Work

An algorithm for locally adaptive bivariate penalized splines

Year: 2025

Type: article

Abstract: This paper introduces a penalized spline model for bivariate smoothing that locally adjusts to gridded data set affected by noise varying across different areas of the domain. As for all penalized spline methods, the approach requires the definition of suitable penalty terms and the selection of the regularization parameters. In our model, the regularization parameters are chosen anisotropically using a data-driven approach that adapts the roughness amount to the noise level. The proposed approach alternates the construction of univariate penalized spline based on B-spline basis functions along both coordinates, and uses a tensor product structure to capture interactions between the two dimensions. Numerical experiments confirm the efficacy of the approach, the anisotropy of the model, and the ability to locally adapt the amount of regression to different noise levels in different areas. The model is compared with two state-of-the-art smoothers, for which we also provide an original reformulation highlighting their construction as penalized splines. • Definition of a locally adaptive bivariate tensor product penalized spline. • An algorithm for locally adapting bivariate regression. • Anisotropic penalized regression of noisy data.

Source: Journal of Computational and Applied Mathematics

DOI: 10.1016/j.cam.2025.117201

Authors: Paola Erminia Calabrese, Rosanna Campagna, Costanza Conti

Institutions: University of Campania "Luigi Vanvitelli", University of Florence

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250