Machine Learning

, Volume 98, Issue 3, pp 407–433 | Cite as

Asymptotic analysis of the learning curve for Gaussian process regression



This paper deals with the learning curve in a Gaussian process regression framework. The learning curve describes the generalization error of the Gaussian process used for the regression. The main result is the proof of a theorem giving the generalization error for a large class of correlation kernels and for any dimension when the number of observations is large. From this theorem, we can deduce the asymptotic behavior of the generalization error when the observation error is small. The presented proof generalizes previous ones that were limited to special kernels or to small dimensions (one or two). The theoretical results are applied to a nuclear safety problem.


Gaussian process regression Asymptotic mean squared error  Learning curves Generalization error Convergence rate 



The authors are grateful to Dr. Yann Richet of the IRSN—Institute for Radiological Protection and Nuclear Safety—for providing the data for the industrial case through the reDICE project.


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Université Paris DiderotParis Cedex 13France
  2. 2.CEA, DAM, DIFArpajonFrance
  3. 3.Laboratoire de Probabilites et Modeles Aleatoires & Laboratoire Jacques-Louis LionsUniversite Paris DiderotParis Cedex 13France

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