标题： 局部差分隐私的两样本检验 显示英文标题

标题： Locally Differentially Private Two-Sample Testing

摘要： 我们研究了在局部差分隐私约束下两样本检验问题，其中使用了置换程序来校准检验。 我们开发了对于一般离散分布和满足平滑性约束的连续分布而言，最优至对数因子的检验程序。 非交互式和交互式的检验都被考虑，并且我们证明允许交互性可以改善最小最大分离率。 我们的结果显示，在局部隐私约束下，尽管无法直接置换非私有数据而只能置换私有视图，置换程序在实践中仍然是可行的。 此外，通过对置换程序进行更精细的理论分析，我们能够避免在置换检验文献中普遍假设的相同样本量条件，无论是否存在隐私约束。 最后，我们进行了数值实验，展示了我们提出的检验方法的性能，并验证了理论发现，特别是允许交互性所带来的改进性能。 显示英文摘要

摘要： We consider the problem of two-sample testing under a local differential privacy constraint where a permutation procedure is used to calibrate the tests. We develop testing procedures which are optimal up to logarithmic factors, for general discrete distributions and continuous distributions subject to a smoothness constraint. Both non-interactive and interactive tests are considered, and we show allowing interactivity results in an improvement in the minimax separation rates. Our results show that permutation procedures remain feasible in practice under local privacy constraints, despite the inability to permute the non-private data directly and only the private views. Further, through a refined theoretical analysis of the permutation procedure, we are able to avoid an equal sample size assumption which has been made in the permutation testing literature regardless of the presence of the privacy constraint. Lastly, we conduct numerical experiments which demonstrate the performance of our proposed test and verify the theoretical findings, especially the improved performance enabled by allowing interactivity.