基于GINI相关系数的超高维分类特征变量筛选

Selection of Ultra-High Dimensional Classification Feature Variables Based on GINI Correlation Coefficient

本文提出了一种基于GINI相关系数的超高维判别分析的GINI相关特征筛选方法。该方法在简单条件下建立了稳健筛选性能。首先,对重尾分布、潜在异常值情况下的数据具有稳健性。其次,它没有具体的数据模型限制,适用于参数及非参数模型。第三,由于所得统计量的有界性,在理论推导上比较简单。第四,筛选指标结构简单,计算成本低。通过蒙特卡罗模拟和实际数据实例验证了该方法的有效性。

We proposed a new method named GINI correlation feature screening for ultrahigh dimensional discriminant analysis based GINI correlation coefficients. We also establish the sure screening property for the proposed procedure under simple assumptions. The new procedure has some additional desirable characters. First, it is robust against heavy-tailed distributions, potential outliers and the sample shortage for some categories. Second, it is model-free without any specification of a regression model and directly applicable to the situation with many categories. Third, it is simple in theoretical derivation due to the boundedness of the resulting statistics. Forth, it is relatively inexpensive in computational cost because of the simple structure of the screening index. Monte Carlo simulations and real data examples are used to demonstrate the finite sample performance.