On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

David Ginsbourger 1, 2, 3 Olivier Roustant 3, 4 Dominic Schuhmacher 5 Nicolas Durrande 4 Nicolas Lenz 1
1 IMSV - Institute of Mathematical Statistics and Actuarial Science [Bern]
2 IDIAP Research Institute
3 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
4 DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation
5 Institut für Mathematische Stochastik, Georg-August-Universität Göttingen
Institut für Mathematische Stochastik
Abstract : The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.
Keywords : Gaussian processes Sensitivity analysis Kriging Covariance functions Conditional simulations
Type de document :
Chapitre d'ouvrage
Ronald Cools, Dirk Nuyens. Monte Carlo and Quasi-Monte Carlo Methods, 163, Springer International Publishing, pp 315-330, 2016, Springer Proceedings in Mathematics & Statistics, 〈10.1007/978-3-319-33507-0_15〉
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https://hal-emse.ccsd.cnrs.fr/emse-01339368
Contributeur : Florent Breuil <>
Soumis le : mercredi 29 juin 2016 - 16:21:41
Dernière modification le : lundi 5 novembre 2018 - 15:34:05

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David Ginsbourger, Olivier Roustant, Dominic Schuhmacher, Nicolas Durrande, Nicolas Lenz. On ANOVA Decompositions of Kernels and Gaussian Random Field Paths. Ronald Cools, Dirk Nuyens. Monte Carlo and Quasi-Monte Carlo Methods, 163, Springer International Publishing, pp 315-330, 2016, Springer Proceedings in Mathematics & Statistics, 〈10.1007/978-3-319-33507-0_15〉. 〈emse-01339368〉

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