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arXiv · 2312.09194

Dyson Equation for Correlated Linearizations and Test Error of Random Features Regression

Hugo Latourelle-Vigeant·Elliot Paquette
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Abstract

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.

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BibTeXRIS

Hugo Latourelle-Vigeant, Elliot Paquette. 2023-12-14. Dyson Equation for Correlated Linearizations and Test Error of Random Features Regression. https://arxiv.org/abs/2312.09194

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