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Generalized Dantzig Selector: Application to the k-support norm

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Soumyadeep Chatterjee, Sheng Chen, Arindam Banerjee

Machine Learning · Submitted 20 Jun 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The experimental results confirm our theoretical analysis.

how it is stated · asserted 1.00 read the record →

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arXiv ID1406.5291 (version 3)
Pith IDUFBJPMHA, Pith's permanent record of this paper and its review
CitationArindam Banerjee, Sheng Chen, Soumyadeep Chatterjee. "Generalized Dantzig Selector: Application to the k-support norm." arXiv:1406.5291 (2014). https://pith.science/paper/UFBJPMHA
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,549 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.81 · states limitation 0.14 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.54 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS, and non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian width of unit norm ball and suitable set encompassing estimation error. Further, we consider a non-trivial example of the GDS using $k$-support norm. We derive an efficient method to compute the proximal operator for $k$-support norm since existing methods are inapplicable in this setting. For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the $k$-support norm. The experimental results confirm our theoretical analysis.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. contribution 0.99 0.92 0.22 asserted 1.00
s1 We investigate both computational and statistical aspects of the GDS. contribution 0.98 0.86 0.04 asserted 0.88
s2 Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS, and non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian width of unit norm ball and suitable set encompassing estimation error. method 0.75 0.95 0.19 asserted 1.00
s3 Further, we consider a non-trivial example of the GDS using $k$-support norm. contribution 0.97 0.84 0.06 asserted 0.96
s4 We derive an efficient method to compute the proximal operator for $k$-support norm since existing methods are inapplicable in this setting. contribution 0.70 0.96 0.06 asserted 1.00
s5 For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the $k$-support norm. contribution 0.59 0.96 0.28 asserted 1.00
s6 The experimental results confirm our theoretical analysis. result 0.95 0.92 0.23 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.98 · evidence from proof or derivation 0.99.

What was examined, and what was not

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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS, and non-asymptotic high-probability bounds are established on the estimation error, which rely on Gaussian width of unit norm ball and suitable set encompassing estimation error. Further, we consider a non-trivial example of the GDS using $k$-support norm. We derive an efficient method to compute the proximal operator for $k$-support norm since existing methods are inapplicable in this setting. For statistical analysis, we provide upper bounds for the Gaussian widths needed in the GDS analysis, yielding the first statistical recovery guarantee for estimation with the $k$-support norm. The experimental results confirm our theoretical analysis.

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