Private independence testing across two parties
This work addresses privacy concerns in distributed hypothesis testing for sensitive data, representing an incremental advancement by applying differential privacy to an existing independence measure.
The paper tackles the problem of testing statistical independence between data distributed across two parties while preserving privacy, by introducing a differentially private algorithm that estimates distance correlation with established error bounds.
We introduce $π$-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 Székely 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.