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

Given a reproducing kernel Hilbert space (H,〈.,.〉) of real-valued functions and a suitable measure μ over the source space D⊂R, we decompose H as the sum of a subspace of centered functions for μ 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.