  This paper carries out a large dimensional analysis of a variation of kernel
ridge regression that we call \emph{centered kernel ridge regression} (CKRR),
also known in the literature as kernel ridge regression with offset. This
modified technique is obtained by accounting for the bias in the regression
problem resulting in the old kernel ridge regression but with \emph{centered}
kernels. The analysis is carried out under the assumption that the data is
drawn from a Gaussian distribution and heavily relies on tools from random
matrix theory (RMT). Under the regime in which the data dimension and the
training size grow infinitely large with fixed ratio and under some mild
assumptions controlling the data statistics, we show that both the empirical
and the prediction risks converge to a deterministic quantities that describe
in closed form fashion the performance of CKRR in terms of the data statistics
and dimensions. Inspired by this theoretical result, we subsequently build a
consistent estimator of the prediction risk based on the training data which
allows to optimally tune the design parameters. A key insight of the proposed
analysis is the fact that asymptotically a large class of kernels achieve the
same minimum prediction risk. This insight is validated with both synthetic and
real data.
