The group Dantzig selector

Han Liu; Jian Zhang; Xiaoye Jiang; Jun Liu

The group Dantzig selector

Han Liu, Jian Zhang, Xiaoye Jiang, Jun Liu

Operations Research & Financial Engineering

Research output: Contribution to journal › Conference article › peer-review

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 language	English (US)
Pages (from-to)	461-468
Number of pages	8
Journal	Journal of Machine Learning Research
Volume	9
State	Published - 2010
Event	13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010 - Sardinia, Italy Duration: May 13 2010 → May 15 2010

All Science Journal Classification (ASJC) codes

Software
Control and Systems Engineering
Statistics and Probability
Artificial Intelligence

Cite this

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title = "The group Dantzig selector",

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.",

author = "Han Liu and Jian Zhang and Xiaoye Jiang and Jun Liu",

note = "Copyright: Copyright 2012 Elsevier B.V., All rights reserved.; 13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010 ; Conference date: 13-05-2010 Through 15-05-2010",

year = "2010",

language = "English (US)",

volume = "9",

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journal = "Journal of Machine Learning Research",

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TY - JOUR

T1 - The group Dantzig selector

AU - Liu, Han

AU - Zhang, Jian

AU - Jiang, Xiaoye

AU - Liu, Jun

PY - 2010

Y1 - 2010

N2 - 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.

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 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.

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M3 - Conference article

AN - SCOPUS:84860608028

SN - 1532-4435

VL - 9

SP - 461

EP - 468

JO - Journal of Machine Learning Research

JF - Journal of Machine Learning Research

T2 - 13th International Conference on Artificial Intelligence and Statistics, AISTATS 2010

Y2 - 13 May 2010 through 15 May 2010

ER -

The group Dantzig selector

Abstract

All Science Journal Classification (ASJC) codes

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