

Department of Engineering  
University of Cambridge > Engineering Department > Machine Intelligence Lab 
ADAPTING SEMITIED FULLCOVARIANCE MATRIX HMMS
M.J.F. Gales
August 1997
There is normally a simple choice made in the form of the covariance matrix to be used with HMMs. Either a diagonal covariance matrix is used, with the underlying assumption that elements of the feature vector are independent, or a full or blockdiagonal matrix is used, where all or some of the correlations are explicitly modelled. Unfortunately when using full or blockdiagonal covariance matrices there tends to be a dramatic increase in the number of parameters per Gaussian component, limiting the number of components which may be robustly estimated. This paper investigates a recently introduced form of covariance matrix, the semitied fullcovariance matrix. This allows a few ``full'' covariance matrices to be shared over many distributions, whilst each distribution maintains its own ``diagonal'' covariance matrix. In current systems it is essential to be able to rapidly adapt the acoustic models to a particular speaker or new acoustic environment. This paper examines two lineartransformation speakeradaptation schemes that may be applied to these semitied models. Both yield maximum likelihood estimates of the transform, but differ in the domains in which the transforms are estimated. A largevocabulary speakerindependent speechrecognition task was used to assess the performance of the techniques. Both the adaptation schemes showed gains in performance. Depending on the semitied model set used and the adaptation scheme improvements over the unadapted models ranged from 3% to 11% relative. Furthermore, a 9% relative reduction in word error rate was achieved over the standard model set adapted using maximum likelihood linear regression.
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