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