Feature Selection for High-Dimensional Varying Coefficient Models via Ordinary Least Squares Projection
Feature Selection for High-Dimensional Varying Coefficient Models via Ordinary Least Squares Projection
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DOI：
10.1007/s40304-022-00326-2
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发表时间：
2023-03
影响因子：
0.9
通讯作者：
Haofeng Wang;Hongxiang Jin;Xuejun Jiang
中科院分区：
文献类型：
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作者：
Haofeng Wang;Hongxiang Jin;Xuejun Jiang
当协变量的维数为1时，变系数模型的特征选择是一个不断变化的问题。传统的显着降维技术是基于非参数平滑的边缘相关筛选方法。然而，边际相关筛选方法可能会筛选出与响应共同相关的变量。为了解决这个问题，我们提出了一种新的筛选器的名称组筛选通过非参数平滑高维普通最小二乘投影，简称为“组HOLP”，并研究其一定的筛选性能。基于这一良好的性质，我们引入了一个改进的特征选择过程，通过采用扩展的贝叶斯信息准则（EBIC）选择合适的子模型在变系数模型，这是创造成组HOLP-EBIC方法。在一定的正则性条件下，我们建立了所提出的方法的特征选择的强一致性。我们的方法的性能进行了评估，通过模拟和进一步说明了两个真实的例子。
Feature selection is a changing issue for varying coefficient models when the dimensionality of covariates is ultrahigh. The traditional technology of significantly reducing dimensionality is the marginal correlation screening method based on nonparametric smoothing. However, marginal correlation screening methods may be screen out variables that are jointly correlated to the response. To address this, we propose a novel screener with the name of group screening via nonparametric smoothing high-dimensional ordinary least squares projection, referred to as “Group HOLP” and study its sure screening property. Based on this nice property, we introduce a refined feature selection procedure via employing the extended Bayesian information criteria (EBIC) to select the suitable submodels in varying coefficient models, which is coined as Group HOLP-EBIC method. Under some regularity conditions, we establish the strong consistency of feature selection for the proposed method. The performance of our method is evaluated by simulations and further illustrated by two real examples.