论文标题
Stein的稳态扩散近似方法
Stein's method for steady-state diffusion approximation in Wasserstein distance
论文作者
论文摘要
我们提供了一个一般的稳态扩散近似结果，该结果界定了可逆度量的扩散过程$μ$之间的瓦斯汀距离与近似Markov链的度量$ν$之间的界限。由于对Stein方法的一种新方法的概括，我们的结果得到了独立的兴趣。作为应用程序，我们研究了在$ k $ neart的邻居图上随机步行的不变度量，为机器学习社区提供了定量答案。
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $μ$ of a diffusion process and the measure $ν$ of an approximating Markov chain. Our result is obtained thanks to a generalization of a new approach to Stein's method which may be of independent interest. As an application, we study the invariant measure of a random walk on a $k$-nearest neighbors graph, providing a quantitative answer to a problem of interest to the machine learning community.
