A0407
Title: Enhancing geometrically designed spline regression through generalized additive models and functional gradient boosting
Authors: Dimitrina Dimitrova - Cass Business School - City - University of London (United Kingdom)
Emilio Luis Saenz Guillen - Bayes Business School (United Kingdom) [presenting]
Vladimir Kaishev - Cass Business School - City - University of London (United Kingdom)
Abstract: Geometrically designed spline (GeDS) regression offers an accurate and efficient solution to the spline regression problem by automatically estimating the number and positions of the knots using a stopping rule controlled by two tuning parameters. Two ground-breaking enhancements to the GeDS methodology are introduced. First, the applicability of GeDS is broadened to cover the family of generalized additive models (GAM) by implementing the local-scoring algorithm using GeD splines as function smoothers. Second, functional gradient boosting (FGB) is integrated to dynamically estimate the number and locations of the knots, as well as the regression coefficients of the spline model. Unlike typical gradient boosting models that generally lack an interpretable representation, the final FGB-GeDS fit is expressed as a single spline model. Additionally, FGB-GeDS automatically determines two main boosting parameters: the number of boosting iterations and the shrinkage/learning rate. On the one hand, the number of boosting iterations is regulated by a stopping rule analogous to the one used in the canonical GeDS method. On the other hand, the weakness of the GeDS base learners is controlled internally by the tuning parameters of the GeDS stopping rule, thus eliminating the need for additional regularization parameters like a shrinkage/learning rate.
