AI 中文总结
针对从超高维基因库中检测与人类面部形状变化相关重要基因的变量选择问题，提出基于张量岭回归模型的数据驱动修剪特征筛选方法TrimTenRidge，证明其理论一致性并评估性能，应用于面部形状数据有新发现。
AI 中文摘要
随着数据收集技术的发展，数据结构从单向量变得越来越复杂，如多维张量。本文受从超高维基因库中检测与人类面部形状变化相关的重要基因这一变量选择问题的驱动。我们基于张量岭回归模型提出了一种数据驱动的修剪特征筛选方法（TrimTenRidge），通过设置张量系数阈值来进行特征筛选。与现有方法不同，它不需要任何稀疏结构，不仅能检测重要预测变量，还能定位张量响应中与所选预测变量相关的特定区域/组件。我们证明了理论选择一致性，并通过各种模拟设置评估其经验性能。该方法同时处理超高维预测变量和张量响应，从理论、方法和五个应用方面为文献做出了贡献。我们还将TrimTenRidge方法应用于全基因组人类面部形状数据，成功检测到几个新的基因位点，并证实了一些与面部形状相关的现有发现。
英文摘要
As data collecting technologies advance, data structures are getting more and more complex, from single vectors to multi-dimensional tensors. This article is motivated by a variable selection problem to detect important genes from an ultrahigh dimensional pool that are associated with human facial shape variations. We propose a data-driven trimmed feature screening method based on a tensor ridge regression model (TrimTenRidge) through setting thresholds on the tensor coefficients to perform a feature screening procedure. Unlike existing approaches, the TrimTenRidge does not require any sparse structures. In addition, it not only detects important predictors but also locates specific regions/components of the tensor response that are associated with each of the selected predictors. We prove the theoretical selection consistency and also assess its empirical performance through various simulation settings. The approach copes with ultra-high dimensional predictors and tensor responses simultaneously and contributes to the literature from theoretical, methodological, and five applicational aspects. We further apply the TrimTenRidge approach to genome-wide human facial shape data, from which the entire facial shapes form a $2,342\times 7,160\times 3$ tensor, and we successfully detect several novel genetic loci and also confirm some existing findings that are associated to facial shape.
