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New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemma. (arXiv:2205.08532v2 [cs.DS] UPDATED)
May 19, 2022, 1:10 a.m. | Gautam Kamath, Argyris Mouzakis, Vikrant Singhal
stat.ML updates on arXiv.org arxiv.org
We prove new lower bounds for statistical estimation tasks under the
constraint of $(\varepsilon, \delta)$-differential privacy. First, we provide
tight lower bounds for private covariance estimation of Gaussian distributions.
We show that estimating the covariance matrix in Frobenius norm requires
$\Omega(d^2)$ samples, and in spectral norm requires $\Omega(d^{3/2})$ samples,
both matching upper bounds up to logarithmic factors. We prove these bounds via
our main technical contribution, a broad generalization of the fingerprinting
method to exponential families. Additionally, using the private …
More from arxiv.org / stat.ML updates on arXiv.org
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