On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

David Ginsbourger 1, 2, 3 Olivier Roustant 3, 4, 5, 6, 7 Dominic Schuhmacher 8 Nicolas Durrande 4, 5, 6, 7 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 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
5 FAYOL-ENSMSE - Institut Henri Fayol
6 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes
7 FAYOL-ENSMSE - Département Génie mathématique et industriel
8 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
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Book sections
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https://hal-emse.ccsd.cnrs.fr/emse-01339368
Contributor : Florent Breuil <>
Submitted on : Wednesday, June 29, 2016 - 4:21:41 PM
Last modification on : Tuesday, January 21, 2020 - 1:26:09 AM

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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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