Quadratic hyper-surface kernel-free large margin distribution machine-based regression and its least-square form

Abstract ε -Support vector regression ( ε -SVR) is a powerful machine learning approach that focuses on minimizing the margin, which represents the tolerance range between predicted and actual values. However, recent theoretical studies have highlighted that simply minimizing structural risk does not necessarily result in well margin distribution. Instead, it has been shown that the distribution of margins plays a more crucial role in achieving better generalization performance. Furthermore, the kernel-free technique offers a significant advantage as it effectively reduces the overall running time and simplifies the parameter selection process compared to the kernel trick. Based on existing kernel-free regression methods, we present two efficient and robust approaches named quadratic hyper-surface kernel-free large margin distribution machine-based regression (QLDMR) and quadratic hyper-surface kernel-free least squares large margin distribution machine-based regression (QLSLDMR). The QLDMR optimizes the margin distribution by considering both ε -insensitive loss and quadratic loss function similar to the large-margin distribution machine-based regression (LDMR). QLSLDMR aims to reduce the cost of the computing process of QLDMR, which transforms inequality constraints into an equality constraint inspired by least squares support vector machines (LSSVR). Both models combined the spirit of optimal margin distribution with kernel-free technique and after simplification are convex so that they can be solved by some classical methods. Experimental results demonstrate the superiority of the optimal margin distribution combined with the kernel-free technique in robustness, generalization, and efficiency.