Quadratic regression (QR) models naturally extend linear models by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain the hierarchical model structure. Existing regularization methods generally achieve this by solving complex optimization problems, which demands high computational cost and hence make them infeasible for high dimensional data analysis. This paper presents a new scalable regularization method, called Regularization Algorithm under Marginality Principle (RAMP), for model selection in high dimensional QR. The hierarchy-preserving regularization path can be computed efficiently by RAMP. Two-stage regularization methods are also studied. These methods are then extended to generalized QR models.
REF further improved interaction detection by proposing a regularization algorithm under marginality principle (RAMP).
Model Selection for High Dimensional Quadratic Regression via Regularization
arXiv: Methodology
Mathematics