On robustness and local differential privacy
On robustness and local differential privacy
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DOI：
10.1214/23-aos2267
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发表时间：
2022-01
期刊：
影响因子：
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通讯作者：
Mengchu Li;Thomas B. Berrett;Yi Yu
中科院分区：
文献类型：
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作者：
Mengchu Li;Thomas B. Berrett;Yi Yu
开发统计分析工具的需求不断飙升，这些工具既能抵御污染，又能保护个人数据所有者的隐私。尽管这两个主题都有丰富的文献，但据我们所知，我们是第一个系统地研究Huber污染模型下的最优性与局部差分隐私（LDP）约束之间的联系的人。在本文中，我们从一个一般的极大极小下界结果出发，解出了对Huber污染的鲁棒性和保持LDP的代价。我们进一步研究了四个具体的例子：两点检验问题、潜在发散均值估计问题、非参数密度估计问题和单变量中值估计问题。对于每个问题，我们展示了在污染和LDP约束存在下的最优程序，评论了仅在污染或隐私约束下研究的最先进方法的联系，并通过部分回答LDP程序是否鲁棒以及鲁棒程序是否可以有效地私有化来揭示鲁棒性和LDP之间的联系。总的来说，我们的工作展示了鲁棒性和局部差异隐私联合研究的前景。
It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners' privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber's contamination model and the local differential privacy (LDP) constraints. In this paper, we start with a general minimax lower bound result, which disentangles the costs of being robust against Huber's contamination and preserving LDP. We further study four concrete examples: a two-point testing problem, a potentially-diverging mean estimation problem, a nonparametric density estimation problem and a univariate median estimation problem. For each problem, we demonstrate procedures that are optimal in the presence of both contamination and LDP constraints, comment on the connections with the state-of-the-art methods that are only studied under either contamination or privacy constraints, and unveil the connections between robustness and LDP via partially answering whether LDP procedures are robust and whether robust procedures can be efficiently privatised. Overall, our work showcases a promising prospect of joint study for robustness and local differential privacy.