# Distribution-free two-sample testing with blurred total variation distance

arXiv: https://arxiv.org/abs/2602.05862 · HTML: https://mlsanity.com/paper/2602.05862/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 23 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Theoretical Foundations of Conformal Prediction](https://mlsanity.com/paper/2411.11824/) (2024)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces](https://mlsanity.com/paper/1804.10556/) (2018)
- [Generalization Bounds via Convex Analysis](https://mlsanity.com/paper/2202.04985/) (2022)
- [Two-sample Test using Projected Wasserstein Distance](https://mlsanity.com/paper/2010.11970/) (2020)
- [A Practical Guide to Sample-based Statistical Distances for Evaluating Generative Models in Science](https://mlsanity.com/paper/2403.12636/) (2024)
- [Robust Estimation for Kernel Exponential Families with Smoothed Total Variation Distances](https://mlsanity.com/paper/2410.20760/) (2024)

## Built on by (most cited first, 1 of 1)

- [Testing hypotheses via orthogonalization](https://mlsanity.com/paper/2606.29732/) (2026)

## Abstract (arXiv)

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.