Work

Smoothing Splines and Rank Structured Matrices: Revisiting the Spline Kernel

Year: 2020

Type: article

Abstract: We show that the spline kernel of order $p$ is a so-called semiseparable function with semiseparability rank $p$. A consequence of this is that kernel matrices generated by the spline kernel are rank structured matrices that can be stored and factorized efficiently. We use this insight to derive new recursive algorithms with linear complexity in the number of knots for various kernel matrix computations. We also discuss applications of these algorithms, including smoothing spline regression, Gaussian process regression, and some related hyperparameter estimation problems.

Source: SIAM Journal on Matrix Analysis and Applications

DOI: 10.1137/19m1267349

Authors: Martin S. Andersen, Tianshi Chen

Institutions: Technical University of Denmark, Chinese University of Hong Kong, Shenzhen Research Institute of Big Data, Chinese University of Hong Kong, Shenzhen

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3015860618

FWCI: 1.183

Cites: 14

Cited by: 17

Related to: 10