A tree-based varying coefficient model

Abstract The paper introduces a tree-based varying coefficient model (VCM) where the varying coefficients are modelled using the cyclic gradient boosting machine (CGBM) from Delong et al. (On cyclic gradient boosting machines, 2023). Modelling the coefficient functions using a CGBM allows for dimension-wise early stopping and feature importance scores. The dimension-wise early stopping not only reduces the risk of dimension-specific overfitting, but also reveals differences in model complexity across dimensions. The use of feature importance scores allows for simple feature selection and easy model interpretation. The model is evaluated on the same simulated and real data examples as those used in Richman and Wüthrich (Scand Actuar J 2023:71–95, 2023), and the results show that it produces results in terms of out of sample loss that are comparable to those of their neural network-based VCM called LocalGLMnet.