# Linear Latent Force Models Using Gaussian Processes

Mauricio A. Álvarez, Universidad Tecnológica de Pereira, Colombia
  @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 %P -- %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.:-