The variational EM algorithm for on-line identification of extended AR models [speech processing example]

The autoregressive (AR) model is extended to cope with a wide class of possible transformations and degradations. The variational Bayes (VB) procedure is used to restore conjugacy. The resulting Bayesian recursive identification procedure has many of the desirable computational properties of the classical RLS procedure. During each time-step, an iterative variational EM (VEM) procedure is required to obtain the necessary moments. The procedure is used to reconstruct an outlier-corrupted AR process and a noisy speech segment. The VB scheme appears to offer improved performance over the related quasi-Bayes (QB) scheme in the case of time-variant component weights.