标题： Sliced和标准$1$- Wasserstein距离之间的精确比较 显示英文标题

标题： Sharp comparisons between sliced and standard $1$-Wasserstein distances

摘要： 切片Wasserstein距离在实践中被广泛使用，作为高维情况下Wasserstein距离的计算效率更高的替代方法。 在本文中，受这种替代方法理论基础的启发，我们证明了切片$1$-Wasserstein距离与$1$-Wasserstein距离之间的定量估计。 我们构建了一个具体例子来展示估计中的指数是精确的。 我们还提供了对切片涉及投影到$k$-平面而非仅直线的情况的一般分析。 显示英文摘要

摘要： Sliced Wasserstein distances are widely used in practice as a computationally efficient alternative to Wasserstein distances in high dimensions. In this paper, motivated by theoretical foundations of this alternative, we prove quantitative estimates between the sliced $1$-Wasserstein distance and the $1$-Wasserstein distance. We construct a concrete example to demonstrate the exponents in the estimate is sharp. We also provide a general analysis for the case where slicing involves projections onto $k$-planes and not just lines.