A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915512815976448 |
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| author | Jia, Zeyu Polyanskiy, Yury Rakhlin, Alexander |
| author_facet | Jia, Zeyu Polyanskiy, Yury Rakhlin, Alexander |
| contents | We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions, generalizing the results of \cite{anthony2000function,alon1997scale}. Moreover, we show that the gapped dimensions lead to lower bounds on offset Rademacher averages, thereby strengthening existing approaches for proving lower bounds on rates of convergence in statistical and online learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity Jia, Zeyu Polyanskiy, Yury Rakhlin, Alexander Machine Learning Statistics Theory We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions, generalizing the results of \cite{anthony2000function,alon1997scale}. Moreover, we show that the gapped dimensions lead to lower bounds on offset Rademacher averages, thereby strengthening existing approaches for proving lower bounds on rates of convergence in statistical and online learning. |
| title | A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2509.20618 |