Cited by 157Bayesian Methods and Mixture ModelsControl Systems and IdentificationGaussian Processes and Bayesian Inference

Variational Bayes for generalized autoregressive models

Roberts, S.J., Penny, W.D.·2002·IEEE Transactions on Signal Processing

Abstract

We describe a variational Bayes (VB) learning algorithm for generalized autoregressive (GAR) models. The noise is modeled as a mixture of Gaussians rather than the usual single Gaussian. This allows different data points to be associated with different noise levels and effectively provides robust estimation of AR coefficients. The VB framework is used to prevent overfitting and provides model-order selection criteria both for AR order and noise model order. We show that for the special case of Gaussian noise and uninformative priors on the noise and weight precisions, the VB framework reduces to the Bayesian evidence framework. The algorithm is applied to synthetic and real data with encouraging results.

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Crossref · 10.1109/tsp.2002.801921

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  • The Free Energy is a better approximation to the model evidence than BIC.

    “This adaptability makes the Free Energy a better approximation to the model evidence, as has been shown empirically [6],[31].”

    From Comparing families of dynamic causal models (2010) · cites this paper as [31]

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Authors
Roberts, S. J., & Penny, W. D.
Affiliations
  • University of Oxford (GB)
  • University College London (GB)
Venue
IEEE Transactions on Signal Processing
Published
2002-09
Volume
50
Issue
9
Pages
2245-2257
ISSN
1053-587X (ISSN-L)
OpenAlex
W2043623344
Cited by
157
References
31
Citations by year
2025: 3 · 2024: 3 · 2023: 5 · 2022: 5 · 2021: 8 · 2020: 2 · 2019: 3 · 2018: 4 · 2017: 5 · 2016: 10 · 2015: 9 · 2014: 15 · 2013: 9 · 2012: 6
FWCI
4.48
Type
journal article
Language
en
Open access
closed
Locations
  • IEEE Transactions on Signal Processing (publishedVersion)
  • UCL Discovery (University College London) (submittedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
  • Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
  • Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
Keywords
variational inference, robust estimation, model order selection, overfitting, marginal likelihood

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