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.

翻译：本文提出了一种基于成对交互的稀疏回归方法，通过推广单变量引导稀疏回归（UniLasso）方法论实现。核心贡献在于引入了单变量（或边际）交互的概念。基于这一概念，我们提出了两种算法——uniPairs与uniPairs-2stage，并在包括Glinternet和Sprinter在内的现有方法中评估其性能。研究表明，我们的框架能够生成更稀疏且交互项更具可解释性的模型。同时，我们在适当条件下证明了所提方法具有交互项支撑集恢复的理论保证。