Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes
Data Structures and Algorithms
2024-04-30 v1 Cryptography and Security
Machine Learning
Machine Learning
Abstract
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the Stein-Haff identity, an extension of the classical Stein's identity used in previous fingerprinting lemma arguments.
Keywords
Cite
@article{arxiv.2404.17714,
title = {Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes},
author = {Victor S. Portella and Nick Harvey},
journal= {arXiv preprint arXiv:2404.17714},
year = {2024}
}
Comments
27 pages, preprint