Low Rank Approximation for Smoothing Spline via Eigensystem Truncation

TL;DR

This paper introduces a low rank eigensystem approximation method for smoothing splines that reduces computational complexity while maintaining accuracy, enabling efficient nonparametric estimation on large datasets.

Contribution

It proposes a novel approach to approximate the eigensystem of smoothing splines, including error bounds and practical algorithms for large-scale data analysis.

Findings

The method is accurate and fast in simulations.

It compares favorably against existing smoothing spline methods.

The approach is easy to implement with existing software.

Abstract

Smoothing splines provide a powerful and flexible means for nonparametric estimation and inference. With a cubic time complexity, fitting smoothing spline models to large data is computationally prohibitive. In this paper, we use the theoretical optimal eigenspace to derive a low rank approximation of the smoothing spline estimates. We develop a method to approximate the eigensystem when it is unknown and derive error bounds for the approximate estimates. The proposed methods are easy to implement with existing software. Extensive simulations show that the new methods are accurate, fast, and compares favorably against existing methods.