Powerful and Theoretically Guaranteed Independence Testing on Heterogeneous Federated Clients

In this paper, we present a novel federated independence testing (FedIT) method that addresses both theoretical and practical challenges arising from client heterogeneity. We begin by revisiting existing federated independence testing methods and showing why they fail to provide valid guarantees or maintain statistical power under data distributional shift across clients. Building on this analysis, we develop a copula-based marginal alignment technique together with a stacking-based aggregation strategy that amplifies intra-client dependence while mitigating inter-client variation, resulting in a theoretically sound and powerful global test. For practicality, we further accelerate the aggregation step and incorporate a privacy-preserving mechanism. On the theoretical side, we prove both the correctness of our method and the validity of the test. Empirically, we conduct extensive experiments on both synthetic and real-world datasets, which demonstrate the superiority of our solution over existing methods.

Machine learning often uses data stored across many separate sources, such as hospitals, phones, or organizations, where raw data cannot be shared due to privacy or ownership concerns. This makes it difficult to determine whether two variables are truly related when the evidence is spread across different clients. Our paper studies this problem when clients have data with different patterns. Existing methods can become unreliable or miss real relationships in this setting. We propose FedIT, a new method that makes data from different clients more comparable and then combines their evidence carefully. This helps detect relationships within clients while reducing misleading differences across clients. We also make FedIT faster and more privacy-preserving. We prove that it gives valid results and show through experiments on simulated and real-world data that it outperforms existing methods.