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Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices

Published on May 2015 by Oliver James
An Architectural Framework for Workload Demand Prediction in Scalable Federated Clouds
Foundation of Computer Science USA
ICCTAC2015 - Number 2
May 2015
Authors: Oliver James
80455375-64df-4db5-97d0-25a71e64682f

Oliver James . Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices. An Architectural Framework for Workload Demand Prediction in Scalable Federated Clouds. ICCTAC2015, 2 (May 2015), 1-5.

@article{
author = { Oliver James },
title = { Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices },
journal = { An Architectural Framework for Workload Demand Prediction in Scalable Federated Clouds },
issue_date = { May 2015 },
volume = { ICCTAC2015 },
number = { 2 },
month = { May },
year = { 2015 },
issn = 0975-8887,
pages = { 1-5 },
numpages = 5,
url = { /proceedings/icctac2015/number2/20924-2020/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 An Architectural Framework for Workload Demand Prediction in Scalable Federated Clouds
%A Oliver James
%T Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices
%J An Architectural Framework for Workload Demand Prediction in Scalable Federated Clouds
%@ 0975-8887
%V ICCTAC2015
%N 2
%P 1-5
%D 2015
%I International Journal of Computer Applications
Abstract

In this paper, we introduce a new framework for interpreting the existing theoretical stability results of sparse signal recovery algorithms in practical terms. Our framework is built on the theory of constrained minimal singular values of Gaussian sensing matrices. Adopting our framework, we study the stability of two algorithms, namely LASSO and Dantzig selector. We demonstrate that for a given stability parameter (noise sensitivity), there exits a minimum undersampling ratio above which the recovery algorithms are guaranteed to be stable.

References
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Index Terms

Computer Science
Information Sciences

Keywords

Compressed Sensing Constrained Minimal Singular Value Stability Analysis Convex Algorithms Undersampling Analysis