Fast Forward Selection to Speed Up Sparse Gaussian Process Regression

Matthias W. Seeger, Christopher K. I. Williams, Neil D. Lawrence
Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, PMLR R4:254-261, 2003.

Abstract

We present a method for the sparse greedy approximation of Bayesian Gaussian process regression, featuring a novel heuristic for very fast forward selection. Our method is essentially as fast as an equivalent one which selects the "support" patterns at random, yet it can outperform random selection on hard curve fitting tasks. More importantly, it leads to a sufficiently stable approximation of the log marginal likelihood of the training data, which can be optimised to adjust a large number of hyperparameters automatically. We demonstrate the model selection capabilities of the algorithm in a range of experiments. In line with the development of our method, we present a simple view on sparse approximations for GP models and their underlying assumptions and show relations to other methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR4-seeger03a, title = {Fast Forward Selection to Speed Up Sparse Gaussian Process Regression}, author = {Seeger, Matthias W. and Williams, Christopher K. I. and Lawrence, Neil D.}, booktitle = {Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics}, pages = {254--261}, year = {2003}, editor = {Bishop, Christopher M. and Frey, Brendan J.}, volume = {R4}, series = {Proceedings of Machine Learning Research}, month = {03--06 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r4/seeger03a/seeger03a.pdf}, url = {https://proceedings.mlr.press/r4/seeger03a.html}, abstract = {We present a method for the sparse greedy approximation of Bayesian Gaussian process regression, featuring a novel heuristic for very fast forward selection. Our method is essentially as fast as an equivalent one which selects the "support" patterns at random, yet it can outperform random selection on hard curve fitting tasks. More importantly, it leads to a sufficiently stable approximation of the log marginal likelihood of the training data, which can be optimised to adjust a large number of hyperparameters automatically. We demonstrate the model selection capabilities of the algorithm in a range of experiments. In line with the development of our method, we present a simple view on sparse approximations for GP models and their underlying assumptions and show relations to other methods.}, note = {Reissued by PMLR on 01 April 2021.} }
Endnote
%0 Conference Paper %T Fast Forward Selection to Speed Up Sparse Gaussian Process Regression %A Matthias W. Seeger %A Christopher K. I. Williams %A Neil D. Lawrence %B Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2003 %E Christopher M. Bishop %E Brendan J. Frey %F pmlr-vR4-seeger03a %I PMLR %P 254--261 %U https://proceedings.mlr.press/r4/seeger03a.html %V R4 %X We present a method for the sparse greedy approximation of Bayesian Gaussian process regression, featuring a novel heuristic for very fast forward selection. Our method is essentially as fast as an equivalent one which selects the "support" patterns at random, yet it can outperform random selection on hard curve fitting tasks. More importantly, it leads to a sufficiently stable approximation of the log marginal likelihood of the training data, which can be optimised to adjust a large number of hyperparameters automatically. We demonstrate the model selection capabilities of the algorithm in a range of experiments. In line with the development of our method, we present a simple view on sparse approximations for GP models and their underlying assumptions and show relations to other methods. %Z Reissued by PMLR on 01 April 2021.
APA
Seeger, M.W., Williams, C.K.I. & Lawrence, N.D.. (2003). Fast Forward Selection to Speed Up Sparse Gaussian Process Regression. Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R4:254-261 Available from https://proceedings.mlr.press/r4/seeger03a.html. Reissued by PMLR on 01 April 2021.

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