Classification is a very important research topic in statist ical machine learning. There are a large amount of literature on various classification methods, ran ging from the very classical distribution-based likelihood approaches such as Fisher linear discriminant analysis (LDA) and logistic regression [3], to the margin-based approaches such as the well-known s upport vector machine (SVM) [1, 2]. Each type of classifiers has their own merits. Recently, Liu a nd his coauthors proposed in [4] the so-called large-margin unified machines (LUMs) which es tablish a unique transition between these two types of classifiers. As noted in [5], SVM may suffer fr om data piling problems in the high-dimension low-sample size (HDLSS) settings, that is, the support vectors will pile up on top of each other at the margin boundaries when projected onto th e normal vector of the separating hyperplane.

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.