Kernel Interpolation for Scalable Online Gaussian Processes

Samuel Stanton, Wesley Maddox, Ian Delbridge, Andrew Gordon Wilson
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3133-3141, 2021.

Abstract

Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential online setting. However, updating a GP posterior to accommodate even a single new observation after having observed $n$ points incurs at least $\mathcal{O}(n)$ computations in the exact setting. We show how to use structured kernel interpolation to efficiently reuse computations for constant-time $\mathcal{O}(1)$ online updates with respect to the number of points $n$, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-stanton21a, title = { Kernel Interpolation for Scalable Online Gaussian Processes }, author = {Stanton, Samuel and Maddox, Wesley and Delbridge, Ian and Gordon Wilson, Andrew}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3133--3141}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/stanton21a/stanton21a.pdf}, url = {https://proceedings.mlr.press/v130/stanton21a.html}, abstract = { Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential online setting. However, updating a GP posterior to accommodate even a single new observation after having observed $n$ points incurs at least $\mathcal{O}(n)$ computations in the exact setting. We show how to use structured kernel interpolation to efficiently reuse computations for constant-time $\mathcal{O}(1)$ online updates with respect to the number of points $n$, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting. } }
Endnote
%0 Conference Paper %T Kernel Interpolation for Scalable Online Gaussian Processes %A Samuel Stanton %A Wesley Maddox %A Ian Delbridge %A Andrew Gordon Wilson %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-stanton21a %I PMLR %P 3133--3141 %U https://proceedings.mlr.press/v130/stanton21a.html %V 130 %X Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential online setting. However, updating a GP posterior to accommodate even a single new observation after having observed $n$ points incurs at least $\mathcal{O}(n)$ computations in the exact setting. We show how to use structured kernel interpolation to efficiently reuse computations for constant-time $\mathcal{O}(1)$ online updates with respect to the number of points $n$, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting.
APA
Stanton, S., Maddox, W., Delbridge, I. & Gordon Wilson, A.. (2021). Kernel Interpolation for Scalable Online Gaussian Processes . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3133-3141 Available from https://proceedings.mlr.press/v130/stanton21a.html.

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