Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression
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 cond...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/946241 |
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| _version_ | 1832550710884958208 |
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| author | Shiqing Wang Yan Shi Limin Su |
| author_facet | Shiqing Wang Yan Shi Limin Su |
| author_sort | Shiqing Wang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-97a5f80b2b0d4040a8edd70d5d4e735f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-97a5f80b2b0d4040a8edd70d5d4e735f2025-02-03T06:06:04ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/946241946241Weaker Regularity Conditions and Sparse Recovery in High-Dimensional RegressionShiqing Wang0Yan Shi1Limin Su2College of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450045, ChinaInstitute of Environmental and Municipal Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450045, ChinaCollege of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450045, ChinaRegularity 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.http://dx.doi.org/10.1155/2014/946241 |
| spellingShingle | Shiqing Wang Yan Shi Limin Su Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression Journal of Applied Mathematics |
| title | Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression |
| title_full | Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression |
| title_fullStr | Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression |
| title_full_unstemmed | Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression |
| title_short | Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression |
| title_sort | weaker regularity conditions and sparse recovery in high dimensional regression |
| url | http://dx.doi.org/10.1155/2014/946241 |
| work_keys_str_mv | AT shiqingwang weakerregularityconditionsandsparserecoveryinhighdimensionalregression AT yanshi weakerregularityconditionsandsparserecoveryinhighdimensionalregression AT liminsu weakerregularityconditionsandsparserecoveryinhighdimensionalregression |