On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces
This work addresses theoretical convergence guarantees for kernel regression in machine learning, but it appears incremental as it builds on existing RKHS frameworks with minimalistic assumptions.
The paper analyzes the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS), proving error estimates in the RKHS norm and new results on uniform convergence for Lipschitz and Hölder continuous kernels.
We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the input data. We first prove error estimates in the kernel's RKHS norm. This leads us to new results concerning uniform convergence of kernel regression on compact domains. For Lipschitz continuous and Hölder continuous kernels, we prove convergence rates.