Univariate-Guided Interaction Modeling

TL;DR

This paper introduces a novel sparse regression method for pairwise interactions, leveraging univariate interaction concepts to produce sparser, more interpretable models with proven support recovery under certain conditions.

Contribution

It generalizes the UniLasso methodology to include univariate interactions and proposes two algorithms, uniPairs and uniPairs-2stage, with demonstrated advantages over existing methods.

Findings

Produces sparser, more interpretable models

Outperforms established methods like Glinternet and Sprinter

Supports recovery under certain conditions

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.