A lasso for 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 only considers an interaction when one or more of its constituent features has a nonzero main effect. It is based on a convex optimization framework that seamlessly considers main effects and interactions together. We provide examples— both real and simulated– that show a potential gain in power and interpretability over a standard (non-hierarchical) interaction test.

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