论文标题
切成薄片的瓦斯林过程的分布收敛
Distributional Convergence of the Sliced Wasserstein Process
论文作者
论文摘要
在高维环境中，由计算机局势距离的统计和计算挑战的激励，机器学习研究人员根据计算距离的计算距离定义了经过修改的Wasserstein距离。如何汇总这些投影距离（平均随机抽样，最大化）的不同选择会导致不同的距离，需要不同的统计分析。我们定义了\ emph {切成薄片的瓦斯汀过程}，这是一个由经验剂量剂量的经验剂量概率指标与所有一维子空间的投影之间定义的随机过程，并证明了此过程的均匀分布限制定理。结果，我们获得了一个统一的框架，在该框架中，基于一维预测，所有Wasserstein距离都证明了分布极限结果。我们在以前未知分布限制的许多示例上说明了这些结果。
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between one-dimensional projections of the measures. Different choices of how to aggregate these projected distances (averaging, random sampling, maximizing) give rise to different distances, requiring different statistical analyses. We define the \emph{Sliced Wasserstein Process}, a stochastic process defined by the empirical Wasserstein distance between projections of empirical probability measures to all one-dimensional subspaces, and prove a uniform distributional limit theorem for this process. As a result, we obtain a unified framework in which to prove distributional limit results for all Wasserstein distances based on one-dimensional projections. We illustrate these results on a number of examples where no distributional limits were previously known.
