Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes

Ben Calderhead; Mark Girolami; Neil D. Lawrence

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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.

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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 = 	 {/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 /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  - /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 /publications/calderhead-accelerating08.html.