Variational bayesian learning for mixture autoregressive models with uncertain-order

Autoregressive (AR) models are fundamental tools for modeling a variety of signals in many fields of study. Selecting the appropriate order for AR models is typically accomplished using an information criterion to compare the models learned for all orders under consideration. The use of an information criterion for model order selection becomes increasingly computationally demanding when AR models are used as part of larger statistical models, such as mixture models, that have their own model order selection issues. Statistical models utilizing Dirichlet process (DP) priors provide a mechanism for automatically selecting the number of components within a mixture model, and have previously been utilized with AR components. These previous investigations utilize different priors for the AR parameters to enable automatic selection of the AR order and each makes us of computationally expensive Markov chain Monte Carlo (MCMC) sampling. This paper develops and evaluates a variational Bayesian (VB) inference procedure for the parameters of DP mixtures of AR components with uncertain order, to enable rapid parameter inference for AR based statistical models that provide automatic model order selection and is suitable for large scale problems. The previously utilized priors for AR models with uncertain order are evaluated to determine which is more appropriate for VB inference and the ability of the VB inference procedure for the developed model to correctly determine the number of mixture components and the AR order of each of the mixture components is shown to be comparable to computationally intensive MCMC inference. The VB inference procedure is then applied to an acoustic signal classification problem to illustrate the efficacy of AR based statistical models utilizing automated model order selection for real-world signal processing tasks. © 2011 IEEE.