Linear Latent Force Models Using Gaussian Processes

Mauricio A. Álvarez; David Luengo; Neil D. Lawrence

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Linear Latent Force Models Using Gaussian Processes

Mauricio A. Álvarez, David Luengo, Neil D. Lawrence

, 2011.

Abstract

Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.

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BibTeX


@Misc{Alvarez:llfm11,
  title = 	 {Linear Latent Force Models Using {G}aussian Processes},
  author = 	 {Álvarez, Mauricio A. and Luengo, David and Lawrence, Neil D.},
  year = 	 {2011},
  pdf = 	 {http://arxiv.org/pdf/1107.2699},
  url = 	 {/publications/alvarez-llfm11.html},
  abstract = 	 {Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.}
}

Endnote

%0 Generic
%T Linear Latent Force Models Using Gaussian Processes
%A Mauricio A. Álvarez
%A David Luengo
%A Neil D. Lawrence
%D 2011	
%F Alvarez:llfm11
%U /publications/alvarez-llfm11.html
%X Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.

RIS


TY  - GEN
TI  - Linear Latent Force Models Using Gaussian Processes
AU  - Mauricio A. Álvarez
AU  - David Luengo
AU  - Neil D. Lawrence
DA  - 2011/07/13	
ID  - Alvarez:llfm11
L1  - http://arxiv.org/pdf/1107.2699
UR  - /publications/alvarez-llfm11.html
AB  - Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data driven modelling with a physical model of the system. We show how different, physically-inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology and geostatistics.
ER  -

APA


Álvarez, M.A., Luengo, D. & Lawrence, N.D.. (2011). Linear Latent Force Models Using Gaussian Processes.  Available from /publications/alvarez-llfm11.html.