Gaussian Processes in Machine Learning

  • Carl Edward Rasmussen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3176)


We give a basic introduction to Gaussian Process regression models. We focus on understanding the role of the stochastic process and how it is used to define a distribution over functions. We present the simple equations for incorporating training data and examine how to learn the hyperparameters using the marginal likelihood. We explain the practical advantages of Gaussian Process and end with conclusions and a look at the current trends in GP work.


Covariance Function Gaussian Process Marginal Likelihood Posterior Variance Joint Gaussian Distribution 
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  1. 1.
    Williams, C.K.I.: Prediction with Gaussian processes: From linear regression to linear prediction and beyond. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 599–621. Kluwer Academic, Dordrecht (1998)CrossRefGoogle Scholar
  2. 2.
    MacKay, D.J.C.: Gaussian processes — a replacement for supervised neural networks?. Tutorial lecture notes for NIPS 1997 (1997)Google Scholar
  3. 3.
    Williams, C.K.I., Barber, D.: Bayesian classification with Gaussian processes. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(12), 1342–1351 (1998)CrossRefGoogle Scholar
  4. 4.
    Csató, L., Opper, M.: Sparse on-line Gaussian processes. Neural Computation 14, 641–668 (2002)CrossRefzbMATHGoogle Scholar
  5. 5.
    Neal, R.M.: Regression and classification using Gaussian process priors (with discussion). In: Bernardo, J.M., et al. (eds.) Bayesian statistics, vol. 6, pp. 475–501. Oxford University Press, Oxford (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Carl Edward Rasmussen
    • 1
  1. 1.Max Planck Institute for Biological CyberneticsTübingenGermany

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