This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction approach uses an interpolator to parameterize the regression function with its values at finite knots, and then estimates these values by (regularized) least squares. Some popular methods including kernel ridge regression can be viewed as its special cases. It is shown that, the reconstruction idea not only provides different angles to look into existing methods, but also produces new effective experimental design and estimation methods for nonparametric models. In particular, for some methods of complexity O(n3), where n is the sample size, this approach provides effective surrogates with much less computational burden. This point makes it very suitable for large datasets.

中文翻译：

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重构方法：从插值到回归

本文介绍了一种基于插值的方法，称为重构方法，用于非参数回归。基于与统计估计相比，插值通常具有可忽略的误差这一事实，重建方法使用插值器将回归函数的值参数化为有限节点，然后通过（正则化）最小二乘法估计这些值。一些流行的方法包括核岭回归可以看作是它的特例。结果表明，重构思想不仅为研究现有方法提供了不同的角度，而且为非参数模型提供了新的有效的实验设计和估计方法。特别是，对于一些复杂度为 O(n3) 的方法，其中 n 是样本大小，这种方法以更少的计算负担提供了有效的代理。这一点使它非常适合大型数据集。