Identifying differences in networks has become a canonical problem in many biological applications. Existing methods try to accomplish this goal by either directly comparing the estimated structures of two networks, or testing the null hypothesis that the covariance or inverse covariance matrices in two populations are identical. However, estimation approaches do not provide measures of uncertainty, e.g., p-values, whereas existing testing approaches could lead to misleading results, as we illustrate in this paper. To address these shortcomings, we propose a qualitative hypothesis testing framework, which tests whether the connectivity structures in the two networks are the same. our framework is especially appropriate if the goal is to identify nodes or edges that are differentially connected. No existing approach could test such hypotheses and provide corresponding measures of uncertainty. Theoretically, we show that under appropriate conditions, our proposal correctly controls the type-I error rate in testing the qualitative hypothesis. Empirically, we demonstrate the performance of our proposal using simulation studies and applications in cancer genomics.
Keywords: biological networks; differential connectivity; high-dimensional data; lasso; significance test.