论文标题
私人信心集的随机响应的非参数扩展
Nonparametric extensions of randomized response for private confidence sets
论文作者
论文摘要
这项工作得出了在当地差异隐私（LDP）约束下对人口均值进行非参数的非参数统计推断的方法。给定的有界观测值$（x_1，\ dots，x_n）$，其平均$μ^\ star $被私有化为$（z_1，\ dots，z_n）$，我们呈现置信区间（CI）和时间均匀的置信序列（CI）和仅适用于$μ^\ star $ for $μ^\ star $，仅适用于$μ^\ star $，而仅给出访问私有化的数据。为了实现这一目标，我们研究了华纳著名的``随机响应''机制的非参数且顺序互动的概括，满足了对任意界定随机变量的LDP，然后为其提供了对所产生的私有化观察的访问的手段提供CIS和CSS。例如，我们的结果在固定时间和时间均匀制度中产生了Hoeffding不平等的私人类似物。我们将这些Hoeffding型CSS扩展到捕获时变（非平稳）手段，并通过说明如何使用这些方法来进行私人在线A/B测试来得出结论。
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 $μ^\star$ that are privatized into $(Z_1, \dots, Z_n)$, we present confidence intervals (CI) and time-uniform confidence sequences (CS) for $μ^\star$ when only given access to the privatized data. To achieve this, we study 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.
