Robust, randomized preconditioning for kernel ridge regression

• URL: http://arxiv.org/abs/2304.12465v4
• Date: Wed, 10 Jul 2024 19:46:15 GMT
• Title: Robust, randomized preconditioning for kernel ridge regression
• Authors: Mateo Díaz, Ethan N. Epperly, Zachary Frangella, Joel A. Tropp, Robert J. Webber,
• Abstract summary: This paper investigates two randomized preconditioning techniques for solving kernel ridge regression problems. It introduces two new methods with state-of-the-art performance. The proposed methods solve a broad range of KRR problems, making them ideal for practical applications.
• Score: 3.521877014965197
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper investigates two randomized preconditioning techniques for solving kernel ridge regression (KRR) problems with a medium to large number of data points ($10^4 \leq N \leq 10^7$), and it introduces two new methods with state-of-the-art performance. The first method, RPCholesky preconditioning, accurately solves the full-data KRR problem in $O(N^2)$ arithmetic operations, assuming sufficiently rapid polynomial decay of the kernel matrix eigenvalues. The second method, KRILL preconditioning, offers an accurate solution to a restricted version of the KRR problem involving $k \ll N$ selected data centers at a cost of $O((N + k^2) k \log k)$ operations. The proposed methods solve a broad range of KRR problems, making them ideal for practical applications.

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