Convex hierarchical testing of interactions

TL;DR

This paper introduces a convex hierarchical testing framework for pairwise interactions in two-class problems, improving power and interpretability by considering main effects before interactions, demonstrated through simulations and genomic data analysis.

Contribution

It presents a novel convex hierarchical testing method that selectively tests interactions based on main effects, enhancing detection power and interpretability.

Findings

Potential gain in power over standard tests

Improved interpretability of interaction effects

Validated on genomic data from SAPPHIRe study

Abstract

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.