RKHSMetaMod: An R Package to Estimate the Hoeffding Decomposition of a Complex Model by Solving RKHS Ridge Group Sparse Optimization Problem

Abstract

In this paper, we propose an R package, called [RKHSMetaMod](https://CRAN.R-project.org/package=RKHSMetaMod), that implements a procedure for estimating a meta-model of a complex model. The meta-model approximates the Hoeffding decomposition of the complex model and allows us to perform sensitivity analysis on it. It belongs to a reproducing kernel Hilbert space that is constructed as a direct sum of Hilbert spaces. The estimator of the meta-model is the solution of a penalized empirical least-squares minimization with the sum of the Hilbert norm and the empirical $L^2$-norm. This procedure, called RKHS ridge group sparse, allows both to select and estimate the terms in the Hoeffding decomposition, and therefore, to select and estimate the Sobol indices that are non-zero. The [RKHSMetaMod](https://CRAN.R-project.org/package=RKHSMetaMod) package provides an interface from the R statistical computing environment to the C++ libraries Eigen and GSL. In order to speed up the execution time and optimize the storage memory, except for a function that is written in R, all of the functions of this package are written using the efficient C++ libraries through [RcppEigen](https://CRAN.R-project.org/package=RcppEigen) and [RcppGSL](https://CRAN.R-project.org/package=RcppGSL) packages. These functions are then interfaced in the R environment in order to propose a user-friendly package.