We study classes of reproducing kernels $K$ on general domains; these are kernels which arise commonly in machine learning models; models based on certain families of reproducing kernel Hilbert spaces. They are the positive definite kernels $K$ with the property that there are countable discrete sample-subsets $S$; i.e., proper subsets $S$ having the property that every function in $\mathscr{H}\left(K\right)$ admits an $S$-sample representation. We give a characterizations of kernels which admit such non-trivial countable discrete sample-sets. A number of applications and concrete kernels are given in the second half of the paper.

中文翻译：

---

使用正定核和相关的二分法进行采样

我们研究了一般域上的复制内核 $K$ 的类；这些是机器学习模型中常见的内核；基于某些可再生核希尔伯特空间系列的模型。它们是具有可数离散样本子集$S$的性质的正定核$K$；即，真子集 $S$ 具有 $\mathscr{H}\left(K\right)$ 中的每个函数都承认 $S$-sample 表示的属性。我们给出了允许这种非平凡可数离散样本集的内核的特征。论文的后半部分给出了一些应用程序和具体的内核。