提出一种新特征筛选方法，能精准识别冗余无效特征。
Sparse minimum Redundancy Maximum Relevance for feature selection
- 结合特征间与特征与目标的关系，用非凸正则化mRMR筛选特征。
- 在控制错误发现率前提下，准确剔除无关特征，比HSIC-LASSO更保守。
- 只需设定FDR阈值，无需预设选多少特征，适合高维数据。
我们提出一种特征筛选方法，同时考虑特征间关系和特征与目标变量的关系。通过惩罚版最小冗余最大相关性（mRMR）识别不活跃特征，该方法是经典mRMR的连续形式，采用非凸正则化，估计为零的参数即为不活跃特征集。我们建立了零系数被正确识别的条件，以保证不活跃特征的准确恢复。引入基于敲扑滤波的多阶段程序，使惩罚mRMR在控制错误发现率（FDR）的同时剔除无关特征。该方法性能与HSIC-LASSO相当，但在选择特征数量上更为保守。仅需设定FDR阈值，无需预先指定保留特征数。通过模拟实验和真实数据集验证了方法的有效性。代码已开源：https://github.com/PeterJackNaylor/SmRMR。
原文摘要 · Abstract (English)
We propose a feature screening method that integrates both feature-feature and feature-target relationships. Inactive features are identified via a penalized minimum Redundancy Maximum Relevance (mRMR) procedure, which is the continuous version of the classic mRMR penalized by a non-convex regularizer, and where the parameters estimated as zero coefficients represent the set of inactive features. We establish the conditions under which zero coefficients are correctly identified to guarantee accurate recovery of inactive features. We introduce a multi-stage procedure based on the knockoff filter enabling the penalized mRMR to discard inactive features while controlling the false discovery rate (FDR). Our method performs comparably to HSIC-LASSO but is more conservative in the number of selected features. It only requires setting an FDR threshold, rather than specifying the number of features to retain. The effectiveness of the method is illustrated through simulations and real-world datasets. The code to reproduce this work is available on the following GitHub: https://github.com/PeterJackNaylor/SmRMR.
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