Model-free Feature Screening and FDR Control with Knockoff Features
This addresses feature selection for high-dimensional data analysis, offering a robust and adaptive method, but it is incremental as it builds on existing screening and knockoff techniques.
The paper tackles feature screening in ultra-high dimensional datasets by proposing a model-free method based on projection correlation, which works with heavy-tailed errors and multivariate responses, achieving sure screening and rank consistency. It also introduces a two-step approach with knockoff features to control false discovery rate (FDR), validated by numerical experiments and real data applications.
This paper proposes a model-free and data-adaptive feature screening method for ultra-high dimensional datasets. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This projection correlation based method does not require specifying a regression model and applies to the data in the presence of heavy-tailed errors and multivariate response. It enjoys both sure screening and rank consistency properties under weak assumptions. Further, a two-step approach is proposed to control the false discovery rate (FDR) in feature screening with the help of knockoff features. It can be shown that the proposed two-step approach enjoys both sure screening and FDR control if the pre-specified FDR level $α$ is greater or equal to $1/s$, where $s$ is the number of active features. The superior empirical performance of the proposed methods is justified by various numerical experiments and real data applications.