Adaptive RKHS Tikhonov Regularization

Adaptive RKHS Tikhonov regularization focuses on improving the robustness and efficiency of learning methods that operate within Reproducing Kernel Hilbert Spaces (RKHSs). Current research emphasizes developing data-adaptive regularization techniques, often employing novel algorithms like L-curve methods for hyperparameter selection and incorporating fractional RKHS norms to enhance stability. This approach addresses challenges in various applications, including functional regression, kernel adaptive filtering, and learning kernels in nonlocal operators, leading to more accurate and robust models in the face of noisy or limited data.