Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations

David Barber, Yali Wang
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1485-1493, 2014.

Abstract

Bayesian parameter estimation in coupled ordinary differential equations (ODEs) is challenging due to the high computational cost of numerical integration. In gradient matching a separate data model is introduced with the property that its gradient can be calculated easily. Parameter estimation is achieved by requiring consistency between the gradients computed from the data model and those specified by the ODE. We propose a Gaussian process model that directly links state derivative information with system observations, simplifying previous approaches and providing a natural generative model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-barber14, title = {Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations}, author = {Barber, David and Wang, Yali}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1485--1493}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/barber14.pdf}, url = {https://proceedings.mlr.press/v32/barber14.html}, abstract = {Bayesian parameter estimation in coupled ordinary differential equations (ODEs) is challenging due to the high computational cost of numerical integration. In gradient matching a separate data model is introduced with the property that its gradient can be calculated easily. Parameter estimation is achieved by requiring consistency between the gradients computed from the data model and those specified by the ODE. We propose a Gaussian process model that directly links state derivative information with system observations, simplifying previous approaches and providing a natural generative model.} }
Endnote
%0 Conference Paper %T Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations %A David Barber %A Yali Wang %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-barber14 %I PMLR %P 1485--1493 %U https://proceedings.mlr.press/v32/barber14.html %V 32 %N 2 %X Bayesian parameter estimation in coupled ordinary differential equations (ODEs) is challenging due to the high computational cost of numerical integration. In gradient matching a separate data model is introduced with the property that its gradient can be calculated easily. Parameter estimation is achieved by requiring consistency between the gradients computed from the data model and those specified by the ODE. We propose a Gaussian process model that directly links state derivative information with system observations, simplifying previous approaches and providing a natural generative model.
RIS
TY - CPAPER TI - Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations AU - David Barber AU - Yali Wang BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-barber14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1485 EP - 1493 L1 - http://proceedings.mlr.press/v32/barber14.pdf UR - https://proceedings.mlr.press/v32/barber14.html AB - Bayesian parameter estimation in coupled ordinary differential equations (ODEs) is challenging due to the high computational cost of numerical integration. In gradient matching a separate data model is introduced with the property that its gradient can be calculated easily. Parameter estimation is achieved by requiring consistency between the gradients computed from the data model and those specified by the ODE. We propose a Gaussian process model that directly links state derivative information with system observations, simplifying previous approaches and providing a natural generative model. ER -
APA
Barber, D. & Wang, Y.. (2014). Gaussian Processes for Bayesian Estimation in Ordinary Differential Equations. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1485-1493 Available from https://proceedings.mlr.press/v32/barber14.html.

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