The Application of Bayesian Inference to Linear Prediction of Speech

The analysis of a speech segment is conventionally performed through linear prediction and the subsequent minimisation of a data error term in the least squares sense. The parameters derived as such maximise the likelihood of the data. In a learning problem, the addition of penalty terms, or regularisers, to the data term facilitates the estimation of the Maximum a Posteriori , or MAP, parameters. A direct equivalence can be drawn between the type of regulariser used and the prior assumptions regarding the solution. The Bayesian evidence procedure provides a framework for MAP parameter estimation and model order selection. In this paper, the use of suitable quadratic regularisers for the determination of linear prediction MAP parameters is addressed. The application of continuity constraints across successive speech segments will be demonstrated to enhance the tracking of formants for speech embedded in gaussian noise. The use of variable order models for speech analysis-synthesis is also addressed and its apparent beneets discussed.