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

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International Conference on Current Trends in Advanced Computing (ICCTAC-2015)
© 2015 by IJCA Journal
ICCTAC 2015 - Number 2
Year of Publication: 2015
Authors:
Oliver James

Oliver James. Article: Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices. International Conference on Current Trends in Advanced Computing (ICCTAC-2015) ICCTAC 2015(2):1-5, May 2015. Full text available. BibTeX

@article{key:article,
	author = {Oliver James},
	title = {Article: Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices},
	journal = {International Conference on Current Trends in Advanced Computing (ICCTAC-2015)},
	year = {2015},
	volume = {ICCTAC 2015},
	number = {2},
	pages = {1-5},
	month = {May},
	note = {Full text available}
}

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.

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