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.

翻译：我们证明了在私有条件下估计高斯分布协方差矩阵所需样本数的下界。我们的下界与现有已知最广泛参数设置下的上界相匹配。分析过程基于Stein-Haff恒等式，这是先前指纹引理论证中使用的经典Stein恒等式的扩展形式。