Basis superposition precision matrix modelling for large vocabulary continuous speech recognition

An important aspect of using Gaussian mixture models in a HMM-based speech recognition systems is the form of the covariance matrix. One successful approach has been to model the inverse covariance, precision, matrix by superimposing multiple bases. This paper presents a general framework of basis superposition. Models are described in terms of parameter tying of the basis coefficients and restrictions in the number of basis. Two forms of parameter tying are described which provide a compact model structure. The first constrains the basis coefficients over multiple basis vectors (or matrices). This is related to the Subspace for Precision and Mean (SPAM) model. The second constrains the basis coefficients over multiple components, yielding as one example heteroscedastic LDA (HLDA). Both maximum likelihood and minimum phone error training of these models are discussed. The performance of various configurations is examined on a conversational telephone speech task, SwitchBoard.