Sparse sufficient dimension reduction for directional regression
Abstract Sufficient dimension reduction has emerged as a powerful tool for extracting meaningful information within high dimensional datasets over the past few decades. These methods aim to reduce the complexity of data by focusing on its most informative components and this allows us to avoid ‘curs...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of Big Data |
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| Online Access: | https://doi.org/10.1186/s40537-025-01219-1 |
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| author | Gayun Kwon Gijeong Noh Kyongwon Kim |
| author_facet | Gayun Kwon Gijeong Noh Kyongwon Kim |
| author_sort | Gayun Kwon |
| collection | DOAJ |
| description | Abstract Sufficient dimension reduction has emerged as a powerful tool for extracting meaningful information within high dimensional datasets over the past few decades. These methods aim to reduce the complexity of data by focusing on its most informative components and this allows us to avoid ‘curse of dimensionality’. However, many sufficient dimension reduction methods have challenges because their outcome has the form of the linear combinations of the original predictors. This can make the interpretation of the extracted components quite difficult, particularly when working with a large number of variables. To address this issue, we introduce a sparse sufficient dimension reduction method for directional regression. Our approach converts generalized eigendecomposition to regression type optimization problem with LASSO constraint and this promotes interpretability by generating sparse estimates. Moreover, we provide theoretical support for our proposed method, establishing non-asymptotic oracle inequalities and convergence guarantees for the associated optimization algorithm. We demonstrate the efficacy of our approach by comparing it against existing methods such as non-sparse directional regression, sparse sliced inverse regression, and sliced average variance estimation through comprehensive numerical experiments. We further apply our method to two real-world datasets to present its practical value in extracting meaningful insights from complex data structures. |
| format | Article |
| id | doaj-art-acf25a0509c64c69872ed6f743d55aab |
| institution | Kabale University |
| issn | 2196-1115 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Big Data |
| spelling | doaj-art-acf25a0509c64c69872ed6f743d55aab2025-08-20T04:02:57ZengSpringerOpenJournal of Big Data2196-11152025-07-0112112210.1186/s40537-025-01219-1Sparse sufficient dimension reduction for directional regressionGayun Kwon0Gijeong Noh1Kyongwon Kim2Department of Statistics, Ewha Womans UniversityR&D Center, Hyundai SteelDepartment of Applied Statistics, Department of Statistics and Data Science, Yonsei UniversityAbstract Sufficient dimension reduction has emerged as a powerful tool for extracting meaningful information within high dimensional datasets over the past few decades. These methods aim to reduce the complexity of data by focusing on its most informative components and this allows us to avoid ‘curse of dimensionality’. However, many sufficient dimension reduction methods have challenges because their outcome has the form of the linear combinations of the original predictors. This can make the interpretation of the extracted components quite difficult, particularly when working with a large number of variables. To address this issue, we introduce a sparse sufficient dimension reduction method for directional regression. Our approach converts generalized eigendecomposition to regression type optimization problem with LASSO constraint and this promotes interpretability by generating sparse estimates. Moreover, we provide theoretical support for our proposed method, establishing non-asymptotic oracle inequalities and convergence guarantees for the associated optimization algorithm. We demonstrate the efficacy of our approach by comparing it against existing methods such as non-sparse directional regression, sparse sliced inverse regression, and sliced average variance estimation through comprehensive numerical experiments. We further apply our method to two real-world datasets to present its practical value in extracting meaningful insights from complex data structures.https://doi.org/10.1186/s40537-025-01219-1Sufficient dimension reductionDirectional regressionLASSOHigh dimensional dataMultivariate analysis |
| spellingShingle | Gayun Kwon Gijeong Noh Kyongwon Kim Sparse sufficient dimension reduction for directional regression Journal of Big Data Sufficient dimension reduction Directional regression LASSO High dimensional data Multivariate analysis |
| title | Sparse sufficient dimension reduction for directional regression |
| title_full | Sparse sufficient dimension reduction for directional regression |
| title_fullStr | Sparse sufficient dimension reduction for directional regression |
| title_full_unstemmed | Sparse sufficient dimension reduction for directional regression |
| title_short | Sparse sufficient dimension reduction for directional regression |
| title_sort | sparse sufficient dimension reduction for directional regression |
| topic | Sufficient dimension reduction Directional regression LASSO High dimensional data Multivariate analysis |
| url | https://doi.org/10.1186/s40537-025-01219-1 |
| work_keys_str_mv | AT gayunkwon sparsesufficientdimensionreductionfordirectionalregression AT gijeongnoh sparsesufficientdimensionreductionfordirectionalregression AT kyongwonkim sparsesufficientdimensionreductionfordirectionalregression |