Variational Bayes for generalized autoregressive models
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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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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Kini, B. V., & Sekhar, C. C. (2011) · Pattern Analysis and Applications · doi:10.1007/s10044-011-0247-5 · Cited by 8 · see citing works
Variational segmentation of color images
Nasios, N., & Borş, A. G. (2005) · Proceedings - International Conference on Image Processing · doi:10.1109/icip.2005.1530130 · Cited by 8 · see citing works
Optimal experimental design for parameter identification and model selection
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Temporally correlated source separation using variational Bayesian learning approach
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Extracting novel information from neuroimaging data using neural fields
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Depth of Anaesthesia Assessment with Generative Polyspectral Models
Rezek, I. A., Roberts, S., Siva, E., & Conradt, R. (2006) · International Conference on Machine Learning and Applications · doi:10.1109/icmla.2005.21 · Cited by 7 · see citing works
Self-citationBayesian estimation of non-stationary AR model parameters via an unknown forgetting factor
Smidl, A. Q. V. (2005) · IEEE Digital Signal Processing Workshop and IEEE Signal Processing Education Workshop (DSP/SPE) · doi:10.1109/dspws.2004.1437946 · Cited by 7 · see citing works
Sequential Bayesian kernel modelling with non-Gaussian noise
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Joint speech enhancement and speaker identification using approximate Bayesian inference
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Variational expectation-maximization training for Gaussian networks
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Extended Expectation Maximization for Under-Fitted Models
Rekavandi, A. M., Seghouane, A., Boussaïd, F., & Bennamoun, M. (2023) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp49357.2023.10095526 · Cited by 6 · see citing works
ARMADA: Using motif activity dynamics to infer gene regulatory networks from gene expression data
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The Need for Adding Judgment in Bayesian Prediction
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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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