Univariate-Guided Interaction Modeling

2025-12-16

AI Summary

To address the challenges of pairwise interaction selection and poor interpretability in high-dimensional sparse regression, this paper introduces a novel modeling paradigm based on a formally defined concept of “marginal interaction” and proposes two algorithms: uniPairs and the two-stage uniPairs-2stage. The methods integrate univariate-guided screening, Lasso-type regularization, and asymptotic statistical testing—bypassing exhaustive enumeration and avoiding strong assumptions such as strong separability or low signal-to-noise ratios. Under mild regularity conditions, we establish theoretical consistency for support set recovery. Empirical evaluations on multiple benchmark datasets demonstrate that our approach significantly outperforms Glinternet and Sprinter, yielding sparser, more stable models with statistically interpretable interaction terms. The key innovation lies in the first formal characterization of marginal interaction and the simultaneous enhancement of model interpretability and predictive accuracy.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Ensemble Methods
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Develops sparse regression with pairwise interactions
• Introduces univariate-guided interaction modeling concept
• Proposes algorithms for sparser interpretable interaction models

Innovation

• Univariate-guided interaction modeling for sparse regression
• Introduces concept of univariate marginal interactions
• Proposes uniPairs algorithms for interpretable sparse models