Hilafu Haileab, Safo Sandra E
Department of Business Analytics and Statistics, University of Tennessee, Knoxville, TN, 37996, USA.
Division of Biostatistics, University of Minnesota, Minneapolis, MN, 55455, USA.
BMC Bioinformatics. 2022 May 7;23(1):168. doi: 10.1186/s12859-022-04700-3.
Dimension reduction and variable selection play a critical role in the analysis of contemporary high-dimensional data. The semi-parametric multi-index model often serves as a reasonable model for analysis of such high-dimensional data. The sliced inverse regression (SIR) method, which can be formulated as a generalized eigenvalue decomposition problem, offers a model-free estimation approach for the indices in the semi-parametric multi-index model. Obtaining sparse estimates of the eigenvectors that constitute the basis matrix that is used to construct the indices is desirable to facilitate variable selection, which in turn facilitates interpretability and model parsimony.
To this end, we propose a group-Dantzig selector type formulation that induces row-sparsity to the sliced inverse regression dimension reduction vectors. Extensive simulation studies are carried out to assess the performance of the proposed method, and compare it with other state of the art methods in the literature.
The proposed method is shown to yield competitive estimation, prediction, and variable selection performance. Three real data applications, including a metabolomics depression study, are presented to demonstrate the method's effectiveness in practice.
降维和变量选择在当代高维数据的分析中起着关键作用。半参数多指标模型通常是分析此类高维数据的合理模型。切片逆回归（SIR）方法可被表述为广义特征值分解问题，为半参数多指标模型中的指标提供了一种无模型估计方法。获得构成用于构建指标的基矩阵的特征向量的稀疏估计有助于变量选择，进而有助于解释性和模型简约性。
为此，我们提出了一种组丹齐格选择器类型的公式，该公式可诱导切片逆回归降维向量的行稀疏性。我们进行了广泛的模拟研究，以评估所提出方法的性能，并将其与文献中其他现有方法进行比较。
结果表明，所提出的方法在估计、预测和变量选择性能方面具有竞争力。我们给出了三个实际数据应用案例，包括一项代谢组学抑郁症研究，以证明该方法在实际中的有效性。
