Modeling inverse covariance matrices by basis expansion

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., Σj⁻¹ = Pj = Σk = 1^D λk^jakak^T, λk^j ∈ ℝ^d. A generalized EM algorithm is proposed to obtain maximum likelihood parameter estimates for the basis set {akak^T} and the expansion coefficients {λk^j}. This model, called the Extended Maximum Likelihood Linear Transform (EMLLT) model, is extremely flexible: by varying the number of basis elements from d to 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.