Maximum likelihood training of subspaces for inverse covariance modeling

Speech recognition systems typically use mixtures of diagonal Gaussians to model the acoustics. Using Gaussians with a more general covariance structure can give improved performance; EM-LLT and SPAM models give improvements by restricting the inverse covariance to a linear/affine subspace spanned by rank one and full rank matrices respectively. We consider training these subspaces to maximize likelihood. For EMLLT ML training the subspace results in significant gains over the scheme proposed by Olsen and Gopinath (see Proceedings of ICASSP, 2002). For SPAM ML training of the subspace slightly improves performance over the method reported by Axelrod, Gopinath and Olsen (see Proceedings of ICSLP, 2002). For the same subspace size an EMLLT model is more efficient computationally than a SPAM model, while the SPAM model is more accurate. This paper proposes a hybrid method of structuring the inverse covariances that both has good accuracy and is computationally efficient.