Dimension-free uniform concentration bound for logistic regression
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916436144816128 |
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| author | Nakakita, Shogo |
| author_facet | Nakakita, Shogo |
| contents | We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by the Rademacher complexity argument and McDiarmid's inequality. The derivation is based on the PAC-Bayes approach with second-order expansion and Rademacher-complexity-based bounds for the residual term of the expansion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension-free uniform concentration bound for logistic regression Nakakita, Shogo Statistics Theory Machine Learning 62J12 (Primary), 62F12 (Secondary) We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by the Rademacher complexity argument and McDiarmid's inequality. The derivation is based on the PAC-Bayes approach with second-order expansion and Rademacher-complexity-based bounds for the residual term of the expansion. |
| title | Dimension-free uniform concentration bound for logistic regression |
| topic | Statistics Theory Machine Learning 62J12 (Primary), 62F12 (Secondary) |
| url | https://arxiv.org/abs/2405.18055 |