Sparse Reluctant Interaction Modelling with Convex Hull Approximation

—For Accurate Modelling of Highly Correlated Variables Based on Diverse Nearly Optimal Solutions—

Abstract

This study presents a variable selection method for large-scale interaction models that include highly-correlated variables. SPRINTER (Sparse reluctant interaction modelling) is an important solution for pairwise interaction modelling. However, the SPRINTER algorithm initially applies Lasso for the variable selection of the main effect in the first and the last steps, which presents the problem of robust selection for highly correlated variables and leads to interaction selection failure. Therefore, this study proposes a combination method of CHANOL (Convex Hull Approximation of Nearly Optimal Lasso) and SPRINTER (referred to hereafter as, SPRINTER-CHANOL) for data with highly-correlated main effects and interactions. A series of experiments based on synthetic data demonstrated that the proposed method can effectively select the main effects and interactions while having a high true positive rate and a low false positive rate.