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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2402.08493 |
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| _version_ | 1866909105210261504 |
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| author | Tao, Qinghua Xi, Xiangming Xu, Jun Suykens, Johan A. K. |
| author_facet | Tao, Qinghua Xi, Xiangming Xu, Jun Suykens, Johan A. K. |
| contents | For the linear inverse problem with sparsity constraints, the $l_0$ regularized problem is NP-hard, and existing approaches either utilize greedy algorithms to find almost-optimal solutions or to approximate the $l_0$ regularization with its convex counterparts. In this paper, we propose a novel and concise regularization, namely the sparse group $k$-max regularization, which can not only simultaneously enhance the group-wise and in-group sparsity, but also casts no additional restraints on the magnitude of variables in each group, which is especially important for variables at different scales, so that it approximate the $l_0$ norm more closely. We also establish an iterative soft thresholding algorithm with local optimality conditions and complexity analysis provided. Through numerical experiments on both synthetic and real-world datasets, we verify the effectiveness and flexibility of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08493 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparsity via Sparse Group $k$-max Regularization Tao, Qinghua Xi, Xiangming Xu, Jun Suykens, Johan A. K. Machine Learning For the linear inverse problem with sparsity constraints, the $l_0$ regularized problem is NP-hard, and existing approaches either utilize greedy algorithms to find almost-optimal solutions or to approximate the $l_0$ regularization with its convex counterparts. In this paper, we propose a novel and concise regularization, namely the sparse group $k$-max regularization, which can not only simultaneously enhance the group-wise and in-group sparsity, but also casts no additional restraints on the magnitude of variables in each group, which is especially important for variables at different scales, so that it approximate the $l_0$ norm more closely. We also establish an iterative soft thresholding algorithm with local optimality conditions and complexity analysis provided. Through numerical experiments on both synthetic and real-world datasets, we verify the effectiveness and flexibility of the proposed method. |
| title | Sparsity via Sparse Group $k$-max Regularization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2402.08493 |