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.
"Convex hierarchical testing of interactions." Ann. Appl. Stat. 9 (1) 27 - 42, March 2015. https://doi.org/10.1214/14-AOAS758