The Group Dantzig Selector

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-liu10a, 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}, pages = {461--468}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/liu10a/liu10a.pdf}, url = {https://proceedings.mlr.press/v9/liu10a.html}, 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.} }
Endnote
%0 Conference Paper %T The Group Dantzig Selector %A Han Liu %A Jian Zhang %A Xiaoye Jiang %A Jun Liu %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-liu10a %I PMLR %P 461--468 %U https://proceedings.mlr.press/v9/liu10a.html %V 9 %X 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.
RIS
TY - CPAPER TI - The Group Dantzig Selector AU - Han Liu AU - Jian Zhang AU - Xiaoye Jiang AU - Jun Liu BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-liu10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 461 EP - 468 L1 - http://proceedings.mlr.press/v9/liu10a/liu10a.pdf UR - https://proceedings.mlr.press/v9/liu10a.html AB - 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. ER -
APA
Liu, H., Zhang, J., Jiang, X. & Liu, J.. (2010). The Group Dantzig Selector. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:461-468 Available from https://proceedings.mlr.press/v9/liu10a.html.

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