发表机构
Department of Statistics, Operations Research and Mathematics Education, Universidad de Oviedo; Department of Statistics, Universidad Carlos III de Madrid（统计、运筹学与数学教育系，奥维耶多大学; 统计系，马德里卡洛斯三世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究光滑加性模型中节点选择问题，提出基于自适应样条扩展及定制方案的新型显式节点选择技术，经实验评估与比较，该方法性能与其他方法相当且能基于更少基元素构建模型。
AI 中文摘要
B样条回归是一种广泛使用的非参数建模框架。其性能取决于在估计过程之前指定称为节点的变化点的数量和位置。传统上，这个问题通过显式选择节点或正则化方法解决。我们引入了一种基于自适应样条节点选择方法扩展的新型显式节点选择技术，并结合定制方案调整相关参数。我们的方法在各种合成和真实数据集上进行了评估，并与P样条和最新节点选择技术进行了比较。结果表明性能相当，同时生成的模型基于数量少得多的基元素构建。
英文摘要
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.
Comments43 pages (29 of which are the main document, the rest are part of the appendix), 31 figures (5 in main document)
