Title: High-dimensional interaction detection with false sign rate control
Authors: Daoji Li - California State University Fullerton (United States) [presenting]
Yingying Fan - University of Southern California (United States)
Yinfei Kong - California State University Fullerton (United States)
Jinchi Lv - University of Southern California (United States)
Abstract: 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. Such a gap is filled. More specifically, we establish some theoretical results on interaction selection for ultrahigh-dimensional quadratic regression models under random design. 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 a simulation study. This is a joint work with Yingying Fan, Yinfei Kong and Jinchi Lv.