We introduce $\pi$-test, a privacy-preserving algorithm for testing statistical independence between data distributed across multiple parties. Our algorithm relies on privately estimating the distance correlation between datasets, a quantitative measure of independence introduced in Sz\'ekely et al. [2007]. We establish both additive and multiplicative error bounds on the utility of our differentially private test, which we believe will find applications in a variety of distributed hypothesis testing settings involving sensitive data.

翻译：我们提出$\pi$-检验，一种用于跨多方分布数据之间统计独立性测试的隐私保护算法。该算法基于对数据集间距离相关性（由Székely等人[2007]提出的独立性定量度量）的私有估计。我们建立了差分隐私检验效用的加性和乘性误差界，相信该检验将在涉及敏感数据的各种分布式假设检验场景中得到应用。