On Generalized Sub-Gaussian Canonical Processes and Their Applications
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913218451996672 |
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| author | Chen, Yiming Wang, Yuxuan Zhu, Kefan |
| author_facet | Chen, Yiming Wang, Yuxuan Zhu, Kefan |
| contents | We obtain the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d case, and we further get a tighter bound of concentration inequality through uniformly randomized techniques. A concentration inequality for general functions involving independent random variables is also derived as an extension. As for applications, we derive convergence results for principal component analysis and the Rademacher complexities method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15314 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Generalized Sub-Gaussian Canonical Processes and Their Applications Chen, Yiming Wang, Yuxuan Zhu, Kefan Probability 60E15, 60F10 We obtain the tail probability of generalized sub-Gaussian canonical processes. It can be viewed as a variant of the Bernstein-type inequality in the i.i.d case, and we further get a tighter bound of concentration inequality through uniformly randomized techniques. A concentration inequality for general functions involving independent random variables is also derived as an extension. As for applications, we derive convergence results for principal component analysis and the Rademacher complexities method. |
| title | On Generalized Sub-Gaussian Canonical Processes and Their Applications |
| topic | Probability 60E15, 60F10 |
| url | https://arxiv.org/abs/2401.15314 |