ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Authors:
N. Durrande;D. Ginsbourger;O. Roustant;L. Carraro
Affiliations:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, UK and 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;TELECOM St Etienne, 25 rue du Dr Rémy Annino - 42000 Saint Etienne, France
Venue:
Journal of Multivariate Analysis
Year:
2013

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Abstract

Given a reproducing kernel Hilbert space (H,) of real-valued functions and a suitable measure @m over the source space D@?R, we decompose H as the sum of a subspace of centered functions for @m and its orthogonal in H. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.