La modélisation par processus gaussiens – aussi appelée krigeage – est souvent utilisée pour obtenir une approximation mathémathique d’une fonction dont l’évaluation est coûteuse. Cependant, le nombre d’évaluations nécessaires pour construire un modèle peut devenir démesuré lorsque la dimension du domaine de définition augmente. Afin de contourner le fléau de la dimension, une alternative bien connue est de se tourner vers des modèles simplifiés comme les modèles additifs. Nous présentons ici une famille de noyaux de covariance permettant de combiner les caractéristiques des modèles de krigeage et les avantages des modèles additifs puis nous décrivons certaines propriétés des modèles obtenus.
Gaussian Process models are often used for predicting and approximating expensive experiments. However, the number of observations required for building such models may become unrealistic when the input dimension increases. In oder to avoid the curse of dimensionality, a popular approach in multivariate smoothing is to make simplifying assumptions like additivity. The ambition of the present work is to give an insight into a family of covariance kernels that allows combining the features of Gaussian Process modeling with the advantages of generalized additive models, and to describe some properties of the resulting models.
@article{AFST_2012_6_21_3_481_0,
author = {Durrande, Nicolas and Ginsbourger, David and Roustant, Olivier},
title = {Additive {Covariance} kernels for high-dimensional {Gaussian} {Process} modeling},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {481--499},
publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 21},
number = {3},
year = {2012},
doi = {10.5802/afst.1342},
zbl = {1266.60068},
mrnumber = {3076409},
language = {en},
url = {http://www.numdam.org/articles/10.5802/afst.1342/}
}
TY - JOUR AU - Durrande, Nicolas AU - Ginsbourger, David AU - Roustant, Olivier TI - Additive Covariance kernels for high-dimensional Gaussian Process modeling JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2012 SP - 481 EP - 499 VL - 21 IS - 3 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1342/ DO - 10.5802/afst.1342 LA - en ID - AFST_2012_6_21_3_481_0 ER -
%0 Journal Article %A Durrande, Nicolas %A Ginsbourger, David %A Roustant, Olivier %T Additive Covariance kernels for high-dimensional Gaussian Process modeling %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2012 %P 481-499 %V 21 %N 3 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1342/ %R 10.5802/afst.1342 %G en %F AFST_2012_6_21_3_481_0
Durrande, Nicolas; Ginsbourger, David; Roustant, Olivier. Additive Covariance kernels for high-dimensional Gaussian Process modeling. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 21 (2012) no. 3, pp. 481-499. doi : 10.5802/afst.1342. http://www.numdam.org/articles/10.5802/afst.1342/
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