FED-$χ^2$: Privacy Preserving Federated Correlation Test

In this paper, we propose the first secure federated $\chi^2$-test protocol Fed-$\chi^2$. To minimize both the privacy leakage and the communication cost, we recast $\chi^2$-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-$\chi^2$ that the joint distribution is hidden in a subspace with exponential possible distributions. Our evaluation results show that Fed-$\chi^2$ achieves negligible accuracy drops with small client-side computation overhead. In several real-world case studies, the performance of Fed-$\chi^2$ is comparable to the centralized $\chi^2$-test.