L 0-regularization for high-dimensional regression with corrupted data
Corrupted data appears widely in many contemporary applications including voting behavior, high-throughput sequencing and sensor networks. In this article, we consider the sparse modeling via L 0 -regularization under the framework of high-dimensional measurement error models. By utilizing the techn...
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| Vydáno v: | Communications in statistics. Theory and methods Ročník 53; číslo 1; s. 215 - 231 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Taylor & Francis
02.01.2024
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| ISSN: | 0361-0926, 1532-415X |
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| Abstract | Corrupted data appears widely in many contemporary applications including voting behavior, high-throughput sequencing and sensor networks. In this article, we consider the sparse modeling via L
0
-regularization under the framework of high-dimensional measurement error models. By utilizing the techniques of the nearest positive semi-definite matrix projection, the resulting regularization problem can be efficiently solved through a polynomial algorithm. Under some interpretable conditions, we prove that the proposed estimator can enjoy comprehensive statistical properties including the model selection consistency and the oracle inequalities. In particular, the nonoptimality of the logarithmic factor of dimensionality will be showed in the oracle inequalities. We demonstrate the effectiveness of the proposed method by simulation studies. |
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| AbstractList | Corrupted data appears widely in many contemporary applications including voting behavior, high-throughput sequencing and sensor networks. In this article, we consider the sparse modeling via L
0
-regularization under the framework of high-dimensional measurement error models. By utilizing the techniques of the nearest positive semi-definite matrix projection, the resulting regularization problem can be efficiently solved through a polynomial algorithm. Under some interpretable conditions, we prove that the proposed estimator can enjoy comprehensive statistical properties including the model selection consistency and the oracle inequalities. In particular, the nonoptimality of the logarithmic factor of dimensionality will be showed in the oracle inequalities. We demonstrate the effectiveness of the proposed method by simulation studies. |
| Author | Zhao, Ni Zhang, Jie Li, Yang Zheng, Zemin |
| Author_xml | – sequence: 1 givenname: Jie surname: Zhang fullname: Zhang, Jie organization: International Institute of Finance, School of Management, University of Science and Technology of China – sequence: 2 givenname: Yang surname: Li fullname: Li, Yang organization: International Institute of Finance, School of Management, University of Science and Technology of China – sequence: 3 givenname: Ni surname: Zhao fullname: Zhao, Ni organization: School of Mathematics and Physics Sciences, Anhui Jianzhu University – sequence: 4 givenname: Zemin surname: Zheng fullname: Zheng, Zemin organization: International Institute of Finance, School of Management, University of Science and Technology of China |
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| Cites_doi | 10.3150/09-BEJ205 10.1214/10-AOS793 10.1214/15-AOS1388 10.1093/biomet/ast047 10.1214/12-IMSCOLL920 10.1214/16-AOS1527 10.1214/009053606000001523 10.1111/rssb.12037 10.1214/08-AOS620 10.1007/s11222-010-9219-7 10.1016/j.csda.2018.04.009 10.1111/j.2517-6161.1996.tb02080.x 10.1016/j.acha.2014.10.001 10.1214/12-AOS1018 10.1198/016214501753382273 10.1073/pnas.2014241117 |
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| References | e_1_3_2_9_1 e_1_3_2_17_1 e_1_3_2_18_1 e_1_3_2_7_1 Sørensen Ø. (e_1_3_2_16_1) 2015; 25 Huang J. (e_1_3_2_10_1) 2018; 19 e_1_3_2_2_1 e_1_3_2_20_1 e_1_3_2_21_1 e_1_3_2_11_1 e_1_3_2_22_1 e_1_3_2_6_1 e_1_3_2_12_1 e_1_3_2_13_1 e_1_3_2_4_1 e_1_3_2_14_1 e_1_3_2_3_1 e_1_3_2_15_1 Ruppert R. D. (e_1_3_2_5_1) 1995 Fan J. (e_1_3_2_8_1) 2010; 20 Zhang C.-H. (e_1_3_2_19_1) 2012; 27 |
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| SubjectTerms | Measurement errors model selection nearest positive semi-definite matrix projection polynomial algorithm regularization |
| Title | L 0-regularization for high-dimensional regression with corrupted data |
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