Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes

Ben Calderhead, Mark GirolamiNeil D. Lawrence
,  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{pmlr-v-calderhead-accelerating08, title = {Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes}, author = {Ben Calderhead and Mark Girolami and Neil D. Lawrence}, pages = {217--224}, year = {}, editor = {}, volume = {21}, address = {Cambridge, MA}, 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 %C Proceedings of Machine Learning Research %D %E %F pmlr-v-calderhead-accelerating08 %I PMLR %J Proceedings of Machine Learning Research %P 217--224 %U http://inverseprobability.com %V %W PMLR %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 - PY - DA - ED - ID - pmlr-v-calderhead-accelerating08 PB - PMLR SP - 217 DP - PMLR EP - 224 L1 - 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.. (). Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes. , in PMLR :217-224

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