Sobolev norm inconsistency of kernel interpolation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914063473180672 |
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| author | Yang, Yunfei |
| author_facet | Yang, Yunfei |
| contents | We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis space. These lower bounds imply that kernel interpolation is always inconsistent, when the smoothness index of the norm is larger than a constant that depends only on the embedding index of the hypothesis space and the decay rate of the eigenvalues. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sobolev norm inconsistency of kernel interpolation Yang, Yunfei Machine Learning We study the consistency of minimum-norm interpolation in reproducing kernel Hilbert spaces corresponding to bounded kernels. Our main result give lower bounds for the generalization error of the kernel interpolation measured in a continuous scale of norms that interpolate between $L^2$ and the hypothesis space. These lower bounds imply that kernel interpolation is always inconsistent, when the smoothness index of the norm is larger than a constant that depends only on the embedding index of the hypothesis space and the decay rate of the eigenvalues. |
| title | Sobolev norm inconsistency of kernel interpolation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2504.20617 |