Multi-Task Nonparametric Regression Under Joint Sparsity
This study investigates a multi-task estimation under joint sparsity. We consider estimating multiple functions when functions of interest share common sparsity patterns. An <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> penalty...
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| Format: | Article |
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IEEE
2025-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10870240/ |
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| author | Jae-Hwan Jhong Gyeongmin Kim Kwan-Young Bak |
| author_facet | Jae-Hwan Jhong Gyeongmin Kim Kwan-Young Bak |
| author_sort | Jae-Hwan Jhong |
| collection | DOAJ |
| description | This study investigates a multi-task estimation under joint sparsity. We consider estimating multiple functions when functions of interest share common sparsity patterns. An <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> penalty is imposed to enforce common sparsity patterns across component functions. A non-asymptotic oracle inequality is established to illustrate a possible improvement of the estimation error bound achieved by the proposed pooled estimator in comparison with the usual projection estimator. The proposed method is implemented with the alternating direction method of multipliers algorithm. Numerical studies are conducted to complement the theoretical results. We apply the proposed method to the ozone data to illustrate a practical applicability. The numerical results show that the proposed method detects the underlying sparsity patterns, thereby providing a desirable estimator that significantly outperforms the projection estimator. |
| format | Article |
| id | doaj-art-4001609a86f74d14847c1a34e056f868 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-4001609a86f74d14847c1a34e056f8682025-02-12T00:01:54ZengIEEEIEEE Access2169-35362025-01-0113251152512610.1109/ACCESS.2025.353848110870240Multi-Task Nonparametric Regression Under Joint SparsityJae-Hwan Jhong0https://orcid.org/0000-0003-2266-4986Gyeongmin Kim1Kwan-Young Bak2https://orcid.org/0000-0002-4541-160XDepartment of Information Statistics, Chungbuk National University, Cheongju, Republic of KoreaSchool of Mathematics, Statistics and Data Science, Sungshin Women’s University, Seoul, Republic of KoreaSchool of Mathematics, Statistics and Data Science, Sungshin Women’s University, Seoul, Republic of KoreaThis study investigates a multi-task estimation under joint sparsity. We consider estimating multiple functions when functions of interest share common sparsity patterns. An <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math></inline-formula> penalty is imposed to enforce common sparsity patterns across component functions. A non-asymptotic oracle inequality is established to illustrate a possible improvement of the estimation error bound achieved by the proposed pooled estimator in comparison with the usual projection estimator. The proposed method is implemented with the alternating direction method of multipliers algorithm. Numerical studies are conducted to complement the theoretical results. We apply the proposed method to the ozone data to illustrate a practical applicability. The numerical results show that the proposed method detects the underlying sparsity patterns, thereby providing a desirable estimator that significantly outperforms the projection estimator.https://ieeexplore.ieee.org/document/10870240/Group sparsityinformation poolingmulti-task learningoracle inequality |
| spellingShingle | Jae-Hwan Jhong Gyeongmin Kim Kwan-Young Bak Multi-Task Nonparametric Regression Under Joint Sparsity IEEE Access Group sparsity information pooling multi-task learning oracle inequality |
| title | Multi-Task Nonparametric Regression Under Joint Sparsity |
| title_full | Multi-Task Nonparametric Regression Under Joint Sparsity |
| title_fullStr | Multi-Task Nonparametric Regression Under Joint Sparsity |
| title_full_unstemmed | Multi-Task Nonparametric Regression Under Joint Sparsity |
| title_short | Multi-Task Nonparametric Regression Under Joint Sparsity |
| title_sort | multi task nonparametric regression under joint sparsity |
| topic | Group sparsity information pooling multi-task learning oracle inequality |
| url | https://ieeexplore.ieee.org/document/10870240/ |
| work_keys_str_mv | AT jaehwanjhong multitasknonparametricregressionunderjointsparsity AT gyeongminkim multitasknonparametricregressionunderjointsparsity AT kwanyoungbak multitasknonparametricregressionunderjointsparsity |