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Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes
April 30, 2024, 4:11 a.m. | Victor S. Portella, Nick Harvey
cs.CR updates on arXiv.org arxiv.org
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.
analysis arxiv cs.cr cs.ds cs.lg distribution identity matrix parameter private privately prove stat.ml under
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