High-Dimensional Interaction Detection With False Sign Rate Control
研究了超高维二次回归模型中交互效应的选择问题，证明了所提方法在随机设计下具有与lasso估计量相同的oracle不等式，并给出了错误符号率的显式界，模拟和实际数据验证了其有效性。
Identifying interaction effects is fundamentally important in many scientific discoveries and contemporary applications, but it is challenging since the number of pairwise interactions increases quadratically with the number of covariates and that of higher-order interactions grows even faster. Although there is a growing literature on interaction detection, little work has been done on the prediction and false sign rate on interaction detection in ultrahigh-dimensional regression models. This article fills such a gap. More specifically, in this article we establish some theoretical results on interaction selection for ultrahigh-dimensional quadratic regression models under random designs. We prove that the examined method enjoys the same oracle inequalities as the lasso estimator and further admits an explicit bound on the false sign rate. Moreover, the false sign rate can be asymptotically vanishing. These new theoretical characterizations are confirmed by simulation studies. The performance of our proposed approach is further illustrated through a real data application.