Optimal Confidence Band for Kernel Gradient Flow Estimator

ArXi:2605.05768v1 Announce Type: cross In this paper, we investigate the supremum-norm generalization error and the uniform inference for a specific class of kernel regression methods, namely the kernel gradient flows. Under the widely adopted capacity-source condition framework in the kernel regression literature, we first establish convergence rates for the supremum norm generalization error of both continuous and discrete kernel gradient flows under the source condition $s>\alpha_0$, where $\alpha_0\in(0,1)$ denotes the embedding index of the kernel function.