Sparse sliced inverse regression for high dimensional data analysis

• Main Authors: Hilafu, H. (Author), Safo, S.E (Author)
• Format: Article
• Language: English
• Published: BioMed Central Ltd 2022
• Subjects: article; Clustering algorithms; data analysis; decomposition; Dimension reduction; dimensionality reduction; discriminant analysis; Discriminant analysis; Eigenvalues and eigenfunctions; Generalized eigenvalue decomposition; Generalized eigenvalues; High dimensional data; High-dimensional data; Inverse problems; Linear discriminant analysis; Linear discriminant analyze; metabolomics; Multi-index; prediction; Regression analysis; Semiparametric; Semiparametric model; Semi-parametric modeling; simulation; Sliced inverse regression; Sliced inverse regressions; Variables selections
• Online Access: View Fulltext in Publisher

 Background: 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. Results: 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. Conclusion: 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. © 2022, The Author(s).