Dimension lower bounds for linear approaches to function approximation
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912541891887104 |
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| author | Hsu, Daniel |
| author_facet | Hsu, Daniel |
| contents | This short note presents a linear algebraic approach to proving dimension lower bounds for linear methods that solve $L^2$ function approximation problems. The basic argument has appeared in the literature before (e.g., Barron, 1993) for establishing lower bounds on Kolmogorov $n$-widths. The argument is applied to give sample size lower bounds for kernel methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13346 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension lower bounds for linear approaches to function approximation Hsu, Daniel Machine Learning Statistics Theory This short note presents a linear algebraic approach to proving dimension lower bounds for linear methods that solve $L^2$ function approximation problems. The basic argument has appeared in the literature before (e.g., Barron, 1993) for establishing lower bounds on Kolmogorov $n$-widths. The argument is applied to give sample size lower bounds for kernel methods. |
| title | Dimension lower bounds for linear approaches to function approximation |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2508.13346 |