Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression
Joint Authors
Wang, Shiqing
Su, Limin
Shi, Yan
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-07-17
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
Regularity conditions play a pivotal role for sparse recovery in high-dimensional regression.
In this paper, we present a weaker regularity condition and further discuss the relationships with other regularity conditions, such as restricted eigenvalue condition.
We study the behavior of our new condition for design matrices with independent random columns uniformly drawn on the unit sphere.
Moreover, the present paper shows that, under a sparsity scenario, the Lasso estimator and Dantzig selector exhibit similar behavior.
Based on both methods, we derive, in parallel, more precise bounds for the estimation loss and the prediction risk in the linear regression model when the number of variables can be much larger than the sample size.
American Psychological Association (APA)
Wang, Shiqing& Shi, Yan& Su, Limin. 2014. Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-510363
Modern Language Association (MLA)
Wang, Shiqing…[et al.]. Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression. Journal of Applied Mathematics No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-510363
American Medical Association (AMA)
Wang, Shiqing& Shi, Yan& Su, Limin. Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-510363
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-510363