Reproducing kernel Hilbert spaces dedicated to sensitivity analysis

Abstract

The Hoeffding-Sobol representation (also called ANOVA decomposition or HDMR) of a multivariate function f is particularly interesting for analysing the influence of the variables on the response of f. For example, this representation plays a key role in global sensitivity analysis for the calculation of the Sobol indices. However the terms of this decomposition are based on several computations of integral which are not affordable when the evaluation of f is costly. A common approach to tackle this issue is to replace f by a surrogate model m (kriging, splines) and to perform the sensitivity analysis on m. In the particular case of RKHS, it is possible to build spaces for which the ANOVA representation can be obtained naturally. Thus, the decomposition of the model m does not require to compute a large number of integrals. The aim of the seminar is to show how to obtain such spaces from RKHS usually considered for interpolation and approximations tasks. Finally we will see that the expression of the Sobol indices can be obtained analytically without recursivity, whatever their order.