Message Passing-Based Inference for Time-Varying Autoregressive Models.

Albert Podusenko,Bert De Vries,Wouter M Kouw

doi:10.3390/e23060683

Albert Podusenko, Bert De Vries + Show 1 more

Open Access

https://doi.org/10.3390/e23060683

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Journal: Entropy	Publication Date: May 28, 2021
Citations: 6	License type: CC BY 4.0

Affiliation: Eindhoven University of Technology

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.

Highlights

Entropy 2021, 23, 683. https://Autoregressive (AR) models are capable of describing a wide range of time series patterns [1,2]
The factor graph representation that we employ in this paper provides some distinct advantages from other works on inference in Time-Varying AR (TVAR) models
We presented a variational message passing approach to tracking states and parameters in latent TVAR models

Summary

Introduction

Entropy 2021, 23, 683. https://Autoregressive (AR) models are capable of describing a wide range of time series patterns [1,2]. The realization of TVAR models in practice often poses some computational issues For many applications, such as speech processing in a hearing aid, both a low computational load and high modeling accuracy are essential. The problem of parameter tracking in TVAR models has been extensively explored in a non-Bayesian setting. In [14], expressions for the mean vector and covariance matrix of TVAR model coefficients are derived and [15] uses wavelets for TVAR model identification. All these approaches provide maximum likelihood estimates of coefficients for TVAR models without measurement noise. In [16], autoregressive parameters were estimated from noisy observations by using a recursive least-squares adaptive filter

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