Year: 2024
Type: preprint
Abstract: We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our results provide sharper control across the spectrum. Our analysis is based on a general-purpose theorem that allows one to convert existing uniform bounds into relative ones. The theorems and techniques emphasize simplicity and should be applicable across various settings.
Source: arXiv (Cornell University)
Authors: Barzilai, Daniel, Shamir, Ohad
Institution: Weizmann Institute of Science
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403346994