Research Based on High-Dimensional Fused Lasso Partially Linear Model
In this paper, a partially linear model based on the fused lasso method is proposed to solve the problem of high correlation between adjacent variables, and then the idea of the two-stage estimation method is used to study the solution of this model. Firstly, the non-parametric part of the partially...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2726 |
| _version_ | 1797593675447926784 |
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| author | Aifen Feng Jingya Fan Zhengfen Jin Mengmeng Zhao Xiaogai Chang |
| author_facet | Aifen Feng Jingya Fan Zhengfen Jin Mengmeng Zhao Xiaogai Chang |
| author_sort | Aifen Feng |
| collection | DOAJ |
| description | In this paper, a partially linear model based on the fused lasso method is proposed to solve the problem of high correlation between adjacent variables, and then the idea of the two-stage estimation method is used to study the solution of this model. Firstly, the non-parametric part of the partially linear model is estimated using the kernel function method and transforming the semiparametric model into a parametric model. Secondly, the fused lasso regularization term is introduced into the model to construct the least squares parameter estimation based on the fused lasso penalty. Then, due to the non-smooth terms of the model, the subproblems may not have closed-form solutions, so the linearized alternating direction multiplier method (LADMM) is used to solve the model, and the convergence of the algorithm and the asymptotic properties of the model are analyzed. Finally, the applicability of this model was demonstrated through two types of simulation data and practical problems in predicting worker wages. |
| first_indexed | 2024-03-11T02:11:42Z |
| format | Article |
| id | doaj.art-c8c3e4f1ad8c43fa98b8e1bf8a6c6857 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T02:11:42Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c8c3e4f1ad8c43fa98b8e1bf8a6c68572023-11-18T11:28:55ZengMDPI AGMathematics2227-73902023-06-011112272610.3390/math11122726Research Based on High-Dimensional Fused Lasso Partially Linear ModelAifen Feng0Jingya Fan1Zhengfen Jin2Mengmeng Zhao3Xiaogai Chang4School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, ChinaIn this paper, a partially linear model based on the fused lasso method is proposed to solve the problem of high correlation between adjacent variables, and then the idea of the two-stage estimation method is used to study the solution of this model. Firstly, the non-parametric part of the partially linear model is estimated using the kernel function method and transforming the semiparametric model into a parametric model. Secondly, the fused lasso regularization term is introduced into the model to construct the least squares parameter estimation based on the fused lasso penalty. Then, due to the non-smooth terms of the model, the subproblems may not have closed-form solutions, so the linearized alternating direction multiplier method (LADMM) is used to solve the model, and the convergence of the algorithm and the asymptotic properties of the model are analyzed. Finally, the applicability of this model was demonstrated through two types of simulation data and practical problems in predicting worker wages.https://www.mdpi.com/2227-7390/11/12/2726partially linear modelfused lassokernel estimationLADMM |
| spellingShingle | Aifen Feng Jingya Fan Zhengfen Jin Mengmeng Zhao Xiaogai Chang Research Based on High-Dimensional Fused Lasso Partially Linear Model Mathematics partially linear model fused lasso kernel estimation LADMM |
| title | Research Based on High-Dimensional Fused Lasso Partially Linear Model |
| title_full | Research Based on High-Dimensional Fused Lasso Partially Linear Model |
| title_fullStr | Research Based on High-Dimensional Fused Lasso Partially Linear Model |
| title_full_unstemmed | Research Based on High-Dimensional Fused Lasso Partially Linear Model |
| title_short | Research Based on High-Dimensional Fused Lasso Partially Linear Model |
| title_sort | research based on high dimensional fused lasso partially linear model |
| topic | partially linear model fused lasso kernel estimation LADMM |
| url | https://www.mdpi.com/2227-7390/11/12/2726 |
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