提出新方法自动选光滑模型的拐点,更简洁且效果不差。
Automatic knot selection in smooth additive models

- 基于自适应样条扩展,显式选择拐点位置
- 相比现有方法,用更少基函数达到相近拟合效果
- 适合需要简洁模型的科研与工程场景
B-样条回归是常用的非参数建模框架,其性能依赖于预先设定转折点(即拐点)的数量和位置。这些拐点决定用于表示回归函数的B-样条基的维数以及需估计的系数数量,从而影响模型的灵活性、平滑性和拟合优度。传统方法或通过显式算法选择拐点,或采用如P-样条等正则化方法自动调节平滑度,后者已成为广义加性模型(GAMs)的标准。相比之下,因计算或建模限制而常被忽视的拐点选择技术,在某些场景下仍具优势。本文提出一种基于自适应样条(A-splines)扩展的新显式拐点选择方法,结合定制化的Fellner-Schall方案优化相关参数。在多种合成与真实数据集上评估,并与P-样条及先进拐点选择方法比较,结果表明性能相当,但使用了显著更少的基元素构建模型。
原文摘要 · Abstract (English)
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.
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