Latent Force Models

Mauricio Álvarez, David Luengo, Neil D. Lawrence
Proceedings of the Twelfth International Conference 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v5-alvarez09a, title = {Latent Force Models}, author = {Álvarez, Mauricio and Luengo, David and Lawrence, Neil D.}, booktitle = {Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics}, pages = {9--16}, year = {2009}, editor = {van Dyk, David and Welling, Max}, volume = {5}, series = {Proceedings of Machine Learning Research}, address = {Hilton Clearwater Beach Resort, Clearwater Beach, Florida USA}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v5/alvarez09a/alvarez09a.pdf}, url = {https://proceedings.mlr.press/v5/alvarez09a.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 Álvarez %A David Luengo %A Neil D. Lawrence %B Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2009 %E David van Dyk %E Max Welling %F pmlr-v5-alvarez09a %I PMLR %P 9--16 %U https://proceedings.mlr.press/v5/alvarez09a.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 Álvarez AU - David Luengo AU - Neil D. Lawrence BT - Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics DA - 2009/04/15 ED - David van Dyk ED - Max Welling ID - pmlr-v5-alvarez09a PB - PMLR DP - Proceedings of Machine Learning Research VL - 5 SP - 9 EP - 16 L1 - http://proceedings.mlr.press/v5/alvarez09a/alvarez09a.pdf UR - https://proceedings.mlr.press/v5/alvarez09a.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., Luengo, D. & Lawrence, N.D.. (2009). Latent Force Models. Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 5:9-16 Available from https://proceedings.mlr.press/v5/alvarez09a.html.

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