caa a22 4500 605478015 CHVBK 20210128100403.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10994-014-5437-0 doi (NATIONALLICENCE)springer-10.1007/s10994-014-5437-0 Asymptotic analysis of the learning curve for Gaussian process regression [Elektronische Daten] [Loic Le Gratiet, Josselin Garnier] 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. The Author(s), 2014 Gaussian process regression nationallicence Asymptotic mean squared error nationallicence Learning curves nationallicence Generalization error nationallicence Convergence rate nationallicence Le Gratiet Loic Université Paris Diderot, 75205, Paris Cedex 13, France aut Garnier Josselin Laboratoire de Probabilites et Modeles Aleatoires & Laboratoire Jacques-Louis Lions, Universite Paris Diderot, 75205, Paris Cedex 13, France aut Machine Learning Springer US; http://www.springer-ny.com 98/3(2015-03-01), 407-433 0885-6125 98:3<407 2015 98 10994 https://doi.org/10.1007/s10994-014-5437-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-014-5437-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Le Gratiet Loic Université Paris Diderot, 75205, Paris Cedex 13, France aut NATIONALLICENCE 700 1- Garnier Josselin Laboratoire de Probabilites et Modeles Aleatoires & Laboratoire Jacques-Louis Lions, Universite Paris Diderot, 75205, Paris Cedex 13, France aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 98/3(2015-03-01), 407-433 0885-6125 98:3<407 2015 98 10994