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

Victor S. Portella; Nick Harvey

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arXiv · 2404.17714

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

Victor S. Portella·Nick Harvey

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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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Victor S. Portella, Nick Harvey. 2024-04-26. Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes. https://arxiv.org/abs/2404.17714

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