تقرير
Robust, randomized preconditioning for kernel ridge regression
| العنوان: | Robust, randomized preconditioning for kernel ridge regression |
|---|---|
| المؤلفون: | Díaz, Mateo, Epperly, Ethan N., Frangella, Zachary, Tropp, Joel A., Webber, Robert J. |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Statistics - Machine Learning, 68W20, 65F10, 65F55 |
| الوصف: | 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. Comment: 29 pages, 11 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.12465 |
| رقم الأكسشن: | edsarx.2304.12465 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |