Improved elastic net algorithm: A novel parameter identification method for grey system models

Qinzi Xiao; Mingyun Gao; Congjun Rao; Qinzi Xiao; Mingyun Gao; Congjun Rao

doi:10.3934/math.20251338

AIMS Mathematics

2025, Volume 10, Issue 12: 30507-30527. doi: 10.3934/math.20251338

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Research article Topical Sections

Improved elastic net algorithm: A novel parameter identification method for grey system models

1.
School of Management, Wuhan Institute of Technology, Wuhan, 430205, China
2.
Research Center for Coordinated Development of Enterprises and Environment, Wuhan Institute of Technology, Wuhan 430205, China
3.
School of Information Management, Central China Normal University, Wuhan, 430079, China
4.
Data Governance and Intelligent Decision Research Center, Central China Normal University, Wuhan, 430079, China
5.
School of Mathematics and Statistics, Wuhan University of Technology, Wuhan, 430070, China

Received: 29 October 2025 Revised: 13 December 2025 Accepted: 19 December 2025 Published: 25 December 2025
MSC : 60G70, 62G32, 65C05

Grey system model is widely employed to address uncertainties in systems characterized by small samples and poor information. In grey modeling, multicollinearity among variables often leads to ill-conditioned estimation, which undermines model stability. While the elastic net regularization method mitigates this issue by combining ridge and lasso regression, it still lacks the oracle property and adaptive group effect. This limitation restricts the applicability of grey models in handling larger datasets and capturing more flexible variable relationships. To overcome these shortcomings, this paper proposes an improved elastic net algorithm within the framework of a grey multivariate power model. The improvement in this paper aims to integrate adaptive lasso regression and correlation-driven penalty, optimize the weight adjustment mechanism of the penalty term, and enhance the adaptability and robustness of the grey model under its specific structure. Theoretically, the proposed algorithm is demonstrated to possess both the oracle property and adaptive group effect. Through an empirical analysis of the annual average of fine particulate matter (PM_2.5) concentrations in Beijing and Shanghai, China, with a comparison to parameter estimation results based on the least squares method and traditional regularization methods. The results show that the improved elastic net algorithm performs well in handling multicollinearity data, obtains more stable and accurate parameter estimates, and effectively improves the goodness of fit and prediction accuracy of the grey prediction model. This research provides a more powerful and reliable new approach for parameter identification of grey models.
- grey system,
- GM(1,N) power model,
- parameter identification,
- elastic net,
- PM_2.5 prediction
Citation: Qinzi Xiao, Mingyun Gao, Congjun Rao. Improved elastic net algorithm: A novel parameter identification method for grey system models[J]. AIMS Mathematics, 2025, 10(12): 30507-30527. doi: 10.3934/math.20251338

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Abstract

Grey system model is widely employed to address uncertainties in systems characterized by small samples and poor information. In grey modeling, multicollinearity among variables often leads to ill-conditioned estimation, which undermines model stability. While the elastic net regularization method mitigates this issue by combining ridge and lasso regression, it still lacks the oracle property and adaptive group effect. This limitation restricts the applicability of grey models in handling larger datasets and capturing more flexible variable relationships. To overcome these shortcomings, this paper proposes an improved elastic net algorithm within the framework of a grey multivariate power model. The improvement in this paper aims to integrate adaptive lasso regression and correlation-driven penalty, optimize the weight adjustment mechanism of the penalty term, and enhance the adaptability and robustness of the grey model under its specific structure. Theoretically, the proposed algorithm is demonstrated to possess both the oracle property and adaptive group effect. Through an empirical analysis of the annual average of fine particulate matter (PM_2.5) concentrations in Beijing and Shanghai, China, with a comparison to parameter estimation results based on the least squares method and traditional regularization methods. The results show that the improved elastic net algorithm performs well in handling multicollinearity data, obtains more stable and accurate parameter estimates, and effectively improves the goodness of fit and prediction accuracy of the grey prediction model. This research provides a more powerful and reliable new approach for parameter identification of grey models.

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