论文标题
在对称组上的电源总内核上
On power sum kernels on symmetric groups
论文作者
论文摘要
在本说明中，我们介绍了一个“功率和”内核家族和对称组上的相应高斯流程$ \ mathrm {s} _n $。这样的过程是双重不景气的：$ \ mathrm {s} _n $对双方的动作不会改变其有限维分布。我们表明，可以有效地计算功率总内核的值，并且我们还提出了一种具有多项式计算复杂性的相应高斯过程的近似采样方法。通过这样做，我们提供了使用引入的内核家族以及各个过程进行统计建模和机器学习所需的工具。
In this note, we introduce a family of "power sum" kernels and the corresponding Gaussian processes on symmetric groups $\mathrm{S}_n$. Such processes are bi-invariant: the action of $\mathrm{S}_n$ on itself from both sides does not change their finite-dimensional distributions. We show that the values of power sum kernels can be efficiently calculated, and we also propose a method enabling approximate sampling of the corresponding Gaussian processes with polynomial computational complexity. By doing this we provide the tools that are required to use the introduced family of kernels and the respective processes for statistical modeling and machine learning.
