A Variational Approach to Robust Bayesian Interpolation

[edit]

Michael E. Tipping
Neil D. Lawrence, University of Sheffield

in Neural Networks for Signal Processing XIII, pp 229-238

Related Material

Abstract

This paper details a robust Bayesian interpolation procedure for linear-in-the-parameter models. Robustness is achieved via a Student-$t$ noise model, defined hierarchically in terms of an inverse-Gamma prior distribution over individual Gaussian observation variances. Variational techniques are exploited to update this prior in light of the data, while also inferring all other model variables. The key to this approach is flexibility; it can infer Gaussian noise where appropriate but can adapt to accommodate heavier-tailed distributions in the presence of outliers.


@InProceedings{tipping-variational03,
  title = 	 {A Variational Approach to Robust Bayesian Interpolation},
  author = 	 {Michael E. Tipping and Neil D. Lawrence},
  booktitle = 	 {Neural Networks for Signal Processing XIII},
  pages = 	 {229},
  year = 	 {2003},
  editor = 	 {Christophe Molina and Tülay Adali and Jan Larsen and Marc Van Hulle and Scott Douglas and Jean Rouat},
  month = 	 {00},
  publisher = 	 {IEEE},
  edit = 	 {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2003-01-01-tipping-variational03.md},
  url =  	 {http://inverseprobability.com/publications/tipping-variational03.html},
  abstract = 	 {This paper details a robust Bayesian interpolation procedure for linear-in-the-parameter models. Robustness is achieved via a Student-$t$ noise model, defined hierarchically in terms of an inverse-Gamma prior distribution over individual Gaussian observation variances. Variational techniques are exploited to update this prior in light of the data, while also inferring all other model variables. The key to this approach is flexibility; it can infer Gaussian noise where appropriate but can adapt to accommodate heavier-tailed distributions in the presence of outliers.},
  crossref =  {Molina:nnsp03},
  key = 	 {Tipping:variational03},
  linkpdf = 	 {ftp://ftp.dcs.shef.ac.uk/home/neil/robustBayesian.pdf},
  group = 	 {shefml}
 

}
%T A Variational Approach to Robust Bayesian Interpolation
%A Michael E. Tipping and Neil D. Lawrence
%B 
%C Neural Networks for Signal Processing XIII
%D 
%E Christophe Molina and Tülay Adali and Jan Larsen and Marc Van Hulle and Scott Douglas and Jean Rouat
%F tipping-variational03
%I IEEE	
%P 229--238
%R 
%U http://inverseprobability.com/publications/tipping-variational03.html
%X This paper details a robust Bayesian interpolation procedure for linear-in-the-parameter models. Robustness is achieved via a Student-$t$ noise model, defined hierarchically in terms of an inverse-Gamma prior distribution over individual Gaussian observation variances. Variational techniques are exploited to update this prior in light of the data, while also inferring all other model variables. The key to this approach is flexibility; it can infer Gaussian noise where appropriate but can adapt to accommodate heavier-tailed distributions in the presence of outliers.
TY  - CPAPER
TI  - A Variational Approach to Robust Bayesian Interpolation
AU  - Michael E. Tipping
AU  - Neil D. Lawrence
BT  - Neural Networks for Signal Processing XIII
PY  - 2003/01/01
DA  - 2003/01/01
ED  - Christophe Molina
ED  - Tülay Adali
ED  - Jan Larsen
ED  - Marc Van Hulle
ED  - Scott Douglas
ED  - Jean Rouat	
ID  - tipping-variational03
PB  - IEEE	
SP  - 229
EP  - 238
L1  - ftp://ftp.dcs.shef.ac.uk/home/neil/robustBayesian.pdf
UR  - http://inverseprobability.com/publications/tipping-variational03.html
AB  - This paper details a robust Bayesian interpolation procedure for linear-in-the-parameter models. Robustness is achieved via a Student-$t$ noise model, defined hierarchically in terms of an inverse-Gamma prior distribution over individual Gaussian observation variances. Variational techniques are exploited to update this prior in light of the data, while also inferring all other model variables. The key to this approach is flexibility; it can infer Gaussian noise where appropriate but can adapt to accommodate heavier-tailed distributions in the presence of outliers.
ER  -

Tipping, M.E. & Lawrence, N.D.. (2003). A Variational Approach to Robust Bayesian Interpolation. Neural Networks for Signal Processing XIII :229-238