We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform the tests. Under the notion of local differential privacy, we propose simple, sample-optimal, and communication-efficient protocols for these two questions in the noninteractive setting, where in addition users may or may not share a common random seed. In particular, we show that the availability of shared (public) randomness greatly reduces the sample complexity. Underlying our public-coin protocols are privacy-preserving mappings which, when applied to the samples, minimally contract the distance between their respective probability distributions.

中文翻译：

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信息约束下的推断III：本地隐私约束

在样本分布于多个用户的环境中，我们研究离散分布的拟合优度和独立性测试。用户希望在使中央服务器执行测试的同时保留其数据的私密性。在局部差异性隐私的概念下，我们针对非交互设置中的这两个问题提出了简单，样本最优且通信高效的协议，其中用户可能共享或可能不共享公共随机种子。特别是，我们证明了共享（公共）随机性的可用性大大降低了样本的复杂性。我们的公共硬币协议的基础是隐私保护映射，将其应用于样本时，可以最小化它们各自概率分布之间的距离。