mRMR变量选择方法在功能数据中的比较研究
The mRMR variable selection method: a comparative study for functional data
摘要：
变量选择方法的使用在函数数据的统计问题中特别有吸引力。选择变量的明显的一般标准是选择“最具代表性”或“最相关”的变量。然而，同样清楚的是，纯粹以关联性为导向的标准可能导致选择许多多余的变量。由Ding和Peng（2005）和Peng等人（2005）提出的mRMR（最小冗余最大相关性）过程是一种系统地执行变量选择的算法，实现了相关性和冗余之间的合理权衡。在其原始形式中，该过程基于使用所谓的互信息标准来评估相关性和冗余性。保持对功能数据问题的关注，我们在这里提出了mRMR方法的修改版本，通过用Székely等人（2007）提出的新关联度量（称为距离相关性）替换互信息来获得。我们还进行了广泛的模拟研究，包括1600个功能实验（100个功能模型$\times$ 4个样本量$\times$ 4个分类器）和3个真实数据的例子，旨在比较不同版本的mRMR方法。结果是相当确凿的，有利于新提出的替代方案。
英文摘要：
The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the `most representative' or `most relevant' variables. However, it is also clear that a purely relevance-oriented criterion could lead to select many redundant variables. The mRMR (minimum Redundance Maximum Relevance) procedure, proposed by Ding and Peng (2005) and Peng et al. (2005) is an algorithm to systematically perform variable selection, achieving a reasonable trade-off between relevance and redundancy. In its original form, this procedure is based on the use of the so-called mutual information criterion to assess relevance and redundancy. Keeping the focus on functional data problems, we propose here a modified version of the mRMR method, obtained by replacing the mutual information by the new association measure (called distance correlation) suggested by Székely et al. (2007). We have also performed an extensive simulation study, including 1600 functional experiments (100 functional models $\times$ 4 sample sizes $\times$ 4 classifiers) and three real-data examples aimed at comparing the different versions of the mRMR methodology. The results are quite conclusive in favor of the new proposed alternative.
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