Related papers: Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes

Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes

URL: http://arxiv.org/abs/2404.17714v1
Date: Fri, 26 Apr 2024 22:17:32 GMT
Title: Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes
Authors: Victor S. Portella, Nick Harvey,
Abstract summary: 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.
Score: 2.7624021966289605
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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