Low Rank Approximation for Smoothing Spline via Eigensystem Truncation
This addresses a computational problem for users of smoothing splines in nonparametric estimation with large data, representing an incremental improvement.
The paper tackles the computational bottleneck of cubic time complexity in fitting smoothing spline models to large datasets by developing a low rank approximation method using eigensystem truncation, with simulations showing the new methods are accurate, fast, and favorable compared to existing approaches.
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.