# A Variational Approach to Robust Bayesian Interpolation

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

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

#### 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