  Statistical machine learning plays an important role in modern statistics and
computer science. One main goal of statistical machine learning is to provide
universally consistent algorithms, i.e., the estimator converges in probability
or in some stronger sense to the Bayes risk or to the Bayes decision function.
Kernel methods based on minimizing the regularized risk over a reproducing
kernel Hilbert space (RKHS) belong to these statistical machine learning
methods. It is in general unknown which kernel yields optimal results for a
particular data set or for the unknown probability measure. Hence various
kernel learning methods were proposed to choose the kernel and therefore also
its RKHS in a data adaptive manner. Nevertheless, many practitioners often use
the classical Gaussian RBF kernel or certain Sobolev kernels with good success.
The goal of this short note is to offer one possible theoretical explanation
for this empirical fact.
