Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between genomic features differ between cases and controls. In this paper, we seek to evaluate whether the relationships between two sets of variables is different across two conditions. Specifically, we assess: do two sets of high-dimensional variables have similar dependence relationships across two conditions?. We propose a new kernel-based test to capture the differential dependence. Specifically, the new test determines whether two measures that detect dependence relationships are similar or not under two conditions. We introduce the asymptotic permutation null distribution of the test statistic and it is shown to work well under finite samples such that the test is computationally efficient, making it easily applicable to analyze large data sets. We demonstrate through numerical studies that our proposed test has high power for detecting differential linear and non-linear relationships. The proposed method is implemented in an R package kerDAA.

翻译：识别依赖关系在不同条件下的变化在许多科学研究中具有重要作用。例如，在比较生物系统时，了解基因组特征之间的关系在病例组与对照组之间是否存在差异至关重要。本文旨在评估两组变量之间的关系在两个不同条件下是否存在差异。具体而言，我们探究：两组高维变量在两个条件下是否具有相似的依赖关系？我们提出了一种基于核的新检验方法来捕捉差异依赖性。具体来说，该新检验用于判断两个条件下检测依赖关系的两种度量是否相似。我们介绍了检验统计量的渐近置换零分布，并证明其在有限样本下表现良好，且计算效率高，易于应用于大规模数据集的分析。通过数值研究，我们证明所提出的检验在检测线性与非线性差异关系方面具有较高功效。该方法已在R包kerDAA中实现。