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

TL;DR

This paper introduces ANOVA kernels within RKHS of zero mean functions, enabling efficient sensitivity analysis by decomposing function spaces and deriving explicit ANOVA representations for predictors.

Contribution

It proposes a novel class of ANOVA kernels for RKHS that simplify sensitivity analysis and variable effect decomposition without recursive computations.

Findings

Derivation of explicit ANOVA representations for predictors.

Efficient computation of sensitivity indices.

Enhanced analysis of variable effects in model-based sensitivity analysis.

Abstract

Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu 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 e ffect of each (group of) variable(s) and computing sensitivity indices without recursivity.