Variational multiple shooting for Bayesian ODEs with Gaussian processes

Pashupati Hegde, Çağatay Yıldız, Harri Lähdesmäki, Samuel Kaski, Markus Heinonen
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:790-799, 2022.

Abstract

Recent machine learning advances have proposed black-box estimation of \textit{unknown continuous-time system dynamics} directly from data. However, earlier works are based on approximative solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method demonstrates the benefit of computing vector field posteriors, with predictive uncertainty scores outperforming alternative methods on multiple ODE learning tasks.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-hegde22a, title = {Variational multiple shooting for Bayesian ODEs with Gaussian processes}, author = {Hegde, Pashupati and Y{\i}ld{\i}z, \c{C}a\u{g}atay and L{\"a}hdesm{\"a}ki, Harri and Kaski, Samuel and Heinonen, Markus}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {790--799}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/hegde22a/hegde22a.pdf}, url = {https://proceedings.mlr.press/v180/hegde22a.html}, abstract = {Recent machine learning advances have proposed black-box estimation of \textit{unknown continuous-time system dynamics} directly from data. However, earlier works are based on approximative solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method demonstrates the benefit of computing vector field posteriors, with predictive uncertainty scores outperforming alternative methods on multiple ODE learning tasks.} }
Endnote
%0 Conference Paper %T Variational multiple shooting for Bayesian ODEs with Gaussian processes %A Pashupati Hegde %A Çağatay Yıldız %A Harri Lähdesmäki %A Samuel Kaski %A Markus Heinonen %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-hegde22a %I PMLR %P 790--799 %U https://proceedings.mlr.press/v180/hegde22a.html %V 180 %X Recent machine learning advances have proposed black-box estimation of \textit{unknown continuous-time system dynamics} directly from data. However, earlier works are based on approximative solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method demonstrates the benefit of computing vector field posteriors, with predictive uncertainty scores outperforming alternative methods on multiple ODE learning tasks.
APA
Hegde, P., Yıldız, Ç., Lähdesmäki, H., Kaski, S. & Heinonen, M.. (2022). Variational multiple shooting for Bayesian ODEs with Gaussian processes. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:790-799 Available from https://proceedings.mlr.press/v180/hegde22a.html.

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