Semi-tied covariance matrices for hidden Markov models

There is normally a simple choice made in the form of the covariance matrix to be used with continuous density HMM's, Either a diagonal covariance mat rix is used, with the underlying assumption that elements of the feature ve ctor are independent, or a full or block-diagonal matrix is used, where all or some of the correlations are explicitly modeled, Unfortunately when usi ng full or block-diagonal covariance matrices there tends to be a dramatic increase in the number of parameters per Gaussian component, limiting the n umber of components which may be robustly estimated. This paper introduces a new form of covariance matrix which allows a few "full" covariance matric es to be shared over many distributions, whilst each distribution maintains its own "diagonal" covariance matrix, In contrast to other schemes which h ave hypothesized a similar form, this technique fits within the standard ma ximum-likelihood criterion used for training HMM's. The ne iv form of covar iance matrix is evaluated on a large-vocabulary speech-recognition task, In initial experiments the performance of the standard system was achieved us ing approximately half the number of parameters. Moreover, a 10% reduction in word error rate compared to a standard system can be achieved with less than a 1% increase in the number of parameters and little increase in recog nition time.