Factored Semi-Tied Covariance Matrices

A new form of covariance modelling for Gaussian mixture models and hidden Markov models is presented. This is an extension to an efficient form of covariance modelling used in speech recognition, semi-tied covariance matrices.In the standard form of semi-tied covariance matrices the covariance matrix is decomposed into a highly shared decorrelating transform and a component-specific diagonal covariance matrix. The use of a factored decorrelating transform is presented in this paper. This factoring effectivelyincreases the number of possible transforms without increasing thenumber of free parameters. Maximum likelihood estimation schemes for all the model parameters are presented including the component/transform assignment,transform and component parameters. This new model form is evaluated on a large vocabulary speech recognition task. It is shown that using this factored form of covariance modelling reduces the word error rate. 1 Introduction A standard problem in machine learning is to how to efficiently model correlations in multidimensional data.Solutions should be efficient both in terms of number of model parameters and cost of the likelihood calculation. For speech recognition this is particularly important due to the large number of Gaussian components used, typically in the tens of thousands, and the relatively large dimensionality of the data, typically 30-60.