Latent Force Models

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

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Latent Force Models

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

Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics, PMLR 5:9-16, 2009.

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 modeling 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 computational biology, motion capture and geostatistics.

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BibTeX


@InProceedings{Alvarez:lfm09,
  title = 	 {Latent Force Models},
  author = 	 {Álvarez, Mauricio A. and Luengo, David and Lawrence, Neil D.},
  booktitle = 	 {Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics},
  pages = 	 {9--16},
  year = 	 {2009},
  editor = 	 {van Dyk, David and Welling, Max},
  volume = 	 {5},
  address = 	 {Clearwater Beach, FL},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v5/alvarez09a/alvarez09a.pdf},
  url = 	 {/publications/alvarez-lfm09.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 modeling 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 computational biology, motion capture and geostatistics.}
}

Endnote

%0 Conference Paper
%T Latent Force Models
%A Mauricio A. Álvarez
%A David Luengo
%A Neil D. Lawrence
%B Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics
%D 2009
%E David van Dyk
%E Max Welling	
%F Alvarez:lfm09
%I PMLR
%P 9--16
%U /publications/alvarez-lfm09.html
%V 5
%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 modeling 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 computational biology, motion capture and geostatistics.

RIS


TY  - CPAPER
TI  - Latent Force Models
AU  - Mauricio A. Álvarez
AU  - David Luengo
AU  - Neil D. Lawrence
BT  - Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics
DA  - 2009/04/15
ED  - David van Dyk
ED  - Max Welling	
ID  - Alvarez:lfm09
PB  - PMLR
VL  - 5
SP  - 9
EP  - 16
L1  - http://proceedings.mlr.press/v5/alvarez09a/alvarez09a.pdf
UR  - /publications/alvarez-lfm09.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 modeling 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 computational biology, motion capture and geostatistics.
ER  -

APA


Álvarez, M.A., Luengo, D. & Lawrence, N.D.. (2009). Latent Force Models. Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics 5:9-16 Available from /publications/alvarez-lfm09.html.