Sharp Bounds for Max-sliced Wasserstein Distances

IF 2.5 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Foundations of Computational Mathematics Pub Date : 2025-01-22 DOI:10.1007/s10208-025-09690-1

March T. Boedihardjo

引用次数: 0

Abstract

We obtain essentially matching upper and lower bounds for the expected max-sliced 1-Wasserstein distance between a probability measure on a separable Hilbert space and its empirical distribution from n samples. By proving a Banach space version of this result, we also obtain an upper bound, that is sharp up to a log factor, for the expected max-sliced 2-Wasserstein distance between a symmetric probability measure \(\mu \) on a Euclidean space and its symmetrized empirical distribution in terms of the operator norm of the covariance matrix of \(\mu \) and the diameter of the support of \(\mu \).

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最大切片Wasserstein距离的尖锐界

我们从n个样本中获得可分离Hilbert空间上的概率测度与其经验分布之间的期望最大切片1-Wasserstein距离的基本匹配上界和下界。通过证明这一结果的Banach空间版本，我们也得到了欧几里德空间上对称概率测度\(\mu \)与其对称经验分布（以协方差矩阵\(\mu \)的算子范数和\(\mu \)的支撑直径表示）之间的期望最大切2-Wasserstein距离的上界，该上界精确到一个对数因子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Computational Mathematics 数学-计算机：理论方法

CiteScore

6.90

自引率

3.30%

发文量

审稿时长

>12 weeks

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