On Exact Feature Screening in Ultrahigh-Dimensional Binary Classification
提出一种基于能量距离的无模型特征筛选方法，用于超高维二分类问题，能高概率保留相关特征并剔除噪声变量，还扩展识别联合分布有差异的变量对，并构建了风险一致的分类器。
We propose a new model-free feature screening method based on energy distances for ultrahigh-dimensional binary classification problems. With a high probability, the proposed method retains only relevant features after discarding all the noise variables. The proposed screening method is also extended to identify pairs of variables that are marginally undetectable but have differences in their joint distributions. Finally, we build a classifier that maintains coherence between the proposed feature selection criteria and discrimination method, and also establish its risk consistency. An extensive numerical study with simulated and real benchmark datasets shows clear and convincing advantages of our proposed method over the state-of-the-art methods. Supplementary materials for this article are available online.