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Support vector regression with imprecise observations based on ε-Huber loss function
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DOI：10.1080/03610926.2026.2666192.png)
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Abstract
En 中文
Support Vector Regression (SVR) and Support Vector Classification (SVC) are learning methods based on structural risk minimization, known for their excellent generalization ability. Traditional statistical learning methods assume precise data, but in practice, most data are imprecise and of low quality. To address this, Liu Baoding introduced uncertainty theory, which uses uncertain variables to represent imprecise observations. Based on this theory, this paper integrates uncertainty theory with Support Vector Regression to propose an uncertain support vector regression model based on the epsilon-Huber loss function, resulting in the UE-HSVR model, which is more robust to noise and outliers. An equal-step lattice search algorithm is then used to optimize the model parameters. Finally, the performance of the UE-HSVR model is validated using synthetic datasets and Shanghai's air quality data, and compared with Uncertain Huber Support Vector Regression (UHSVR), Uncertain epsilon- Insensitive Support Vector Regression (UE-SVR), and Uncertain Linear Regression (ULinear) models. The results show that the UE-HSVR model has a smaller Root Mean Square Error (RMSE), demonstrating its superior performance. Meanwhile, in order to verify the difference in performance between the models, the nonparametric Friedman test was used, with a p-value of 0.0067, so there is sufficient statistical basis to reject the original hypothesis at a significant level of 0.05, confirming that there is indeed a significant difference in the prediction performance between the different models. In terms of computational performance evaluation, the computational efficiency of the UE-HSVR model is greatly improved compared to the UHSVR model in accomplishing the same task.
Keywords:
Uncertainty theory
uncertain variables
support vector regression
epsilon-Huber loss function
Journal
C
IF:
0.8
Papers:
211
Citations:
0