A novel variable selection method in nonlinear multivariate models using B-splines with an application to geoscience

In this article, we introduce a novel data-driven variable selection approach in a multivariate nonparametric regression model designed to capture only the variables on which the regression function depends. The core concept of our method consists in approximating the underlying function by a linear combination of B-splines of order M and their pairwise interactions. The coefficients of this linear combination are estimated by minimizing the standard least-squares criterion penalized by the sum of the ${\ell }_2$ -norms of the partial derivatives with respect to the different variables on which the function depends. We validate our approach through numerical experiments varying the number of observations, the noise level and the total number of variables and compare it to four other state-of-the-art methods. An application to a geochemical system based on calcite precipitation is also considered. In most of these contexts, our approach outperforms the other procedures. Our completely data-driven method is implemented in the absorber R package which is available on the Comprehensive R Archive Network (CRAN).