Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications
As major components of the random matrix theory, Gaussian random matrices have been playing an important role in many fields, because they are both unitary invariant and have independent entries and can be used as models for multivariate data or multivariate phenomena. Tail bounds for eigenvalues of...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1456713 |
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| _version_ | 1832549061127831552 |
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| author | Xianjie Gao Mingliang Zhang Jinming Luo |
| author_facet | Xianjie Gao Mingliang Zhang Jinming Luo |
| author_sort | Xianjie Gao |
| collection | DOAJ |
| description | As major components of the random matrix theory, Gaussian random matrices have been playing an important role in many fields, because they are both unitary invariant and have independent entries and can be used as models for multivariate data or multivariate phenomena. Tail bounds for eigenvalues of Gaussian random matrices are one of the hot study problems. In this paper, we present tail and expectation bounds for the ℓ1 norm of Gaussian random matrices, respectively. Moreover, the tail and expectation bounds for the ℓ1 norm of the Gaussian Wigner matrix are calculated based on the resulting bounds. Compared with existing results, our results are more suitable for the high-dimensional matrix case. Finally, we study the tail bounds for the parameter vector of some existing regularization algorithms. |
| format | Article |
| id | doaj-art-cd124a87d0cc45b9afb3147e4320e03b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-cd124a87d0cc45b9afb3147e4320e03b2025-02-03T06:12:24ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1456713Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with ApplicationsXianjie Gao0Mingliang Zhang1Jinming Luo2Department of Basic SciencesSchool of Mathematics and StatisticsSchool of Mathematical SciencesAs major components of the random matrix theory, Gaussian random matrices have been playing an important role in many fields, because they are both unitary invariant and have independent entries and can be used as models for multivariate data or multivariate phenomena. Tail bounds for eigenvalues of Gaussian random matrices are one of the hot study problems. In this paper, we present tail and expectation bounds for the ℓ1 norm of Gaussian random matrices, respectively. Moreover, the tail and expectation bounds for the ℓ1 norm of the Gaussian Wigner matrix are calculated based on the resulting bounds. Compared with existing results, our results are more suitable for the high-dimensional matrix case. Finally, we study the tail bounds for the parameter vector of some existing regularization algorithms.http://dx.doi.org/10.1155/2022/1456713 |
| spellingShingle | Xianjie Gao Mingliang Zhang Jinming Luo Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications Journal of Mathematics |
| title | Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications |
| title_full | Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications |
| title_fullStr | Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications |
| title_full_unstemmed | Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications |
| title_short | Tail Bounds for ℓ1 Norm of Gaussian Random Matrices with Applications |
| title_sort | tail bounds for l1 norm of gaussian random matrices with applications |
| url | http://dx.doi.org/10.1155/2022/1456713 |
| work_keys_str_mv | AT xianjiegao tailboundsforl1normofgaussianrandommatriceswithapplications AT mingliangzhang tailboundsforl1normofgaussianrandommatriceswithapplications AT jinmingluo tailboundsforl1normofgaussianrandommatriceswithapplications |