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

Autor:	Latourelle-Vigeant, Hugo, Paquette, Elliot
Rok vydání:	2023
Předmět:	Mathematics - Statistics Theory Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	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 correlated linear pencils. 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. Comment: 57 page, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.09194 Zobrazit plný text záznamu View this record from Arxiv