Selecting hidden Markov model state number with cross-validated likelihood |
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Authors: | Gilles Celeux Jean-Baptiste Durand |
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Institution: | 1. Département de Mathématiques, INRIA Futurs, Orsay, Université Paris-Sud, Batiment 425, 91405, Orsay Cedex, France 2. Laboratoire Jean Kuntzmann, INRIA Rh?ne-Alpes, Grenoble Universités, 51 rue des Mathématiques, B.P. 53,, 38 041, Grenoble Cedex 9, France
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Abstract: | 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. |
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Keywords: | Hidden Markov models Model selection Cross-validation Missing values at random EM algorithm |
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