Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes

[edit]

Ben Calderhead
Mark Girolami, University of Warwick
Neil D. Lawrence, University of Sheffield

in Advances in Neural Information Processing Systems 21, pp 217-224

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.


@InProceedings{calderhead-accelerating08,
  title = 	 {Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes},
  author = 	 {Ben Calderhead and Mark Girolami and Neil D. Lawrence},
  booktitle = 	 {Advances in Neural Information Processing Systems},
  pages = 	 {217},
  year = 	 {2009},
  editor = 	 {Daphne Koller and Dale Schuurmans and Yoshua Bengio and Leon Bottou},
  volume = 	 {21},
  address = 	 {Cambridge, MA},
  month = 	 {00},
  publisher = 	 {MIT Press},
  edit = 	 {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2009-01-01-calderhead-accelerating08.md},
  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.},
  crossref =  {Koller:nips08},
  key = 	 {Calderhead:accelerating08},
  group = 	 {GP, differential equations, systems biology}
 

}
%T Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes
%A Ben Calderhead and Mark Girolami and Neil D. Lawrence
%B 
%C Advances in Neural Information Processing Systems
%D 
%E Daphne Koller and Dale Schuurmans and Yoshua Bengio and Leon Bottou
%F calderhead-accelerating08
%I MIT Press	
%P 217--224
%R 
%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.
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
PY  - 2009/01/01
DA  - 2009/01/01
ED  - Daphne Koller
ED  - Dale Schuurmans
ED  - Yoshua Bengio
ED  - Leon Bottou	
ID  - calderhead-accelerating08
PB  - MIT Press	
SP  - 217
EP  - 224
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  -

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