The Group Dantzig Selector

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Han Liu, Jian Zhang, Xiaoye Jiang, Jun Liu ;
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:461-468, 2010.

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 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.

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