Linear Latent Force Models Using Gaussian Processes

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Mauricio A. Álvarez, Universidad Tecnológica de Pereira, Colombia
David Luengo, Universidad Politécnica de Madrid
Neil D. Lawrence, University of Sheffield

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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.


@TechReport{alvarez-llfm11,
  title = 	 {Linear Latent Force Models Using Gaussian Processes},
  author = 	 {Mauricio A. Álvarez and David Luengo and Neil D. Lawrence},
  year = 	 {2011},
  institution = 	 {University of Sheffield},
  month = 	 {00},
  edit = 	 {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2011-01-01-alvarez-llfm11.md},
  url =  	 {http://inverseprobability.com/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.},
  key = 	 {Alvarez:llfm11},
  linkpdf = 	 {http://arxiv.org/pdf/1107.2699},
  linksoftware = {https://github.com/SheffieldML/multigp},
  OPTgroup = 	 {}
 

}
%T Linear Latent Force Models Using Gaussian Processes
%A Mauricio A. Álvarez and David Luengo and Neil D. Lawrence
%B 
%D 
%F alvarez-llfm11	
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%R 
%U http://inverseprobability.com/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.
TY  - CPAPER
TI  - Linear Latent Force Models Using Gaussian Processes
AU  - Mauricio A. Álvarez
AU  - David Luengo
AU  - Neil D. Lawrence
PY  - 2011/01/01
DA  - 2011/01/01	
ID  - alvarez-llfm11	
SP  - 
EP  - 
L1  - http://arxiv.org/pdf/1107.2699
UR  - http://inverseprobability.com/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  -

Álvarez, M.A., Luengo, D. & Lawrence, N.D.. (2011). Linear Latent Force Models Using Gaussian Processes.:-