Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Condition. (arXiv:2204.07856v2 [math.ST] UPDATED)

We derive minimax adaptive rates for a new, broad class of
Tikhonov-regularized learning problems in Hilbert scales under general source
conditions. Our analysis does not require the regression function to be
contained in the hypothesis class, and most notably does not employ the
conventional \textit{a priori} assumptions on kernel eigendecay. Using the
theory of interpolation, we demonstrate that the spectrum of the Mercer
operator can be inferred in the presence of "tight'' $L^{\infty}$ embeddings of
suitable Hilbert scales. Our analysis …

arxiv capacity least math squares