A fundamental task in systems biology is the identification of groups of genes that are involved in the cellular response to particular signals. At its simplest level, this often reduces to identifying biological quantities (mRNA abundance, enzyme concentrations, etc.) which are differentially expressed in two different conditions. Popular approaches involve using t-test statistics, based on modelling the data as arising from a mixture distribution. A common assumption of these approaches is that the data are independent and identically distributed, however, biological quantities are usually related through a complex (weighted) network of interactions, and often the more pertinent question is which subnetworks are differentially expressed, rather than which genes. Furthermore, in many interesting cases (such as high-throughput proteomics and metabolomics), only very partial observations are available, resulting in the need for efficient imputation techniques.