Sparsity via Sparse Group $k$-max Regularization
<|reference_start|>Sparsity via Sparse Group $k$-max Regularization: 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.<|reference_end|>
@article{tao2024sparsity,
    title={Sparsity via Sparse Group $k$-max Regularization},
    author={Qinghua Tao, Xiangming Xi, Jun Xu and Johan A.K. Suykens},
    journal={arXiv preprint arXiv:2402.08493},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08493},
    primaryClass={cs.LG stat.ML}
}