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

arXiv:2404.17714v1 Announce Type: cross
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.

abstract analysis arxiv covariance cs.cr cs.ds cs.lg distribution identity match matrix parameters prove samples stat.ml type