Multivariate differential association analysis.

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 relationships between two sets of variables are different or not 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, significantly enhancing its usability in analyzing large datasets. 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.