Advertisement

Streaming-Data Selection for Gaussian-Process Modelling

  • Dejan Petelin
  • Juš Kocijan
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 285)

Abstract

The Gaussian-process (GP) model is an example of a probabilistic, non-parametric model with uncertainty predictions. It can be used for the modelling of complex, non-linear systems and also for the identification of dynamic systems. The output of the GP model is a normal distribution, expressed in terms of the mean and the variance. One of the noticeable drawbacks of a system identification with GP models is the computation time necessary for the modelling. The modelling procedure involves the inverse of the covariance matrix, which has the dimension as large as the length of the input samples vector. The computation time for this inverse, regardless of the use of an efficient algorithm, is increasing with the third power of the number of input data. In this chapter we propose a method for the sequential selection of streaming data so that the size of the active set remains constrained. Furthermore, for better adjustment of the model to the system the hyperparameter values are optimised as well. The viability of the proposed method is tested on data obtained from two, nonlinear, dynamic systems.

Keywords

Covariance Function Gaussian Process Real Output Streaming Data Relevance Vector Machine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ažman, K., Kocijan, J.: Application of Gaussian processes for black-box modelling of biosystems. ISA Transactions 46(4), 443–457 (2007)CrossRefGoogle Scholar
  2. 2.
    Quiñonero Candela, J., Rasmussen, C.E.: A Unifying View of Sparse Approximate Gaussian Process Regression. J. Mach. Learn. Res. 6, 1939–1959 (2005)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Quiñonero Candela, J., Rasmussen, C.E., Williams, C.K.I.: Approximation Methods for Gaussian Process Regression. Tech. rep., Microsoft Research (2007)Google Scholar
  4. 4.
    Csató, L., Opper, M.: Sparse on-line Gaussian processes. Neural Comput. 14(3), 641–668 (2002)zbMATHCrossRefGoogle Scholar
  5. 5.
    Deisenroth, M.P.: Efficient Reinforcement Learning using Gaussian Processes. PhD thesis, Karlsruhe Institute of Technology (2010)Google Scholar
  6. 6.
    Kocijan, J.: Gaussian process models for systems identification. In: Proc. 9th Int. PhD Workshop on Systems and Control: Young Generation Viewpoint, Izola, Slovenia (2008)Google Scholar
  7. 7.
    Kocijan, J., Girard, A., Banko, B., Murray-Smith, R.: Dynamic systems identification with Gaussian processes. Mathematical and Computer Modelling of Dynamic Systems 11(4), 411–424 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kocijan, J., Likar, B.: Gas-liquid separator modelling and simulation with Gaussian-process models. Simulation Modelling Practice and Theory 16(8), 910–922 (2008)CrossRefGoogle Scholar
  9. 9.
    Lázaro-Gredilla, M., Quiñonero Candela, J., Rasmussen, C.E., Figueiras-Vidal, A.R.: Sparse spectrum gaussian process regression. The Journal of Machine Learning Research 11, 1865–1881 (2010)zbMATHGoogle Scholar
  10. 10.
    Ranganathan, A., Yang, M.-H.: Online Sparse Matrix Gaussian Process Regression and Vision Applications. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part I. LNCS, vol. 5302, pp. 468–482. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Rassmusen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press (2006)Google Scholar
  12. 12.
    Seeger, M., Williams, C.K.I., Lawrence, N.D.: Fast Forward Selection to Speed Up Sparse Gaussian Process Regression. In: 9th Int. Workshop on Artificial Intelligence and Statistics. Society for Artificial Intelligence and Statistics (2003)Google Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Jožef Stefan InstituteLjubljanaSlovenia
  2. 2.University of Nova GoricaNova GoricaSlovenia

Personalised recommendations