差分私有匿名直方图的紧边界

Pasin Manurangsi
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引用次数: 4

摘要

在本文中,我们考虑差分私有(DP)计算匿名直方图的问题,该直方图被定义为输入数据集的多集计数(没有桶标签)。在低隐私体制$\epsilon \geq 1$下,我们给出了一个$\epsilon$ -DP算法,其期望$\ell_1$ -误差界为$O(\sqrt{n} / e^\epsilon)$。在高隐私状态$\epsilon<1$下,我们给出了预期$\ell_1$误差的$\Omega(\sqrt{n \log(1/\epsilon) / \epsilon})$下界。在这两种情况下,由于[Suresh, NeurIPS 2019],我们的边界渐近地匹配先前已知的下界/上界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tight Bounds for Differentially Private Anonymized Histograms
In this note, we consider the problem of differentially privately (DP) computing an anonymized histogram, which is defined as the multiset of counts of the input dataset (without bucket labels). In the low-privacy regime $\epsilon \geq 1$, we give an $\epsilon$-DP algorithm with an expected $\ell_1$-error bound of $O(\sqrt{n} / e^\epsilon)$. In the high-privacy regime $\epsilon<1$, we give an $\Omega(\sqrt{n \log(1/\epsilon) / \epsilon})$ lower bound on the expected $\ell_1$ error. In both cases, our bounds asymptotically match the previously known lower/upper bounds due to [Suresh, NeurIPS 2019].
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