in French). Ph.D. thesis, Université Grenoble 1 - Joseph Fourier
13. Y Ephraim N Merhav 2002 Hidden Markov processes IEEE Trans Inform Theory 48 1518 1569
14. C Fraley AE Raftery 2002 Model-based clustering, discriminant Analysis, and density estimation J Am Stat Assoc 97 611 631
15. E Gassiat 2002 Likelihood ratio inequalities with application to various mixtures Ann Inst Henri Poincaré 38 897 906
16. E Gassiat C Kéribin 2000 The likelihood ratio test for the number of components in a mixture with Markov regime ESAIM P S 4 25 52
17. RE Kass AE Raftery 1995 Bayes factors J Am Stat Assoc 90 430 773 795
18. C Kéribin 2000 Consistent estimation of the order of mixture models Sankhya Ser A 62 49 66
19. McLachlan GJ and Peel D (1997). On a resampling approach to choosing the number of components in normal mixture models. In: Billard, L and Fisher, NI (eds) Computing science and statistics, vol 28, pp 260-266. Interface Foundation of North America, Fairfax Station
20. McLachlan GJ and Peel D (2000). Finite mixture models. Wiley Series in probability and statistics. Wiley, London
21. LR Rabiner 1989 A tutorial on hidden Markov models and selected Applications in speech recognition Proc IEEE 77 257 286 (February)
22. RA Redner HF Walker 1984 Mixture densities, maximum likelihood and the EM algorithm SIAM Rev 26 2 195 239
23. Ripley BD (1996). Pattern recognition and neural networks. Cambridge University Press, London
24. CP Robert G Celeux J Diebolt 1993 Bayesian estimation of hidden Markov chains: A stochastic implementation Stat Probab Lett 16 1 77 83
25. AW Robertson S Kirshner P Smyth 2004 Downscaling of daily rainfall occurence over Northeast Brazil using a hidden Markov model J Clim 17 7 4407 4424
26. K Roeder L Wasserman 1997 Practical Bayesian density estimation using mixtures of normals J Am Stat Assoc 92 439 894 902
27. G Schwarz 1978 Estimating the dimension of a model Ann Stat 6 461 464
28. P Smyth 2000 Model selection for probabilistic clustering using cross-validated likelihood Stat Comput 10 1 63 72
29. DJ Spiegelhalter NG Best BP Carlin A van der Linde 2000 Bayesian measures of model complexity and fit (with discussion) J R Stat Soc Ser B 64 4 583 639
30. Y Yang 2005 Can the strengths of AIC and BIC be shared? A confict between model identification and regression estimation Biometrika 92 937 950
31. P Zhang 1993 Model selection via multifold cross validation Ann Stat 21 1 299 313
32. NR Zhang DO Siegmund 2007 A modified Bayes information criterion with applications to the analysis of comparative genomic hybridization data Biometrics 63 1 22 32