Dyson Equation for Correlated Linearizations and Test Error of Random Features Regression
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917101057343488 |
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| author | Latourelle-Vigeant, Hugo Paquette, Elliot |
| author_facet | Latourelle-Vigeant, Hugo Paquette, Elliot |
| contents | This paper develops some theory of the Dyson equation for correlated linearizations and uses it to solve a problem on asymptotic deterministic equivalent for the test error in random features regression. The theory developed for the correlated Dyson equation includes existence-uniqueness, spectral support bounds, and stability properties. This theory is new for constructing deterministic equivalents for pseudo-resolvents of a class of linearizations with correlated entries. In the application, this theory is used to give a deterministic equivalent of the test error in random features ridge regression, in a proportional scaling regime, wherein we have conditioned on both training and test datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_09194 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dyson Equation for Correlated Linearizations and Test Error of Random Features Regression Latourelle-Vigeant, Hugo Paquette, Elliot Statistics Theory Probability This paper develops some theory of the Dyson equation for correlated linearizations and uses it to solve a problem on asymptotic deterministic equivalent for the test error in random features regression. The theory developed for the correlated Dyson equation includes existence-uniqueness, spectral support bounds, and stability properties. This theory is new for constructing deterministic equivalents for pseudo-resolvents of a class of linearizations with correlated entries. In the application, this theory is used to give a deterministic equivalent of the test error in random features ridge regression, in a proportional scaling regime, wherein we have conditioned on both training and test datasets. |
| title | Dyson Equation for Correlated Linearizations and Test Error of Random Features Regression |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2312.09194 |