# Latent Force Models

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

in Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics 5, pp 9-16

#### 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.

  @InProceedings{alvarez-lfm09, title = {Latent Force Models}, author = {Mauricio A. Álvarez and David Luengo and Neil D. Lawrence}, booktitle = {Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics}, pages = {9}, year = {2009}, editor = {David van Dyk and Max Welling}, volume = {5}, address = {Clearwater Beach, FL}, month = {00}, publisher = {JMLR W\&CP 5}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2009-01-01-alvarez-lfm09.md}, url = {http://inverseprobability.com/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.}, crossref = {Welling:aistats09}, key = {Alvarez:lfm09}, linkpdf = {http://jmlr.csail.mit.edu/proceedings/papers/v5/alvarez09a/alvarez09a.pdf}, linksoftware = {https://github.com/SheffieldML/multigp}, OPTgroup = {} }
 %T Latent Force Models %A Mauricio A. Álvarez and David Luengo and Neil D. Lawrence %B %C Proceedings of the Twelfth International Workshop on Artificial Intelligence and Statistics %D %E David van Dyk and Max Welling %F alvarez-lfm09 %I JMLR W\&CP 5 %P 9--16 %R %U http://inverseprobability.com/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. 
 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 PY - 2009/01/01 DA - 2009/01/01 ED - David van Dyk ED - Max Welling ID - alvarez-lfm09 PB - JMLR W\&CP 5 SP - 9 EP - 16 L1 - http://jmlr.csail.mit.edu/proceedings/papers/v5/alvarez09a/alvarez09a.pdf UR - http://inverseprobability.com/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 - 
 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