Selecting Hidden Markov Model State Number with Cross-Validated Likelihood - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Computational Statistics Year : 2008

Selecting Hidden Markov Model State Number with Cross-Validated Likelihood


The problem of estimating the number of hidden states in a hidden Markov model is considered. Emphasis is placed on cross-validated likelihood criteria. Using cross-validation to assess the number of hidden states allows to circumvent the well-documented technical difficulties of the order identification problem in mixture models. Moreover, in a predictive perspective, it does not require that the sampling distribution belongs to one of the models in competition. However, computing cross-validated likelihood for hidden Markov models for which only one training sample is available, involves difficulties since the data are not independent. Two approaches are proposed to compute cross-validated likelihood for a hidden Markov model. The first one consists of using a deterministic half-sampling procedure, and the second one consists of an adaptation of the EM algorithm for hidden Markov models, to take into account randomly missing values induced by cross-validation. Numerical experiments on both simulated and real data sets compare different versions of cross-validated likelihood criterion and penalised likelihood criteria, including BIC and a penalised marginal likelihood criterion. Those numerical experiments highlight a promising behaviour of the deterministic half-sampling criterion.
Fichier principal
Vignette du fichier
cs2007.pdf (1.2 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

inria-00193098 , version 1 (10-11-2008)



Gilles Celeux, Jean-Baptiste Durand. Selecting Hidden Markov Model State Number with Cross-Validated Likelihood. Computational Statistics, 2008, 23 (4), pp.541-564. ⟨10.1007/s00180-007-0097-1⟩. ⟨inria-00193098⟩
421 View
5643 Download



Gmail Facebook X LinkedIn More