Linear Latent Force Models Using Gaussian Processes

Mauricio A. Álvarez, David Luengo, Neil D. Lawrence
IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(11):2693-2705, 2013.

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.

Cite this Paper

BibTeX
@Article{Alvarez-llfm13, title = {Linear Latent Force Models Using {G}aussian Processes}, author = {Álvarez, Mauricio A. and Luengo, David and Lawrence, Neil D.}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, pages = {2693--2705}, year = {2013}, volume = {35}, number = {11}, doi = {10.1109/TPAMI.2013.86}, pdf = {http://arxiv.org/pdf/1107.2699}, url = {http://inverseprobability.com/publications/linear-latent-force-models-using-gaussian-processes.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 Journal Article %T Linear Latent Force Models Using Gaussian Processes %A Mauricio A. Álvarez %A David Luengo %A Neil D. Lawrence %J IEEE Transactions on Pattern Analysis and Machine Intelligence %D 2013 %F Alvarez-llfm13 %P 2693--2705 %R 10.1109/TPAMI.2013.86 %U http://inverseprobability.com/publications/linear-latent-force-models-using-gaussian-processes.html %V 35 %N 11 %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 - JOUR TI - Linear Latent Force Models Using Gaussian Processes AU - Mauricio A. Álvarez AU - David Luengo AU - Neil D. Lawrence DA - 2013/05/13 ID - Alvarez-llfm13 VL - 35 IS - 11 SP - 2693 EP - 2705 DO - 10.1109/TPAMI.2013.86 L1 - http://arxiv.org/pdf/1107.2699 UR - http://inverseprobability.com/publications/linear-latent-force-models-using-gaussian-processes.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.. (2013). Linear Latent Force Models Using Gaussian Processes. IEEE Transactions on Pattern Analysis and Machine Intelligence 35(11):2693-2705 doi:10.1109/TPAMI.2013.86 Available from http://inverseprobability.com/publications/linear-latent-force-models-using-gaussian-processes.html.

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