Han Liu, Jian Zhang, Xiaoye Jiang, and Jun Liu. The Group Dantzig Selector. The Thirteenth International Conference on Artificial Intelligence and Statistics (AISTATS). Sardinia, Italy, May 2010.


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 bene cial. Under a group restricted isometry condition, we obtain a significantly improved nonasymptotic L2-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 L1-norm bound, which is easily accessible to a broad audience in machine learning community. Encouraging numerical results are also provided to support our theory.


title = {The Group Dantzig Selector},
author = {Han Liu and Jian Zhang and Xiaoye Jiang and Jun Liu},
booktitle = {In Artificial Intelligence and Statistics (AISTATS)},
year = 2010,
month = {May},
address = {Sardinia, Italy},