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| The posterior selection method for hyperparameters in regularized least squares method |
| YanxinZhang1,JingChen1,2,YawenMao1,QuanminZhu3 |
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| (1 School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China;2 The Science and Technology on Near-Surface Detection Laboratory, Wuxi 214122, Jiangsu, China;3 Department of Engineering Design and Mathematics, University of the West of England, Bristol BS161QY, UK) |
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| 摘要: |
| The selection of hyperparameters in regularized least squares plays an important role in large-scale system identification. The
traditional methods for selecting hyperparameters are based on experience or marginal likelihood maximization method, which
are inaccurate or computationally expensive. In this paper, two posterior methods are proposed to select hyperparameters
based on different prior knowledge (constraints), which can obtain the optimal hyperparameters using the optimization theory.
Moreover, we also give the theoretical optimal constraints, and verify its effectiveness. Numerical simulation shows that the
hyperparameters and parameter vector estimate obtained by the proposed methods are the optimal ones. |
| 关键词: Regularization method · Hyperparameter · System identification · Least squares algorithm |
| DOI：https://doi.org/10.1007/s11768-024-00213-x |
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| 基金项目: |
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| The posterior selection method for hyperparameters in regularized least squares method |
| Yanxin Zhang1,Jing Chen1,2,Yawen Mao1,Quanmin Zhu3 |
| (1 School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China;2 The Science and Technology on Near-Surface Detection Laboratory, Wuxi 214122, Jiangsu, China;3 Department of Engineering Design and Mathematics, University of the West of England, Bristol BS161QY, UK) |
| Abstract: |
| The selection of hyperparameters in regularized least squares plays an important role in large-scale system identification. The
traditional methods for selecting hyperparameters are based on experience or marginal likelihood maximization method, which
are inaccurate or computationally expensive. In this paper, two posterior methods are proposed to select hyperparameters
based on different prior knowledge (constraints), which can obtain the optimal hyperparameters using the optimization theory.
Moreover, we also give the theoretical optimal constraints, and verify its effectiveness. Numerical simulation shows that the
hyperparameters and parameter vector estimate obtained by the proposed methods are the optimal ones. |
| Key words: Regularization method · Hyperparameter · System identification · Least squares algorithm |
