The Group Dantzig Selector
Abstract
We introduce a new method – the group Dantzig selector – for high dimensional sparse regression with group structure, which has a convincing theory about why utilizing the group structure can be beneficial. Under a group restricted isometry condition, we obtain a significantly improved nonasymptotic $\ell_2$-norm bound over the basis pursuit or the Dantzig selector which ignores the group structure. To gain more insight, we also introduce a surprisingly simple and intuitive “sparsity oracle condition” to obtain a block $\ell_1$-norm bound, which is easily accessible to a broad audience in machine learning community. Encouraging numerical results are also provided to support our theory.
Cite
Text
Liu et al. "The Group Dantzig Selector." Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010.Markdown
[Liu et al. "The Group Dantzig Selector." Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 2010.](https://mlanthology.org/aistats/2010/liu2010aistats-group/)BibTeX
@inproceedings{liu2010aistats-group,
title = {{The Group Dantzig Selector}},
author = {Liu, Han and Zhang, Jian and Jiang, Xiaoye and Liu, Jun},
booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics},
year = {2010},
pages = {461-468},
volume = {9},
url = {https://mlanthology.org/aistats/2010/liu2010aistats-group/}
}