On Regularization Based Twin Support Vector Regression with Huber Loss.

Area of Science:

• Machine Learning
• Computational Statistics
• Data Mining

Background:

• Traditional Twin Support Vector Regression (TSVR) with epsilon-insensitive loss struggles with noisy data and outliers.
• Huber loss offers improved robustness against noise and outliers compared to Gaussian loss.
• Existing Huber-based TSVR (HN-TSVR) methods suffer from singularity issues, degrading model performance.

Purpose of the Study:

• To propose a novel Regularized Huber Twin Support Vector Regression (RHN-TSVR) model.
• To address the singularity problem inherent in HN-TSVR.
• To enhance the model's capability in handling noise and outliers while maintaining convexity and well-posedness.

Main Methods:

• Developed a regularized version of HN-TSVR using the structured risk minimization principle.
• Ensured the proposed RHN-TSVR model is convex and well-posed.
• Conducted experiments on artificial datasets with uniform, Gaussian, and Laplacian noise, and on benchmark real-world datasets.

Main Results:

• The proposed RHN-TSVR model effectively handles noise and outliers.
• RHN-TSVR successfully avoids the singularity issue present in HN-TSVR.
• Experiments demonstrated that RHN-TSVR outperforms Support Vector Regression, TSVR, epsilon-asymmetric Huber SVR, and HN-TSVR in prediction accuracy.
• Performance was validated across datasets with varying noise levels (0%, 5%, 10%).

Conclusions:

• The novel RHN-TSVR model provides a robust and effective solution for regression tasks with noisy data.
• RHN-TSVR offers improved prediction performance and stability compared to existing methods.
• The proposed approach is well-suited for real-world applications where data often contains noise and outliers.