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Factor Graph-Based Online Bayesian Identification and Component Evaluation for Multivariate Autoregressive Exogenous

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  • 1Department of Electrical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands.

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Summary
This summary is machine-generated.

We introduce a novel factor graph for multivariate autoregressive models, enabling online Bayesian parameter identification. This method effectively tracks uncertainty propagation for improved predictive performance in time series analysis.

Keywords:
Bayesian inferenceautoregressive modelsmessage passingprobabilistic graphical modelsstochastic systemssystem identification

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Area of Science:

  • Machine Learning
  • Statistical Modeling
  • Time Series Analysis

Background:

  • Multivariate autoregressive (MAR) models with exogenous inputs are widely used for time series analysis.
  • Accurate parameter identification is crucial for reliable model predictions.
  • Existing methods may struggle with online updates and uncertainty quantification.

Purpose of the Study:

  • To develop a unified framework for parameter identification in MAR models using factor graphs.
  • To propose an online Bayesian procedure for parameter estimation based on message passing.
  • To analyze the propagation of uncertainty within the model and its impact on predictions.

Main Methods:

  • A Forney-style factor graph representation for MAR models with exogenous inputs was developed.
  • An online Bayesian parameter-identification procedure utilizing message passing was proposed.
  • Custom factor nodes for the MAR likelihood and matrix normal-Wishart distribution were derived.
  • Message-update rules were formulated to track parameter uncertainty and model evidence.

Main Results:

  • The message-passing procedure demonstrated convergence on a simulated autoregressive system.
  • The method achieved strong predictive performance on a benchmark task.
  • The analysis revealed how parameter uncertainty influences predictive uncertainty.
  • The contribution of individual model components to the overall evidence was elucidated.

Conclusions:

  • The proposed factor graph and message-passing approach provide an effective method for online parameter identification in MAR models.
  • This framework enhances uncertainty quantification and predictive accuracy.
  • The approach offers insights into model structure and evidence contributions.