Adaptive Lasso based on regularized weight and its application in variable selection for regression

Jialu Lin; Yili Zhang; Mei Xiong; Hanyan Huang

doi:10.1117/12.2656938

13 January 2023 Adaptive Lasso based on regularized weight and its application in variable selection for regression

Jialu Lin, Yili Zhang, Mei Xiong, Hanyan Huang

Proceedings Volume 12510, International Conference on Statistics, Data Science, and Computational Intelligence (CSDSCI 2022); 125100Q (2023) https://doi.org/10.1117/12.2656938
Event: International Conference on Statistics, Data Science, and Computational Intelligence (CSDSCI 2022), 2022, Qingdao, China

Abstract

Regression analysis has always been a popular method of data analysis because of its good interpretation of causality. Variable selection can effectively reduce the complexity of the model and improve the modeling accuracy. As a classical variable selection method, Lasso can realize variable selection and parameter estimation at the same time, but the optimal regularized parameters may lead to inconsistent variable selection results. Adaptive Lasso improves the consistency of variable selection by adopting the least square estimation of coefficients as the weight correction regulars. However, the design matrix of least square estimation is not invertible for ill-conditioned data. In this paper, a modified Adaptive Lasso based on regularization weights and its ADMM regularization algorithm are proposed, taking the Ridge estimation of coefficients as the weight parameters to modify the Lasso regularization terms. Numerical experiments with sparse coefficients, large coefficients, grouping effects, and polynomial regression simulation experiments are carried out to compare the proposed method with Lasso, Adaptive Lasso, Elastic net and the Adaptive Elastic net. The results show that the proposed Adaptive Lasso based on regularized weight has higher prediction accuracy and more sparse variable selection, which effectively improves the accuracy of regression model.

Citation Download Citation

Jialu Lin, Yili Zhang, Mei Xiong, and Hanyan Huang "Adaptive Lasso based on regularized weight and its application in variable selection for regression", Proc. SPIE 12510, International Conference on Statistics, Data Science, and Computational Intelligence (CSDSCI 2022), 125100Q (13 January 2023); https://doi.org/10.1117/12.2656938

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KEYWORDS

Feature selection

Statistical analysis

Computer simulations

Performance modeling

Error analysis

Systems modeling

Data analysis

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