Predictive hidden Markov model selection for decision tree state tying

This paper presents a novel predictive information criterion (PIC) for hidden Markov model (HMM) selection. The PIC criterion is exploited to select the best HMMs, which provide the largest prediction information for generalization of future data. When the randomness of HMM parameters is expressed by a product of conjugate prior densities, the prediction information is derived without integral approximation. In particular, a multivariate t distribution is attained to characterize the prediction information corresponding to HMM mean vector and precision matrix. When performing HMM selection in tree structure HMMs, we develop a top-down prior/posterior propagation algorithm for estimation of structural hyperparameters. The prediction information is accordingly determined so as to choose the best HMM tree model. The parameters of chosen HMMs can be rapidly computed via maximum a posteriori (MAP) estimation. In the evaluation of continuous speech recognition using decision tree HMMs, the PIC model selection criterion performs better than conventional maximum likelihood and minimum description length criteria in building a compact tree structure with moderate tree size and higher recognition rate.