Mixture-based extension of the AR model and its recursive Bayesian identification

Abstract

Abstract-An extension of the AutoRegressive (AR) model is studied, which allows transformations and distortions on the regressor to be handled. Many important signal processing problems are amenable to this Extended AR (i.e. EAR) model. It is shown that Bayesian identification and prediction of the EAR model can be performed recursively, in common with the AR model itself. The EAR model does, however, require that the transformation be known. When it is unknown, the associated transformation space is represented by a finite set of candidates. What follows is a Mixture-based EAR model, i.e. the MEAR model. An approximate identification algorithm for MEAR is developed, using a restricted Variational Bayes (VB) procedure. It preserves the efficient recursive update of sufficient statistics. The MEAR model is applied to the robust identification of AR processes corrupted by outliers and burst noise respectively, and to click removal for speech.

Real-time regulated sliding mode controller design of multiple manipulator space free-flying robot

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“…Our novel approach is based on variational approximation methods [8], which have recently emerged as a deterministic alternative to Markov chain Monte-Carlo (MCMC) algorithms for doing Bayesian inference for probabilistic generative models [9,10], with better scalability in terms of computational cost [11]. Variational Bayesian inference has previously been applied to relevance vector machines [12], GMMs [13], autoregressive models [14,15], SMMs [16,17], mixtures of factor analyzers [18,19,20], discrete HMMs [21], Gaussian HMMs [22], as well as HMMs with…”