A Sparse L∞-Norm Regularized Least Squares Support Vector Regression

Although Least Squares Support Vector Regression (LSSVR) reduces the hyperparameter space to two, it sacrifices sparsity, causing all training samples to become support vectors and increasing storage costs. In contrast, standard Support Vector Regression (SVR) preserves sparsity but requires tuning three highly coupled hyperparameters, leading to higher computational burden. To address these limitations, this paper proposes a sparse L∞-norm regularized least squares SVR framework that incorporates the infinity norm of approximation errors into both the objective function and inequality constraints. The resulting optimization problem minimizes model complexity while controlling the maximum prediction deviation through a single slack variable, thereby transforming the conventional three-hyperparameter SVR tuning task into a two-parameter problem involving only the regularization coefficient and kernel width. This formulation restores sparsity by enabling a compact support vector set, while preserving the stability and convexity advantages of LSSVR. Experiments on both static and dynamic datasets demonstrate that the proposed method consistently achieves higher predictive accuracy and improved robustness compared with standard SVR and LSSVR. These results indicate that the proposed L∞-norm regularized framework offers a mathematically principled and computationally efficient alternative for sparse, robust, and scalable regression modeling.