Univariate-Guided Interaction Modeling
Methodology
2026-01-05 v2
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 a concept of univariate (or marginal) interactions. Using this concept, we propose two algorithms -- uniPairs and uniPairs-2stage -- , and evaluate their performance against established methods, including Glinternet and Sprinter. We show that our framework yields sparser models with more interpretable interactions. We also prove support recovery results for our proposal under suitable conditions.
Cite
@article{arxiv.2512.14413,
title = {Univariate-Guided Interaction Modeling},
author = {Aymen Echarghaoui and Robert Tibshirani},
journal= {arXiv preprint arXiv:2512.14413},
year = {2026}
}