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

Victor S. Portella, Nick Harvey
4/26/2024
cs.DScs.CRcs.LG

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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.

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Cite this paper

@article{portella2024lower,
  title  = {Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes},
  author = {Victor S. Portella and Nick Harvey},
  year   = {2024},
  eprint = {2404.17714},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2404.17714v1}
}

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