Enhancing Adaptive Spline Regression: An Evolutionary Approach to Optimal Knot Placement and Smoothing Parameter Selection
提出一种基于粒子群优化的方法，同时优化样条回归中的节点位置和平滑参数，克服了传统方法独立优化的局限，适用于单变量和多变量样条，以及均值回归之外的分布回归场景。
Standard approaches for nonparametric curve fitting are often too restrictive when trying to estimate covariate effects that feature sudden changes or drastically changing curvature. In this context, adaptive smoothing approaches have received a lot of attention, but are typically limited in their ability to study additive models with multiple covariate effects, the consideration of nonnormal data and/or distributional regression scenarios, and usually rely on either optimizing number and location of knots for the basis functions in nonparametric smoothing or on making the smoothing parameter covariate-dependent. Another inherent problem lies in the independent optimization of knots and smoothing parameters, overlooking the essential interdependence that ensures accurate modeling results. In this article, we propose an approach based on particle swarm optimization that overcomes these limitations and shows very promising performance in complex simulations and applications. Our methodology is adaptable to all types of splines, including univariate and multivariate, and extends to regression techniques beyond the mean, such as models for location, scale and shape and additive quantile regression. The source code is available at https://github.com/AnFreTh/OKPSPS. Supplementary materials for this article are available online.