Experiments with a Gaussian Merging-Splitting Algorithm for HMM Training for Speech Recognition

It is well known that the expectation-maximization (EM) algorithm, commonly used to estimate hidden Markov model (HMM) parameters for speech recognition, is sensitive to the initial model parameter values, making appropriate parameter initialization important. We investigate the use of iterative Gaussian splitting and EM training to initialize the desired number of Gaussians per HMM state (or state cluster). We then study merging of Gaussians which contain little training data as an approach to robust parameter estimation. Finally Gaussian merging and splitting is combined to form the Gaussian Merging-Splitting (GMS) algorithm. Detailed experimental studies show that Gaussian splitting gives similar performance to our previous training algorithm, even though the two algorithms give very different parameter values. The robust parameter estimation from Gaussian merging results in better performance than our old algorithm for speaker-independent models that have a large number of parameters relative to the amount of training data. In addition, in one experiment, speaker adaptation gave a 7% relative improvement in word error rate over the SI models when the SI models were trained with Gaussian splitting alone, as compared to a 15.5% improvement when the SI models were trained with both splitting and merging, even though the unadapted SI models gave similar performance. Finally, experiments with the GMS algorithm show that, for a given number of Gaussian parameters, better performance is achieved by reducing the number of HMM state clusters and increasing the number of Gaussians per state cluster.