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Support vector regression with imprecise observations based on Huber loss function
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AI
DOI：10.1080/03610918.2026.2643718.png)
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Abstract
En 中文
Support vector regression (SVR) and support vector machines (SVM) are learning machines with excellent generalization performance. Classical statistical learning methods assume that the data are exact, but in real life, most of the data are imprecise and suffer from the disadvantage of low data quality. Uncertainty theory and uncertain statistics give a good way of dealing with imprecise data. In the framework of uncertainty theory, a method based on the optimally separated hyperplanes is proposed to solve the original uncertain SVR by using slack variables. Also, to enhance the generalization performance of the model, Huber loss function which can better handle outliers is introduced and Huber support vector regression (Huber-SVR) under imprecise observations is proposed. After Lagrange multiplier and Lagrange dual method, the optimization algorithm that can be done by gradient descent is derived. In addition, the cross-validation (CV) method is used to find optimal hyperparameters, and the predicted values are given while the root mean square error (RMSE) is used to measure the effect of the model. Finally, a numerical example is given to illustrate the excellent performance of Huber-SVR based on imprecise observations.
Keywords:
Huber loss function
Support vector regression
Uncertain variables
Uncertainty theory
Journal
C
IF:
0.8
Papers:
213
Citations:
4.7K