RKHSMetaMod : An R package to estimate the Hoeffding decomposition of an unknown function by solving RKHS Ridge Group Sparse optimization problem

Abstract

In the context of the Gaussian regression model, the package RKHSMetaMod allows to estimate a meta model by solving the ridge group sparse optimization problem based on the Reproducing Kernel Hilbert Spaces (RKHS). The obtained estimator is an additive model that satisfies the properties of the Hoeffding decomposition, and its terms estimate the terms in the Hoeffding decomposition of the unknown regression function. The estimators of the Sobol indices are deduced from the estimated meta model. This package provides an interface from R statistical computing environment to the C++ libraries Eigen and GSL. In order to speed up the execution time, almost all of the functions of the RKHSMetaMod package are written using the efficient C++ libraries through RcppEigen and RcppGSL packages. These functions are then interfaced in the R environment in order to propose an user friendly package.