# Two-sample Test using Projected Wasserstein Distance

arXiv: https://arxiv.org/abs/2010.11970 · HTML: https://mlsanity.com/paper/2010.11970/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2020.

## Built on by (most cited first, 17 of 17)

- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Diffusion Models for Tabular Data Imputation and Synthetic Data Generation](https://mlsanity.com/paper/2407.02549/) (2024)
- [Sharp bounds for max-sliced Wasserstein distances](https://mlsanity.com/paper/2403.00666/) (2024)
- [Variable Selection for Kernel Two-Sample Tests](https://mlsanity.com/paper/2302.07415/) (2023)
- [Provably Convergent Policy Optimization via Metric-aware Trust Region Methods](https://mlsanity.com/paper/2306.14133/) (2023)
- [A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks](https://mlsanity.com/paper/2205.02043/) (2022)
- [Clustering Market Regimes using the Wasserstein Distance](https://mlsanity.com/paper/2110.11848/) (2021)
- [Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distances](https://mlsanity.com/paper/2405.15441/) (2024)
- [Learning Sinkhorn divergences for supervised change point detection](https://mlsanity.com/paper/2202.04000/) (2022)
- [Tight Non-asymptotic Inference via Sub-Gaussian Intrinsic Moment Norm](https://mlsanity.com/paper/2303.07287/) (2023)
- [Minimax-Optimal Two-Sample Test with Sliced Wasserstein](https://mlsanity.com/paper/2510.27498/) (2025)
- [Distribution-free two-sample testing with blurred total variation distance](https://mlsanity.com/paper/2602.05862/) (2026)
- [Soft and subspace robust multivariate rank tests based on entropy regularized optimal transport](https://mlsanity.com/paper/2103.08811/) (2021)
- [Personalized Federated Learning under Model Dissimilarity Constraints](https://mlsanity.com/paper/2505.07575/) (2025)
- [WWAggr: A Window Wasserstein-based Aggregation for Ensemble Change Point Detection](https://mlsanity.com/paper/2506.08066/) (2025)
- [Split Conformal Classification with Unsupervised Calibration](https://mlsanity.com/paper/2510.07185/) (2025)
- [High-Dimensional Online Change Point Detection with Adaptive Thresholding and Interpretability](https://mlsanity.com/paper/2609.24278/) (2026)

## Abstract (arXiv)

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to circumvent the curse of dimensionality in Wasserstein distance: when the dimension is high, it has diminishing testing power, which is inherently due to the slow concentration property of Wasserstein metrics in the high dimension space. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions. We characterize the theoretical property of the finite-sample convergence rate on IPMs and present practical algorithms for computing this metric. Numerical examples validate our theoretical results.