A Variational Approach to Robust Bayesian Interpolation

Michael E. Tipping, Neil D. Lawrence
Neural Networks for Signal Processing XIII, IEEE :229-238, 2003.

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.

Cite this Paper

BibTeX
@InProceedings{Tipping:variational03, title = {A Variational Approach to Robust {B}ayesian Interpolation}, author = {Tipping, Michael E. and Lawrence, Neil D.}, booktitle = {Neural Networks for Signal Processing XIII}, pages = {229--238}, year = {2003}, editor = {Molina, Christophe and Adali, Tülay and Larsen, Jan and Hulle, Marc Van and Douglas, Scott and Rouat, Jean}, publisher = {IEEE}, pdf = {https://lawrennd.github.io/publications/files/robustBayesian.pdf}, 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.} }
Endnote
%0 Conference Paper %T A Variational Approach to Robust Bayesian Interpolation %A Michael E. Tipping %A Neil D. Lawrence %B Neural Networks for Signal Processing XIII %D 2003 %E Christophe Molina %E Tülay Adali %E Jan Larsen %E Marc Van Hulle %E Scott Douglas %E Jean Rouat %F Tipping:variational03 %I IEEE %P 229--238 %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.
RIS
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 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 - https://lawrennd.github.io/publications/files/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 -
APA
Tipping, M.E. & Lawrence, N.D.. (2003). A Variational Approach to Robust Bayesian Interpolation. Neural Networks for Signal Processing XIII:229-238 Available from http://inverseprobability.com/publications/tipping-variational03.html.

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