Deep Structured Mixtures of Gaussian Processes

Martin Trapp, Robert Peharz, Franz Pernkopf, Carl Edward Rasmussen
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:2251-2261, 2020.

Abstract

Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is based on local GP experts. However, local-expert techniques proposed so far are either not well-principled, come with limited approximation guarantees, or lead to intractable models. In this paper, we introduce deep structured mixtures of GP experts, a stochastic process model which i) allows exact posterior inference, ii) has attractive computational and memory costs, and iii) when used as GP approximation, captures predictive uncertainties consistently better than previous expert-based approximations. In a variety of experiments, we show that deep structured mixtures have a low approximation error and often perform competitive or outperform prior work.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-trapp20a, title = {Deep Structured Mixtures of Gaussian Processes}, author = {Trapp, Martin and Peharz, Robert and Pernkopf, Franz and Rasmussen, Carl Edward}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {2251--2261}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/trapp20a/trapp20a.pdf}, url = {https://proceedings.mlr.press/v108/trapp20a.html}, abstract = {Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is based on local GP experts. However, local-expert techniques proposed so far are either not well-principled, come with limited approximation guarantees, or lead to intractable models. In this paper, we introduce deep structured mixtures of GP experts, a stochastic process model which i) allows exact posterior inference, ii) has attractive computational and memory costs, and iii) when used as GP approximation, captures predictive uncertainties consistently better than previous expert-based approximations. In a variety of experiments, we show that deep structured mixtures have a low approximation error and often perform competitive or outperform prior work.} }
Endnote
%0 Conference Paper %T Deep Structured Mixtures of Gaussian Processes %A Martin Trapp %A Robert Peharz %A Franz Pernkopf %A Carl Edward Rasmussen %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-trapp20a %I PMLR %P 2251--2261 %U https://proceedings.mlr.press/v108/trapp20a.html %V 108 %X Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is based on local GP experts. However, local-expert techniques proposed so far are either not well-principled, come with limited approximation guarantees, or lead to intractable models. In this paper, we introduce deep structured mixtures of GP experts, a stochastic process model which i) allows exact posterior inference, ii) has attractive computational and memory costs, and iii) when used as GP approximation, captures predictive uncertainties consistently better than previous expert-based approximations. In a variety of experiments, we show that deep structured mixtures have a low approximation error and often perform competitive or outperform prior work.
APA
Trapp, M., Peharz, R., Pernkopf, F. & Rasmussen, C.E.. (2020). Deep Structured Mixtures of Gaussian Processes. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:2251-2261 Available from https://proceedings.mlr.press/v108/trapp20a.html.

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