[1.1. Motivations for regression with sparse interaction terms. ] Regression with interaction terms

We thank all the reviewers for the helpful comments. Here, we address the main concerns raised by the reviewers. While the traditional method (e.g., Lasso) can find important individual The motivations and application are discussed in [1.1.] When the sparse assumption doesn't hold] Theoretically, the sparsity assumption is commonly Motivations] The motivations and one real application where sparsity holds are discussed in [1.1.]