Uniform convergence for Gaussian kernel ridge regression
It provides theoretical justification for using Gaussian KRR in nonparametric regression, addressing a gap in understanding for researchers in machine learning theory.
This paper tackles the problem of establishing convergence rates for Gaussian kernel ridge regression with fixed hyperparameters, proving the first polynomial rates in both uniform and L²-norms, which were previously unknown or sub-polynomial.
This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical understanding of KRR with the Gaussian kernel, where no such rates were previously known. In addition, we prove a polynomial $L^{2}$-convergence rate in the case, where the Gaussian kernel's width parameter is fixed. This also contributes to the broader understanding of smooth kernels, for which previously only sub-polynomial $L^{2}$-rates were known in similar settings. Together, these results provide new theoretical justification for the use of Gaussian KRR with fixed hyperparameters in nonparametric regression.