Additive Covariance kernels for high-dimensional Gaussian Process modeling

Nicolas Durrande[1]; David Ginsbourger[2]; Olivier Roustant[3]

  • [1] School of mathematics and statistics, University of Sheffield, Sheffield S3 7RH, UK, Ecole Nationale Supérieure des Mines, FAYOL-EMSE, LSTI, F-42023 Saint-Etienne, France
  • [2] Institute of Mathematical Statistics and Actuarial Science, University of Berne, Alpeneggstrasse 22, 3012 Bern, Switzerland
  • [3] Ecole Nationale Supérieure des Mines, FAYOL-EMSE, LSTI, F-42023 Saint-Etienne, France

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

  • Volume: 21, Issue: 3, page 481-499
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Durrande, Nicolas, Ginsbourger, David, and Roustant, Olivier. "Additive Covariance kernels for high-dimensional Gaussian Process modeling." Annales de la faculté des sciences de Toulouse Mathématiques 21.3 (2012): 481-499. <http://eudml.org/doc/251000>.

@article{Durrande2012,
abstract = {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.},
affiliation = {School of mathematics and statistics, University of Sheffield, Sheffield S3 7RH, UK, Ecole Nationale Supérieure des Mines, FAYOL-EMSE, LSTI, F-42023 Saint-Etienne, France; Institute of Mathematical Statistics and Actuarial Science, University of Berne, Alpeneggstrasse 22, 3012 Bern, Switzerland; Ecole Nationale Supérieure des Mines, FAYOL-EMSE, LSTI, F-42023 Saint-Etienne, France},
author = {Durrande, Nicolas, Ginsbourger, David, Roustant, Olivier},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {additive covariance kernels; Gaussian process modeling; additive Kriging},
language = {eng},
month = {4},
number = {3},
pages = {481-499},
publisher = {Université Paul Sabatier, Toulouse},
title = {Additive Covariance kernels for high-dimensional Gaussian Process modeling},
url = {http://eudml.org/doc/251000},
volume = {21},
year = {2012},
}

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
DA - 2012/4//
PB - Université Paul Sabatier, Toulouse
VL - 21
IS - 3
SP - 481
EP - 499
AB - 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.
LA - eng
KW - additive covariance kernels; Gaussian process modeling; additive Kriging
UR - http://eudml.org/doc/251000
ER -

References

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