Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Information Theory

arXiv:1501.03643 (cs)
[Submitted on 15 Jan 2015 (v1), last revised 3 Apr 2016 (this version, v2)]

Title:On robust width property for Lasso and Dantzig selector

Authors:Hui Zhang
View PDF
Abstract:Recently, Cahill and Mixon completely characterized the sensing operators in many compressed sensing instances with a robust width property. The proposed property allows uniformly stable and robust reconstruction of certain solutions from an underdetermined linear system via convex optimization. However, their theory does not cover the Lasso and Dantzig selector models, both of which are popular alternatives in the statistics community. In this letter, we show that the robust width property can be perfectly applied to these two models as well. Our results solve an open problem left by Cahill and Mixon.
Comments: 8 pages; A mistake has been corrected
Subjects: Information Theory (cs.IT); Optimization and Control (math.OC)
Cite as: arXiv:1501.03643 [cs.IT]
  (or arXiv:1501.03643v2 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1501.03643

Submission history

From: Hui Zhang [view email]
[v1] Thu, 15 Jan 2015 12:28:39 UTC (6 KB)
[v2] Sun, 3 Apr 2016 13:27:12 UTC (7 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cs.IT
< prev   |   next >
new | recent | 2015-01
Change to browse by:
cs
math
math.IT
math.OC

References & Citations

DBLP - CS Bibliography

listing | bibtex
Hui Zhang
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)