Message passing-based Inference for time-varying autoregressive models

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Abstract

Time-varying autoregressive (TVAR) models are widely used for modeling of non-stationary signals. Unfortunately, online joint adaptation of both states and parameters in these models remains a challenge. In this paper, we represent the TVAR model by a factor graph and solve the inference problem by automated message passing-based inference for states and parameters. We derive structured variational update rules for a composite "AR node" with probabilistic observations that can be used as a plug-in module in hierarchical models, for example, to model the time-varying behavior of the hyper-parameters of a time-varying AR model. Our method includes tracking of variational free energy (FE) as a Bayesian measure of TVAR model performance. The proposed methods are verified on a synthetic data set and validated on real-world data from temperature modeling and speech enhancement tasks.

Original languageEnglish
Pages (from-to)1-32
JournalEntropy
Volume23
Issue number6
DOIs
Publication statusPublished - 28 May 2021

Keywords

  • Bayesian inference
  • free energy
  • factor graph
  • hybrid message passing
  • model selection
  • nonstationary systems
  • probabilistic graphical models

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