Bayesian Learning of Gaussian Mixture Densities for Hidden Markov Models

Bayesian Learning of Gaussian Mixture Densities for Hidden Markov Models Jean-Luc Gauvain I and Chin-Hui Lee Speech Research Department AT&T Bell Laboratories Murray Hill, NJ 07974 ABSTRACT An investigation into the use of Bayesian learning of the parame- ters of a multivariate Gaassian mixture density has been carried out. In a continuous density hidden Markov model (CDHMM) framework, Bayesian learning serves as a unified approach for parameter smooth- ing, speaker adaptation, speaker clustering, and corrective training. The goal of this study is to enhance model robustness in a CDHMM- based speech recognition system so as to improve performance. Our ap- proach is to use Bayesian learning to incorporate prior knowledge into the CDHMM training process in the form of prior densities of the HMM parameters. The theoretical basis for this procedure is presented and preliminary results applying to HMM parameter smoothing, speaker adaptation, and speaker clustering are given. Performance improvements were observed on tests using the DARPA RM task. For speaker adaptation, under a supervised learning mode with 2 minutes of speaker-specific training data, a 31% reduction in word error rate was obtained compared to speaker-lndependent results. Using Baysesian learning for HMM parameter smoothing and sex-depen- dent modeling, a 21% error reduction was observed on the FEB91 test. INTRODUCTION When training sub-word units foi" continuous speech recogni- tion using probabilistic methods, we are faced with the general problem of sparse training data. This limits the effectiveness of conventional maximum likelihood approaches. The sparse train- ing data problem can not always be solved by the acquisition of more training data. For example, in the case of rapid adaptation to new speakers or environments, the amount of data available for adaptation is usually much less than what is needed to achieve good performance for speaker-dependent applications. Techniques used to alleviate the insufficient training data prob- lem include probability density ruction (pdf) smoothing, model interpolation, corrective training, and parameter sharing. The first three techniques have been developed for HMM with dis- crete pdfs and cannot be directly extended to the general case of continuous density hidden Markov model (CDHMM). For ex- ample, the classical scheme of model interpolation [4] [9] can be applied to CDHMM only if tied mixture HMMs or an increased number of mixture components are used. Our solution to the problem is to use Bayesian learning to incorporate prior knowledge into the CDHMM training process. 1Jeaa-Luc Gauvain is on leave from the Speech Commur, ication Group at LIMSI/CNRS, Orsay, France. The prior information consists of prior densities of the HMM pa- rameters. Such an approach was shown to be effective for speaker adaptation in isolated word recognition of a 39-word, English alpha-digit vocabulary where adaptation involved only the pa- rameters of a multivariate Gaussian state observation density of whole-word HMM's [12]. In this paper, Bayesian adaptation is extended to handle parameters of mixtures of Gaussian densi- ties. The theoretical basis for Bayesian learning of parameters of a multivariate Gaussian mixture density for HMM is developed. In a CDHMM framework, Bayesian …

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