Support vector regression (SVR) is a well-established kernel-based method for nonlinear regression. However, standard SVR formulations minimize absolute-error losses, which are not consistent with the scale-free, relative-accuracy criteria prevalent in forecasting and industrial applications, where uncertainty is typically expressed as a percentage. This study proposes a unified SVR framework that incorporates percentage-error loss functions and symmetry constraints. Four specific variants are introduced: ε-SVR with mean absolute percentage error (MAPE), its symmetric kernel extension, least-squares SVR (LS-SVR) with root mean square percentage error (RMSPE), and its symmetric counterpart. Each variant is formulated in primal, Lagrangian, and dual forms using Karush–Kuhn–Tucker analysis. The principal structural finding is that percentage scaling results in sample-dependent box constraints for ε-SVR and a target-weighted diagonal regularization matrix for LS-SVR. In contrast, symmetry modifies only the kernel matrix, leaving the optimization structure unchanged. Convexity and the representer theorem are preserved in all cases. Experiments are conducted on three cross-sectional datasets (Boston Housing, Diabetes, and Energy Efficiency) and a time-series dataset on Victorian electricity demand. Evaluation utilizes three metrics (MAPE, MASE, and MAAPE), 95% bootstrap confidence intervals, and paired Wilcoxon tests, and compares performance against percentage-error-native baselines (weighted-MAE, quantile regression, and log-target SVR), classical ε-SVR, Random Forest, and XGBoost. An additional reflection-based experiment assesses the symmetric-kernel variants. The results demonstrate that optimizing for percentage error consistently improves the targeted metric without adversely affecting absolute-error metrics.
Benavides-Herrera et al. (Thu,) studied this question.