Prediction under Uncertainty in Sparse Spectrum Gaussian Processes with Applications to Filtering and Control

Yunpeng Pan, Xinyan Yan, Evangelos A. Theodorou, Byron Boots
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:2760-2768, 2017.

Abstract

Sparse Spectrum Gaussian Processes (SSGPs) are a powerful tool for scaling Gaussian processes (GPs) to large datasets. Existing SSGP algorithms for regression assume deterministic inputs, precluding their use in many real-world robotics and engineering applications where accounting for input uncertainty is crucial. We address this problem by proposing two analytic moment-based approaches with closed-form expressions for SSGP regression with uncertain inputs. Our methods are more general and scalable than their standard GP counterparts, and are naturally applicable to multi-step prediction or uncertainty propagation. We show that efficient algorithms for Bayesian filtering and stochastic model predictive control can use these methods, and we evaluate our algorithms with comparative analyses and both real-world and simulated experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-pan17a, title = {Prediction under Uncertainty in Sparse Spectrum {G}aussian Processes with Applications to Filtering and Control}, author = {Yunpeng Pan and Xinyan Yan and Evangelos A. Theodorou and Byron Boots}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {2760--2768}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/pan17a/pan17a.pdf}, url = {https://proceedings.mlr.press/v70/pan17a.html}, abstract = {Sparse Spectrum Gaussian Processes (SSGPs) are a powerful tool for scaling Gaussian processes (GPs) to large datasets. Existing SSGP algorithms for regression assume deterministic inputs, precluding their use in many real-world robotics and engineering applications where accounting for input uncertainty is crucial. We address this problem by proposing two analytic moment-based approaches with closed-form expressions for SSGP regression with uncertain inputs. Our methods are more general and scalable than their standard GP counterparts, and are naturally applicable to multi-step prediction or uncertainty propagation. We show that efficient algorithms for Bayesian filtering and stochastic model predictive control can use these methods, and we evaluate our algorithms with comparative analyses and both real-world and simulated experiments.} }
Endnote
%0 Conference Paper %T Prediction under Uncertainty in Sparse Spectrum Gaussian Processes with Applications to Filtering and Control %A Yunpeng Pan %A Xinyan Yan %A Evangelos A. Theodorou %A Byron Boots %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-pan17a %I PMLR %P 2760--2768 %U https://proceedings.mlr.press/v70/pan17a.html %V 70 %X Sparse Spectrum Gaussian Processes (SSGPs) are a powerful tool for scaling Gaussian processes (GPs) to large datasets. Existing SSGP algorithms for regression assume deterministic inputs, precluding their use in many real-world robotics and engineering applications where accounting for input uncertainty is crucial. We address this problem by proposing two analytic moment-based approaches with closed-form expressions for SSGP regression with uncertain inputs. Our methods are more general and scalable than their standard GP counterparts, and are naturally applicable to multi-step prediction or uncertainty propagation. We show that efficient algorithms for Bayesian filtering and stochastic model predictive control can use these methods, and we evaluate our algorithms with comparative analyses and both real-world and simulated experiments.
APA
Pan, Y., Yan, X., Theodorou, E.A. & Boots, B.. (2017). Prediction under Uncertainty in Sparse Spectrum Gaussian Processes with Applications to Filtering and Control. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:2760-2768 Available from https://proceedings.mlr.press/v70/pan17a.html.

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