Convex hierarchical testing of interactions

We consider the testing of all pairwise interactions in a two-class problem with many features. We devise a hierarchical testing framework that considers an interaction only when one or more of its constituent features has a nonzero main effect. The test is based on a convex optimization framework that seamlessly considers main effects and interactions together. We show - both in simulation and on a genomic data set from the SAPPHIRe study - a potential gain in power and interpretability over a standard (nonhierarchical) interaction test.