Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model
This paper mainly studies the application of the linearized alternating direction method of multiplier (LADMM) and the accelerated symmetric linearized alternating direction method of multipliers (As-LADMM) for high dimensional partially linear models. First, we construct a <inline-formula><...
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/19/4220 |
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| author | Aifen Feng Xiaogai Chang Jingya Fan Zhengfen Jin |
| author_facet | Aifen Feng Xiaogai Chang Jingya Fan Zhengfen Jin |
| author_sort | Aifen Feng |
| collection | DOAJ |
| description | This paper mainly studies the application of the linearized alternating direction method of multiplier (LADMM) and the accelerated symmetric linearized alternating direction method of multipliers (As-LADMM) for high dimensional partially linear models. First, we construct a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>1</mn></msub></semantics></math></inline-formula>-penalty for the least squares estimation of partially linear models under constrained contours. Next, we design the LADMM algorithm to solve the model, in which the linearization technique is introduced to linearize one of the subproblems to obtain an approximate solution. Furthermore, we add the appropriate acceleration techniques to form the As-LADMM algorithm and to solve the model. Then numerical simulations are conducted to compare and analyze the effectiveness of the algorithms. It indicates that the As-LADMM algorithm is better than the LADMM algorithm from the view of the mean squared error, the number of iterations and the running time of the algorithm. Finally, we apply them to the practical problem of predicting Boston housing price data analysis. This indicates that the loss between the predicted and actual values is relatively small, and the As-LADMM algorithm has a good prediction effect. |
| first_indexed | 2024-03-10T21:40:16Z |
| format | Article |
| id | doaj.art-ea31113d6a3248bf9bdb034d669b6fac |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:40:16Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
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| spelling | doaj.art-ea31113d6a3248bf9bdb034d669b6fac2023-11-19T14:45:00ZengMDPI AGMathematics2227-73902023-10-011119422010.3390/math11194220Application of LADMM and As-LADMM for a High-Dimensional Partially Linear ModelAifen Feng0Xiaogai Chang1Jingya Fan2Zhengfen Jin3School 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, ChinaThis paper mainly studies the application of the linearized alternating direction method of multiplier (LADMM) and the accelerated symmetric linearized alternating direction method of multipliers (As-LADMM) for high dimensional partially linear models. First, we construct a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>1</mn></msub></semantics></math></inline-formula>-penalty for the least squares estimation of partially linear models under constrained contours. Next, we design the LADMM algorithm to solve the model, in which the linearization technique is introduced to linearize one of the subproblems to obtain an approximate solution. Furthermore, we add the appropriate acceleration techniques to form the As-LADMM algorithm and to solve the model. Then numerical simulations are conducted to compare and analyze the effectiveness of the algorithms. It indicates that the As-LADMM algorithm is better than the LADMM algorithm from the view of the mean squared error, the number of iterations and the running time of the algorithm. Finally, we apply them to the practical problem of predicting Boston housing price data analysis. This indicates that the loss between the predicted and actual values is relatively small, and the As-LADMM algorithm has a good prediction effect.https://www.mdpi.com/2227-7390/11/19/4220partially linear model<i>l</i><sub>1</sub>-penalty estimationLADMMAs-LADMM |
| spellingShingle | Aifen Feng Xiaogai Chang Jingya Fan Zhengfen Jin Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model Mathematics partially linear model <i>l</i><sub>1</sub>-penalty estimation LADMM As-LADMM |
| title | Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model |
| title_full | Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model |
| title_fullStr | Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model |
| title_full_unstemmed | Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model |
| title_short | Application of LADMM and As-LADMM for a High-Dimensional Partially Linear Model |
| title_sort | application of ladmm and as ladmm for a high dimensional partially linear model |
| topic | partially linear model <i>l</i><sub>1</sub>-penalty estimation LADMM As-LADMM |
| url | https://www.mdpi.com/2227-7390/11/19/4220 |
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