Title: Powerful Independence Testing on Heterogeneous Federated Clients with Theoretical Guarantees
Primary area: causal reasoning
Keywords: Independence Testing, Causal Discovery, Heterogeneous Federated Clients

Abstract: We propose a novel federated independence testing framework that addresses both theoretical and practical challenges arising from client heterogeneity. We begin by revisiting existing federated independence testing methods and showing why they often fail to provide valid guarantees or maintain statistical power under data distributional shift across clients. Building on this analysis, we introduce a copula-based marginal alignment technique together with a stacking-based aggregation strategy that amplifies intra-client dependence while mitigating inter-client variation, yielding 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 establish both the correctness of our method and the validity of the test. Extensive experiments on both synthetic and real-world datasets demonstrate the superiority of our solution over existing methods.

TL;DR: A theoretically grounded and powerful framework for federated independence testing