## Semi-Tied Covariance Matrices For Hidden Markov Models (1999)

Venue: | IEEE Transactions on Speech and Audio Processing |

Citations: | 181 - 27 self |

### BibTeX

@ARTICLE{Gales99semi-tiedcovariance,

author = {M.J.F. Gales},

title = {Semi-Tied Covariance Matrices For Hidden Markov Models},

journal = {IEEE Transactions on Speech and Audio Processing},

year = {1999},

volume = {7},

pages = {272--281}

}

### Years of Citing Articles

### OpenURL

### Abstract

There is normally a simple choice made in the form of the covariance matrix to be used with continuous-density HMMs. Either a diagonal covariance matrix is used, with the underlying assumption that elements of the feature vector are independent, or a full or block-diagonal matrix is used, where all or some of the correlations are explicitly modelled. Unfortunately when using full or block-diagonal 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 introduces a new form of covariance matrix which allows a few \full" covariance matrices to be shared over many distributions, whilst each distribution maintains its own \diagonal" covariance matrix. In contrast to other schemes which have hypothesised a similar form, this technique ts within the standard maximumlikelihood criterion used for training HMMs. The new form of covariance matrix is evaluated on a large-vocabulary speech-recognition task. In initial experiments the performance of the standard system was achieved using 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 recognition time. 2 1

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