Fast Gaussian Process Posteriors with Product Trees

David Moore, Stuart Russell
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, PMLR R12:843-852, 2014.

Abstract

Gaussian processes (GP) are a powerful tool for nonparametric regression; unfortunately, calcu- lating the posterior variance in a standard GP model requires time O(n2) in the size of the training set. Previous work by Shen et al. (2006) used a k-d tree structure to approximate the pos- terior mean in certain GP models. We extend this approach to achieve efficient approximation of the posterior covariance using a tree clustering on pairs of training points, and demonstrate sig- nificant improvements in performance with neg- ligible loss of accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR12-moore14a, title = {Fast {G}aussian Process Posteriors with Product Trees}, author = {Moore, David and Russell, Stuart}, booktitle = {Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence}, pages = {843--852}, year = {2014}, editor = {Zhang, Nevin L. and Tian, Jin}, volume = {R12}, series = {Proceedings of Machine Learning Research}, month = {23--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r12/main/assets/moore14a/moore14a.pdf}, url = {https://proceedings.mlr.press/r12/moore14a.html}, abstract = {Gaussian processes (GP) are a powerful tool for nonparametric regression; unfortunately, calcu- lating the posterior variance in a standard GP model requires time O(n2) in the size of the training set. Previous work by Shen et al. (2006) used a k-d tree structure to approximate the pos- terior mean in certain GP models. We extend this approach to achieve efficient approximation of the posterior covariance using a tree clustering on pairs of training points, and demonstrate sig- nificant improvements in performance with neg- ligible loss of accuracy.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Fast Gaussian Process Posteriors with Product Trees %A David Moore %A Stuart Russell %B Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2014 %E Nevin L. Zhang %E Jin Tian %F pmlr-vR12-moore14a %I PMLR %P 843--852 %U https://proceedings.mlr.press/r12/moore14a.html %V R12 %X Gaussian processes (GP) are a powerful tool for nonparametric regression; unfortunately, calcu- lating the posterior variance in a standard GP model requires time O(n2) in the size of the training set. Previous work by Shen et al. (2006) used a k-d tree structure to approximate the pos- terior mean in certain GP models. We extend this approach to achieve efficient approximation of the posterior covariance using a tree clustering on pairs of training points, and demonstrate sig- nificant improvements in performance with neg- ligible loss of accuracy. %Z Reissued by PMLR on 04 October 2026.
APA
Moore, D. & Russell, S.. (2014). Fast Gaussian Process Posteriors with Product Trees. Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R12:843-852 Available from https://proceedings.mlr.press/r12/moore14a.html. Reissued by PMLR on 04 October 2026.

Related Material