### Web: http://arxiv.org/abs/2111.11320

June 23, 2022, 1:11 a.m. | Hassan Ashtiani, Christopher Liaw

We present a fairly general framework for reducing $(\varepsilon, \delta)$
differentially private (DP) statistical estimation to its non-private
counterpart. As the main application of this framework, we give a polynomial
time and $(\varepsilon,\delta)$-DP algorithm for learning (unrestricted)
Gaussian distributions in $\mathbb{R}^d$. The sample complexity of our approach
for learning the Gaussian up to total variation distance $\alpha$ is
$\widetilde{O}(d^2/\alpha^2 + d^2\sqrt{\ln(1/\delta)}/\alpha \varepsilon + d\ln(1/\delta) / \alpha \varepsilon)$ matching (up to logarithmic factors) the
best known information-theoretic (non-efficient) sample complexity upper …

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