Sparse sliced inverse regression for high dimensional data analysis
Abstract 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,...
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| Format: | Article |
| Language: | English |
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BMC
2022-05-01
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| Series: | BMC Bioinformatics |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s12859-022-04700-3 |
| _version_ | 1811306262514630656 |
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| author | Haileab Hilafu Sandra E. Safo |
| author_facet | Haileab Hilafu Sandra E. Safo |
| author_sort | Haileab Hilafu |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-04-13T08:42:13Z |
| format | Article |
| id | doaj.art-7035e9cc87b548debfa61916f3dc2a9b |
| institution | Directory Open Access Journal |
| issn | 1471-2105 |
| language | English |
| last_indexed | 2024-04-13T08:42:13Z |
| publishDate | 2022-05-01 |
| publisher | BMC |
| record_format | Article |
| series | BMC Bioinformatics |
| spelling | doaj.art-7035e9cc87b548debfa61916f3dc2a9b2022-12-22T02:53:52ZengBMCBMC Bioinformatics1471-21052022-05-0123111910.1186/s12859-022-04700-3Sparse sliced inverse regression for high dimensional data analysisHaileab Hilafu0Sandra E. Safo1Department of Business Analytics and Statistics, University of TennesseeDivision of Biostatistics, University of MinnesotaAbstract 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.https://doi.org/10.1186/s12859-022-04700-3Semiparametric modelGeneralized eigenvalue decompositionSliced inverse regressionLinear discriminant analysisHigh-dimensional data |
| spellingShingle | Haileab Hilafu Sandra E. Safo Sparse sliced inverse regression for high dimensional data analysis BMC Bioinformatics Semiparametric model Generalized eigenvalue decomposition Sliced inverse regression Linear discriminant analysis High-dimensional data |
| title | Sparse sliced inverse regression for high dimensional data analysis |
| title_full | Sparse sliced inverse regression for high dimensional data analysis |
| title_fullStr | Sparse sliced inverse regression for high dimensional data analysis |
| title_full_unstemmed | Sparse sliced inverse regression for high dimensional data analysis |
| title_short | Sparse sliced inverse regression for high dimensional data analysis |
| title_sort | sparse sliced inverse regression for high dimensional data analysis |
| topic | Semiparametric model Generalized eigenvalue decomposition Sliced inverse regression Linear discriminant analysis High-dimensional data |
| url | https://doi.org/10.1186/s12859-022-04700-3 |
| work_keys_str_mv | AT haileabhilafu sparseslicedinverseregressionforhighdimensionaldataanalysis AT sandraesafo sparseslicedinverseregressionforhighdimensionaldataanalysis |