# Dimension-free Structured Covariance Estimation

arXiv: https://arxiv.org/abs/2402.10032 · HTML: https://mlsanity.com/paper/2402.10032/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [A variational approach to dimension-free self-normalized concentration](https://mlsanity.com/paper/2508.06483/) (2025)

## Abstract (arXiv)

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.