提出无分布假设下的模糊总变差距离，实现无需先验的两样本检验。
Distribution-free two-sample testing with blurred total variation distance
- 引入模糊总变差距离，放宽传统距离对分布假设的要求。
- 给出无分布假设下的上下界理论保证，适用于高维数据。
- 适合无先验知识的分布比较场景，如隐私保护或未知数据建模。
两样本检验旨在基于来自两个分布的样本判断它们是否相等，但若无法对分布性质做假设，验证分布相等性或提供总变差（TV）距离的紧上界将不可行。本文研究了模糊总变差距离，一种放松了传统TV距离的度量，使其可在无分布假设下进行推断。我们为模糊TV距离提供了分布自由的上下界理论保证，并分析了其在高维情形下的性质。
原文摘要 · Abstract (English)
Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular, certifying equality of distributions, or even providing a tight upper bound on the total variation (TV) distance between the distributions, is impossible to achieve in a distribution-free regime. In this work, we examine the blurred TV distance, a relaxation of TV distance that enables us to perform inference without assumptions on the distributions. We provide theoretical guarantees for distribution-free upper and lower bounds on the blurred TV distance, and examine its properties in high dimensions.
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