Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes
arXiv:2404.17714v110 citationsh-index: 5
Originality Incremental advance
AI Analysis
This work addresses the challenge of ensuring privacy in statistical estimation for data analysts, providing fundamental limits that are incremental to prior results.
The paper tackles the problem of privately estimating the covariance matrix of a Gaussian distribution, proving lower bounds on sample complexity that match existing upper bounds across the widest known parameter settings.
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.