On Bayesian Networks in Speech Signal Processing

This paper describes a class of relevant speech signal processing algorithms as probabilistic inference problems. Starting with an observation model that relates all involved random variables, we convert the respective joint probability density function into its Bayesian network representation in order to infer the desired signal estimates. After recalling the well-known Bayesian network descriptions of Wiener filtering and adaptive filtering, we show how the proportionate normalized least mean square (PNLMS) algorithm arises under certain restrictive assumptions on the covariance matrices of the latent random variables. In this context, the inherent relation of the Kalman filter, the normalized least mean square (NLMS), and the PNLMS algorithm is moreover outlined. We finally recall that also unsupervised signal estimation problems, such as dereverberation, can be considered from the same point of view.