Independence testing plays a central role in statistical and causal inference
from observational data. Standard independence tests assume that the data
samples are independent and identically distributed (i.i.d.) but that
assumption is violated in many real-world datasets and applications centered on
relational systems. This work examines the problem of estimating independence
in data drawn from relational systems by defining sufficient representations
for the sets of observations influencing individual instances. Specifically, we
define marginal and conditional independence tests for relational data by
considering the kernel mean embedding as a flexible aggregation function for
relational variables. We propose a consistent, non-parametric, scalable kernel
test to operationalize the relational independence test for non-i.i.d.
observational data under a set of structural assumptions. We empirically
evaluate our proposed method on a variety of synthetic and semi-synthetic
networks and demonstrate its effectiveness compared to state-of-the-art
kernel-based independence tests.

本文研究了如何在关系系统中估计数据之间的独立性，提出了一种基于核均值嵌入的方法，用于定义条件和边缘独立性测试，并在结构假设下实现了可伸缩的核测试方法。实证研究表明，该方法在合成网络和半合成网络等数据集上比基于核的独立性测试的现有方法更为有效。