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Reports (Research Report) Year : 2006

Selecting Hidden Markov Chain States Number with Cross-Validated Likelihood


The problem of estimating the number of hidden states in a hidden Markov chain 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 chains involves difficulties since the data are not independent. Two approaches are proposed to compute cross-validated likelihood for a hidden Markov chain. 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 chains, 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 hightlight a promising behaviour of the deterministic half-sampling criterion.
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Dates and versions

inria-00071392 , version 1 (23-05-2006)


  • HAL Id : inria-00071392 , version 1


Gilles Celeux, Jean-Baptiste Durand. Selecting Hidden Markov Chain States Number with Cross-Validated Likelihood. [Research Report] RR-5877, INRIA. 2006. ⟨inria-00071392⟩
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