Nonparametric regression frameworks, such as generalized additive models (GAMs) and smoothing spline analysis of variance (SSANOVA) models, extend the generalized linear model (GLM) by allowing for unknown functional relationships between an exponential family response variable and a collection of predictor variables. The unknown functional relationships are typically estimated using penalized likelihood estimation, which adds a roughness penalty to the (negative) log-likelihood function. In this paper, I propose a spectral parameterization of a smoothing spline, which allows for an efficient application of Elastic Net regression to smooth and select eigenvectors of a kernel matrix. The classic (ridge regression) solution for a smoothing spline is a special case of the proposed kernel eigenvector smoothing and selection operator. Extensions for tensor product smoothers are developed for both the GAM and SSANOVA frameworks. Using simulated and real data examples, I demonstrate that the proposed approach offers practical and computational gains over typical approaches for fitting GAMs, SSANOVA models, and Elastic Net penalized GLMs.

非参数回归框架（例如广义加性模型（GAM）和方差平滑样条分析（SSANOVA）模型）通过允许指数族响应变量和一组预测变量之间的未知函数关系来扩展广义线性模型（GLM）。通常使用惩罚似然估计来估计未知函数关系，这会给（负）对数似然函数增加粗糙度损失。在本文中，我提出了一个平滑样条的频谱参数化，它可以有效地应用Elastic Net回归来平滑和选择核矩阵的特征向量。平滑样条的经典（岭回归）解决方案是所提出的核特征向量平滑和选择算子的特例。GAM和SSANOVA框架都开发了张量积平滑器的扩展。通过使用模拟和真实数据示例，我证明了所提出的方法在拟合GAM，SSANOVA模型和Elastic Net惩罚性GLM的典型方法方面，具有实际和计算上的优势。