  We consider multivariate two-sample tests of means, where the location shift
between the two populations is expected to be related to a known graph
structure. An important application of such tests is the detection of
differentially expressed genes between two patient populations, as shifts in
expression levels are expected to be coherent with the structure of graphs
reflecting gene properties such as biological process, molecular function,
regulation or metabolism. For a fixed graph of interest, we demonstrate that
accounting for graph structure can yield more powerful tests under the
assumption of smooth distribution shift on the graph. We also investigate the
identification of nonhomogeneous subgraphs of a given large graph, which poses
both computational and multiple hypothesis testing problems. The relevance and
benefits of the proposed approach are illustrated on synthetic data and on
breast and bladder cancer gene expression data analyzed in the context of KEGG
and NCI pathways.
