enhancing kernel ridge regression models with compact support wendland functions

Radial basis functions (rbfs) have gained significant attention in various machine learning applications, including regression modeling, due to their ability to approximate complex, nonlinear relationships. rbfs offer a flexible approach to capturing intricate dependencies between input features and the target variable, making them particularly useful in high-dimensional and nonparametric settings. this paper investigates the use of a specific class of compactly supported rbfs, known as wendland functions, within the framework of kernel ridge regression (krr). we discuss their theoretical advantages—such as sparsity enforcement and computational efficiency as well as practical challenges, including parameter selection and scalability. a comprehensive overview of rbfs is provided, along with their mathematical formulation and a comparison of different rbf kernels in terms of smoothness and locality. we detail the integration of wendland functions into krr models, emphasizing their suitability for problems requiring robustness and interpretability. through extensive simulation studies, the performance of the proposed approach is evaluated against conventional rbf kernels and other widely used regression techniques. our results demonstrate that wendland-based krr achieves competitive accuracy while offering improved stability in the presence of noise and outliers. furthermore, real-world case studies illustrate the effectiveness of wendland functions in handling datasets with high collinearity, where traditional kernels often struggle. the practical implications of our findings are discussed, along with guidelines for implementation and potential extensions to large-scale or sparse data scenarios. this work contributes to the growing body of research on interpretable and efficient kernel methods, providing insights for both theoretical and applied machine learning practitioners.