Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes
<|reference_start|>Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes: 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.<|reference_end|>
@article{portella2024lower,
    title={Lower Bounds for Private Estimation of Gaussian Covariance Matrices
  under All Reasonable Parameter Regimes},
    author={Victor S. Portella, Nick Harvey},
    journal={arXiv preprint arXiv:2404.17714},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.17714},
    primaryClass={cs.DS cs.CR cs.LG stat.ML}
}