Private independence testing across two parties

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\ékely 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.