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arXiv 2007.13660cs.LGcs.CRcs.DScs.ITmath.ITstat.ML
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学习离散分布:用户与项目级隐私

Learning discrete distributions: user vs item-level privacy

Cornell University(康奈尔大学);Google Research(谷歌研究院)

Yuhan Liu, Ananda Theertha Suresh, Felix Yu, Sanjiv Kumar, Michael Riley

摘要:

大部分关于差分隐私的文献都集中在项目级隐私上,粗略地说,目标是为每个项目或训练示例提供隐私。然而,最近许多实际应用,如联邦学习,需要保护单个用户的所有项目的隐私,这是很难实现的。因此,理解用户级隐私的理论极限变得至关重要。我们研究的基本问题,学习离散分布在$k$符号与用户级差分隐私。如果每个用户都有$m$样本,我们表明,拉普拉斯或高斯机制的直接应用程序需要用户的数量是$\mathcal{O}(k/(mα^2) + k/εα)$,以实现真正的和估计的分布之间的$α$的$\ell_1$距离,与隐私引起的惩罚$k/εα$独立于每个用户的样本数$m$。此外,我们表明,任何机制,只对最终的总计数操作,应该需要一个用户的复杂性相同的顺序。然后,我们提出了一种机制,使用户的数量规模为$\tilde{\mathcal{O}}(k/(mα^2) + k/\sqrt{m}εα)$,因此隐私的惩罚是$\tildeΘ(\sqrt{m})$倍小于标准的机制,在某些设置的兴趣。我们进一步表明,所提出的机制在某些制度下是接近最优的。我们还提出了一般的技术,以获得下限限制差分私人估计和二项分布之间的总变异的下限,这两者可能是独立的利益。

英文摘要:

Much of the literature on differential privacy focuses on item-level privacy, where loosely speaking, the goal is to provide privacy per item or training example. However, recently many practical applications such as federated learning require preserving privacy for all items of a single user, which is much harder to achieve. Therefore understanding the theoretical limit of user-level privacy becomes crucial. We study the fundamental problem of learning discrete distributions over $k$ symbols with user-level differential privacy. If each user has $m$ samples, we show that straightforward applications of Laplace or Gaussian mechanisms require the number of users to be $\mathcal{O}(k/(mα^2) + k/εα)$ to achieve an $\ell_1$ distance of $α$ between the true and estimated distributions, with the privacy-induced penalty $k/εα$ independent of the number of samples per user $m$. Moreover, we show that any mechanism that only operates on the final aggregate counts should require a user complexity of the same order. We then propose a mechanism such that the number of users scales as $\tilde{\mathcal{O}}(k/(mα^2) + k/\sqrt{m}εα)$ and hence the privacy penalty is $\tildeΘ(\sqrt{m})$ times smaller compared to the standard mechanisms in certain settings of interest. We further show that the proposed mechanism is nearly-optimal under certain regimes. We also propose general techniques for obtaining lower bounds on restricted differentially private estimators and a lower bound on the total variation between binomial distributions, both of which might be of independent interest.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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