Univariate-Guided Interaction Modeling

Abstract

We propose a procedure for sparse regression with pairwise interactions, by generalizing the Univariate Guided Sparse Regression (UniLasso) methodology. A central contribution is our introduction of TripletScan, which screens a pair $(j,k)$ using the coefficient of $X_j{X}_k$ in the local regression of the response on $1$, $X_j$, $X_k$, and $X_j{X}_k$. The retained products are incorporated either jointly with the main effects through UniLasso, yielding uniPairs, or after a first-stage main-effects fit, yielding uniPairs-2stage. For the UniLasso components of the procedures, we prove false-positive exclusion and uniform coefficient-error bounds. In simulations and an HIV drug-resistance application, the proposed procedures produce substantially smaller fitted models than competing interaction methods while retaining competitive predictive performance.