Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes

Ben Calderhead, Mark Girolami, Neil D. Lawrence
Advances in Neural Information Processing Systems, MIT Press 21:217-224, 2009.

Abstract

Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our methdo involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible *without* solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and elay differential equations, and provide a comprehensive comparison with current state of the art methods.

Cite this Paper

BibTeX
@InProceedings{Calderhead:accelerating08, title = {Accelerating {B}ayesian Inference over Nonlinear Differential Equations with {G}aussian Processes}, author = {Calderhead, Ben and Girolami, Mark and Lawrence, Neil D.}, booktitle = {Advances in Neural Information Processing Systems}, pages = {217--224}, year = {2009}, editor = {Koller, Daphne and Schuurmans, Dale and Bengio, Yoshua and Bottou, Leon}, volume = {21}, address = {Cambridge, MA}, publisher = {MIT Press}, pdf = {https://proceedings.neurips.cc/paper/2008/file/07563a3fe3bbe7e3ba84431ad9d055af-Paper.pdf}, url = {http://inverseprobability.com/publications/calderhead-accelerating08.html}, abstract = {Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our methdo involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible *without* solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and elay differential equations, and provide a comprehensive comparison with current state of the art methods.} }
Endnote
%0 Conference Paper %T Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes %A Ben Calderhead %A Mark Girolami %A Neil D. Lawrence %B Advances in Neural Information Processing Systems %D 2009 %E Daphne Koller %E Dale Schuurmans %E Yoshua Bengio %E Leon Bottou %F Calderhead:accelerating08 %I MIT Press %P 217--224 %U http://inverseprobability.com/publications/calderhead-accelerating08.html %V 21 %X Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our methdo involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible *without* solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and elay differential equations, and provide a comprehensive comparison with current state of the art methods.
RIS
TY - CPAPER TI - Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes AU - Ben Calderhead AU - Mark Girolami AU - Neil D. Lawrence BT - Advances in Neural Information Processing Systems DA - 2009/01/01 ED - Daphne Koller ED - Dale Schuurmans ED - Yoshua Bengio ED - Leon Bottou ID - Calderhead:accelerating08 PB - MIT Press VL - 21 SP - 217 EP - 224 L1 - https://proceedings.neurips.cc/paper/2008/file/07563a3fe3bbe7e3ba84431ad9d055af-Paper.pdf UR - http://inverseprobability.com/publications/calderhead-accelerating08.html AB - Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our methdo involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible *without* solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and elay differential equations, and provide a comprehensive comparison with current state of the art methods. ER -
APA
Calderhead, B., Girolami, M. & Lawrence, N.D.. (2009). Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes. Advances in Neural Information Processing Systems 21:217-224 Available from http://inverseprobability.com/publications/calderhead-accelerating08.html.

Related Material