A0306
Title: A novel approach for estimating functions in the multivariate setting based on an adaptive knot selection for B-splines
Authors: Mary Savino - University Paris-Saclay, AgroParisTech, INRAE, UMR MIA Paris-Saclay and Andra (France) [presenting]
Celine Levy-Leduc - University Paris-Saclay, AgroParisTech, INRAE, UMR MIA Paris-Saclay (France)
Abstract: A novel data-driven method is outlined for estimating functions in a multivariate nonparametric regression model based on an adaptive knot selection for B-splines. The underlying idea of our approach for selecting knots is to apply the Generalized Lasso, since the knots of the B-spline basis can be seen as changes in the derivatives of the function to be estimated. This method was then extended to functions depending on several variables by processing each dimension independently, thus reducing the problem to a univariate setting. The regularization parameters were chosen by means of a criterion based on EBIC. The nonparametric estimator was obtained using a multivariate B-spline regression with the corresponding selected knots. Our procedure was validated through numerical experiments by varying the number of observations and the level of noise to investigate its robustness. The influence of observation sampling was also assessed, and our method was applied to a chemical system commonly used in geoscience. For each different framework considered in this presentation, our approach performed better than state-of-the-art methods. Our completely data-driven method is implemented in the GLOBER R package, which will soon be available on the Comprehensive R Archive Network (CRAN).
