FED-$χ^2$: Privacy Preserving Federated Correlation Test
This addresses privacy concerns in federated learning for statistical testing, offering a novel solution with practical applications, though it is incremental in combining existing techniques.
The paper tackles the problem of performing a chi-squared test in a federated setting while preserving privacy, proposing Fed-$χ^2$ as the first secure protocol that recasts the test to a second moment estimation problem, achieving negligible accuracy drops and performance comparable to centralized methods in real-world case studies.
In this paper, we propose the first secure federated $χ^2$-test protocol Fed-$χ^2$. To minimize both the privacy leakage and the communication cost, we recast $χ^2$-test to the second moment estimation problem and thus can take advantage of stable projection to encode the local information in a short vector. As such encodings can be aggregated with only summation, secure aggregation can be naturally applied to hide the individual updates. We formally prove the security guarantee of Fed-$χ^2$ that the joint distribution is hidden in a subspace with exponential possible distributions. Our evaluation results show that Fed-$χ^2$ achieves negligible accuracy drops with small client-side computation overhead. In several real-world case studies, the performance of Fed-$χ^2$ is comparable to the centralized $χ^2$-test.