🤖 AI Summary
This work addresses the critical dependence of B-spline regression performance in generalized additive models (GAMs) on knot placement, a challenge wherein conventional approaches struggle to balance fitting accuracy and model parsimony. The authors propose an explicit, automated knot selection method that integrates the knot placement mechanism of adaptive splines (A-splines) with a tailored Fellner–Schall smoothing parameter optimization strategy, enabling efficient sparse modeling. By reintroducing explicit knot selection—an aspect often overlooked—into the GAM framework, the method achieves predictive performance comparable to P-splines and state-of-the-art alternatives while substantially reducing the number of basis functions, thereby enhancing both model interpretability and computational efficiency.
📝 Abstract
B-spline regression constitutes a widely used framework for nonparametric modeling. The performance of this methodology depends on specifying the number and placement of changepoints, known as knots, prior to the estimation process. Such knot sequence determines the dimension of the B-spline basis used to represent the regression function and the number of coefficients to be estimated. Therefore, the knots' choice affects the model's flexibility, influencing its smoothness and goodness-of-fit. Traditionally, this problem has been addressed either by explicitly selecting knots, via knot-selection algorithms, or by regularization methods, such as P-splines, which automatically tune the regressor's smoothness. The latter have become the standard in generalized additive models (GAMs). In contrast, knot-selection techniques, frequently neglected because of computational or modeling limitations, provide certain advantages which can be valuable in some contexts. In this work, we introduce a novel explicit knot-selection technique for GAMs based on an extension of the adaptive splines (A-splines) knot selection methodology, combined with a customized Fellner-Schall scheme for tuning the associated parameters. Our approach is evaluated on various synthetic and real datasets and compared with P-splines and state-of-the-art knot-selection techniques. The results indicate comparable performance, while producing models built on a substantially smaller number of basis elements.