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Dimension-free Structured Covariance Estimation

15 February 2024
Nikita Puchkin
Maxim Rakhuba
ArXiv (abs)PDFHTML
Abstract

Given a sample of i.i.d. high-dimensional centered random vectors, we consider a problem of estimation of their covariance matrix Σ\SigmaΣ with an additional assumption that Σ\SigmaΣ 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 Σ\SigmaΣ 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.

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