## Modeling Inverse Covariance Matrices by Basis Expansion (2003)

Citations: | 35 - 9 self |

### BibTeX

@MISC{Olsen03modelinginverse,

author = {Peder A. Olsen and Ramesh A. Gopinath and Senior Member},

title = {Modeling Inverse Covariance Matrices by Basis Expansion},

year = {2003}

}

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### OpenURL

### Abstract

This paper proposes a new covariance modeling technique for Gaussian Mixture Models. Specifically the inverse covariance (precision) matrix of each Gaussian is expanded in a rank-1 basis i.e., j = P j = k , 2 R; a k 2 R . A generalized EM algorithm is proposed to obtain maximum likelihood parameter estimates for the basis set fa k a k=1 and the expansion coefficients f g. This model, called the Extended Maximum Likelihood Linear Transform (EMLLT) model, is extremely flexible: by varying the number of basis elements from D = d to D = d(d + 1)=2 one gradually moves from a Maximum Likelihood Linear Transform (MLLT) model to a full-covariance model. Experimental results on two speech recognition tasks show that the EMLLT model can give relative gains of up to 35% in the word error rate over a standard diagonal covariance model, 30% over a standard MLLT model.