Private independence testing across two parties

TL;DR

This paper presents $ ext{pi}$-test, a novel privacy-preserving method for testing statistical independence across distributed datasets, with theoretical error bounds suitable for sensitive data scenarios.

Contribution

Introduction of $ ext{pi}$-test, a differentially private algorithm for independence testing based on privately estimating distance correlation in multi-party data.

Findings

Provides additive and multiplicative error bounds for the private test.

Applicable to distributed hypothesis testing with sensitive data.

Enhances privacy in statistical independence testing across parties.

Abstract

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.