The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction
The minimum average variance estimation (MAVE) method has proven to be an effective approach to sufficient dimension reduction. In this study, we apply the computationally efficient optimization algorithm named alternating direction method of multipliers (ADMM) to a particular approach (MAVE or mini...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/3692883 |
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| _version_ | 1832546252121702400 |
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| author | Sheng Ma Qin Jiang Zaiqiang Ku |
| author_facet | Sheng Ma Qin Jiang Zaiqiang Ku |
| author_sort | Sheng Ma |
| collection | DOAJ |
| description | The minimum average variance estimation (MAVE) method has proven to be an effective approach to sufficient dimension reduction. In this study, we apply the computationally efficient optimization algorithm named alternating direction method of multipliers (ADMM) to a particular approach (MAVE or minimum average variance estimation) to the problem of sufficient dimension reduction (SDR). Under some assumptions, we prove that the iterative sequence generated by ADMM converges to some point of the associated augmented Lagrangian function. Moreover, that point is stationary. It also presents some numerical simulations on synthetic data to demonstrate the computational efficiency of the algorithm. |
| format | Article |
| id | doaj-art-22b940da899b4cc9895b18cf1afc5b58 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-22b940da899b4cc9895b18cf1afc5b582025-02-03T07:23:23ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/3692883The Alternating Direction Method of Multipliers for Sufficient Dimension ReductionSheng Ma0Qin Jiang1Zaiqiang Ku2Department of MathematicsDepartment of MathematicsDepartment of MathematicsThe minimum average variance estimation (MAVE) method has proven to be an effective approach to sufficient dimension reduction. In this study, we apply the computationally efficient optimization algorithm named alternating direction method of multipliers (ADMM) to a particular approach (MAVE or minimum average variance estimation) to the problem of sufficient dimension reduction (SDR). Under some assumptions, we prove that the iterative sequence generated by ADMM converges to some point of the associated augmented Lagrangian function. Moreover, that point is stationary. It also presents some numerical simulations on synthetic data to demonstrate the computational efficiency of the algorithm.http://dx.doi.org/10.1155/2024/3692883 |
| spellingShingle | Sheng Ma Qin Jiang Zaiqiang Ku The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction Journal of Mathematics |
| title | The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction |
| title_full | The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction |
| title_fullStr | The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction |
| title_full_unstemmed | The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction |
| title_short | The Alternating Direction Method of Multipliers for Sufficient Dimension Reduction |
| title_sort | alternating direction method of multipliers for sufficient dimension reduction |
| url | http://dx.doi.org/10.1155/2024/3692883 |
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