Tao, Yuanhu Charles (2026) Randomized approaches to approximating solutions of large kernel systems for Kernel Ridge Regression using the Nyström Approximation. Bachelor's Thesis, Applied Mathematics.
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Abstract
Kernel ridge regression uses a kernel function to measure pairwise similarities between n data points, and these values form the n × n kernel matrix K. This leads to a linear system involving the matrix K. For large datasets, the main computational difficulty is the need to explicitly form the full matrix K and directly solve the system. This project therefore studies randomized Nyström approximations, where only l ≪ n columns of K are used to build a low rank approximation. Uniform sampling, approximate leverage score sampling and recursive ridge leverage score sampling were compared against a full KRR baseline. The final experiments used five independent column selections on the three datasets. Uniform sampling was the strongest practical baseline and performed similarly to the informed methods with almost no sampling cost. The required value of l varied strongly across datasets, but the experiments generally showed diminishing returns as l increased. These results suggest using uniform sampling as the default but no universal value of l can be recommended across datasets.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Meier, M. and Peypouquet, J.G. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 28 Jul 2026 06:49 |
| Last Modified: | 28 Jul 2026 06:49 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37468 |
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