Privacy protection methods, such as differentially private mechanisms, introduce noise into resulting statistics which often results in complex and intractable sampling distributions. In this paper, we propose to use the simulation-based "repro sample" approach to produce statistically valid confidence intervals and hypothesis tests based on privatized statistics. We show that this methodology is applicable to a wide variety of private inference problems, appropriately accounts for biases introduced by privacy mechanisms (such as by clamping), and improves over other state-of-the-art inference methods such as the parametric bootstrap in terms of the coverage and type I error of the private inference. We also develop significant improvements and extensions for the repro sample methodology for general models (not necessarily related to privacy), including 1) modifying the procedure to ensure guaranteed coverage and type I errors, even accounting for Monte Carlo error, and 2) proposing efficient numerical algorithms to implement the confidence intervals and $p$-values.
翻译:在本文件中,我们提议采用模拟“反抽样”法,根据私营化的统计数字,提出具有统计效力的互信间隔和假设测试;我们表明,这种方法适用于各种私人推断问题,适当说明隐私机制(例如通过夹住)引入的偏见,并改进其他最先进的推理方法,例如参数靴,从私人推理的覆盖范围和类型I错误的角度来说,这往往导致复杂和棘手的抽样分布;我们还提议采用基于模拟的“反抽样”法,根据私营化的统计数字,提出具有统计效力的互信间隔和假设测试;我们表明,这一方法适用于广泛的私人推断问题,适当说明隐私机制(例如通过夹住)引入的偏差,并改进其他最先进的推理方法,例如参数靴,从私人推理的覆盖面和类型I错误角度讲,我们还提出大幅改进和扩展通用模型(不一定与隐私有关)的重选抽样法,包括1)修改程序,以确保保证覆盖面和类型I错误得到保证,甚至计算蒙特卡洛错误,以及2 提出执行信任间隔和美元价值的有效数字算法。</s>