# Minimax Distribution Estimation in Wasserstein Distance

arXiv: https://arxiv.org/abs/1802.08855 · HTML: https://mlsanity.com/paper/1802.08855/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2018.

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

- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)

## Abstract (arXiv)

The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on statistical minimax rates for the problem of estimating a probability distribution under Wasserstein loss, using only metric properties, such as covering and packing numbers, of the sample space, and weak moment assumptions on the probability distributions.