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：我们提出了一种用于稀疏回归中成对交互建模的方法，通过推广单变量引导稀疏回归（UniLasso）方法论。核心贡献在于引入了单变量（或边际）交互的概念。基于此概念，我们提出了两种算法——uniPairs和uniPairs-2stage，并与现有方法（包括Glinternet和Sprinter）进行了性能比较。研究表明，我们的框架能产生更稀疏且交互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的支持恢复理论结果。