The Group Dantzig Selector

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 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 1norm bound, which is easily accessible to a broad audience in machine learning community. Encouraging numerical results are also provided to support our theory.

• Type: Journal
• Year: 2010
• Where: JMLR
• Authors: Han Liu, Jian Zhang 0003, Xiaoye Jiang, Jun Liu
• Keywords: Dantzig Selector, Group Dantzig Selector, Group Structure, JMLR 2010