The group Dantzig selector

Han Liu, Jian Zhang, Xiaoye Jiang, Jun Liu

Research output: Contribution to journalConference article

14 Scopus citations

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 ℓ 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 ℓ 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.

Original languageEnglish (US)
Pages (from-to)461-468
Number of pages8
JournalJournal of Machine Learning Research
Volume9
StatePublished - Dec 1 2010
Event13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010 - Sardinia, Italy
Duration: May 13 2010May 15 2010

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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