Advanced Quantile Regression with Pinball Loss: Leveraging Lagrangian Asymmetric-vTwin SVR and Enhanced Model Optimization for Superior Performance

Abstract

This study presents a comparative analysis of three regression models—Lagrangian Asymmetric-vTwin Support Vector Regression (SVR), Standard SVR, and Linear Regression—focusing on their performance in quantile prediction using Pinball Loss. The models are evaluated at different quantiles (α = 0.1, 0.5, and 0.9) and conventional metrics, such as RMSE and MAE. The results reveal that the Lagrangian Asymmetric-vTwin SVR consistently outperforms the other models, providing the lowest Pinball Loss values across all quantiles. Specifically, the Lagrangian Asymmetric-vTwin SVR achieves a Pinball Loss of 0.045 at α = 0.1, 0.029 at α = 0.5, and 0.038 at α = 0.9. In comparison, the Standard SVR shows Pinball Loss values of 0.062, 0.038, and 0.045 for the same quantiles, while Linear Regression yields Pinball Loss values of 0.089, 0.076, and 0.082. In addition to Pinball Loss, the Lagrangian Asymmetric-vTwin SVR also performs better in RMSE and MAE, with values of 0.12 and 0.10, respectively, compared to Standard SVR's 0.18 and 0.14, and Linear Regression's 0.22 and 0.19. Furthermore, the optimal regularization parameter (C) of 1.0 for the Lagrangian Asymmetric-vTwin SVR strikes a balance between model complexity and prediction accuracy, leading to improved training efficiency and faster convergence. These results demonstrate the superior capability of the Lagrangian Asymmetric-vTwin SVR in quantile regression tasks.