  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.
