Dimension-Free Structured Covariance Estimation
Abstract
Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix $\Sigma$ with an additional assumption that $\Sigma$ can be represented as a sum of a few Kronecker products of smaller matrices. Under mild conditions, we derive the first non-asymptotic dimension-free high-probability bound on the Frobenius distance between $\Sigma$ and a widely used penalized permuted least squares estimate. Because of the hidden structure, the established rate of convergence is faster than in the standard covariance estimation problem.
Cite
Text
Puchkin and Rakhuba. "Dimension-Free Structured Covariance Estimation." Conference on Learning Theory, 2024.Markdown
[Puchkin and Rakhuba. "Dimension-Free Structured Covariance Estimation." Conference on Learning Theory, 2024.](https://mlanthology.org/colt/2024/puchkin2024colt-dimensionfree/)BibTeX
@inproceedings{puchkin2024colt-dimensionfree,
title = {{Dimension-Free Structured Covariance Estimation}},
author = {Puchkin, Nikita and Rakhuba, Maxim},
booktitle = {Conference on Learning Theory},
year = {2024},
pages = {4276-4306},
volume = {247},
url = {https://mlanthology.org/colt/2024/puchkin2024colt-dimensionfree/}
}