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We then introduce a general orthogonal truncation method: starting from a feature expansion of the kernel, we construct the associated RKHS by introducing an inner product that makes the feature functions orthonormal, and then use the spans of the first basis functions as finite-dimensional approximation spaces. The resulting subspace reduction is applied to several approximation schemes. Explicit feature expansions yield fast-regime bounds for Gaussian and analytic dot-product kernels. Mercer truncations provide a spectral approximation method and lead to dynamic regret bounds in fast and slow regimes, depending on the eigenvalue decay. Finally, we study subspaces spanned by kernel sections and apply this construction to Matérn kernels.
| Comments: | 26 pages |
| Subjects: | Machine Learning (cs.LG) |
| MSC classes: | 68W27, 62G08, 46E22 |
| Cite as: | arXiv:2604.25021 [cs.LG] |
| (or arXiv:2604.25021v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2604.25021 arXiv-issued DOI via DataCite (pending registration) |
From: Dmitry Rokhlin B. [view email]
[v1]
Mon, 27 Apr 2026 21:53:54 UTC (34 KB)
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