# RKHSMetaMod: An R package to estimate the Hoeffding decomposition of a complex model by solving RKHS ridge group sparse optimization problem

## TL;DR

The paper introduces RKHSMetaMod, an R package that estimates the Hoeffding decomposition of complex models using RKHS ridge group sparse optimization, enabling sensitivity analysis and Sobol index estimation.

## Contribution

It presents a novel R package implementing a penalized least-squares method for estimating Hoeffding decompositions in complex models, combining kernel methods with sparse optimization.

## Key findings

- Efficient estimation of Hoeffding decomposition terms.
- Ability to select non-zero Sobol indices.
- Enhanced sensitivity analysis capabilities.

## Abstract

In this paper, we propose an R package, called 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 package provides an interface from 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 and RcppGSL packages. These functions are then interfaced in the R environment in order to propose a user-friendly package.