Nonparametric Extensions of Randomized Response for Private Confidence Sets
Nonparametric Extensions of Randomized Response for Private Confidence Sets
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发表时间：
2022-02
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通讯作者：
Ian Waudby-Smith;Zhiwei Steven Wu;Aaditya Ramdas
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作者：
Ian Waudby-Smith;Zhiwei Steven Wu;Aaditya Ramdas
这项工作推导出的方法进行非参数，非渐近统计推断的人口平均数的约束下的局部差分隐私（LDP）。给定均值为$\mu^\星星$的有界观测值$（X_1，\dots，X_n）$被私有化为$（Z_1，\dots，Z_n）$，当只允许访问私有化数据时，给出了$\mu^\星星$的置信区间（CI）和时间一致置信序列（CS）.为了实现这一目标，我们引入了一个非参数和顺序交互式推广华纳著名的“随机响应”机制，满足LDP的任意有界随机变量，然后提供CI和CS的手段访问所产生的私有化的意见。例如，我们的结果产生私人类似物Hoeffding的不等式在固定时间和时间均匀的制度。我们扩展这些Hoeffding型CS捕获随时间变化（非平稳）的手段，并通过说明这些方法可以用来进行私人在线A/B测试的结论。
This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP). Given bounded observations $(X_1, \dots, X_n)$ with mean $\mu^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we present confidence intervals (CI) and time-uniform confidence sequences (CS) for $\mu^\star$ when only given access to the privatized data. To achieve this, we introduce a nonparametric and sequentially interactive generalization of Warner's famous ``randomized response'' mechanism, satisfying LDP for arbitrary bounded random variables, and then provide CIs and CSs for their means given access to the resulting privatized observations. For example, our results yield private analogues of Hoeffding's inequality in both fixed-time and time-uniform regimes. We extend these Hoeffding-type CSs to capture time-varying (non-stationary) means, and conclude by illustrating how these methods can be used to conduct private online A/B tests.