# Reweighting samples under covariate shift using a Wasserstein distance criterion

arXiv: https://arxiv.org/abs/2010.09267 · HTML: https://mlsanity.com/paper/2010.09267/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [Learning to Re-weight Examples with Optimal Transport for Imbalanced Classification](https://mlsanity.com/paper/2208.02951/) (2022)
- [Optimal transport weights for causal inference](https://mlsanity.com/paper/2109.01991/) (2021)
- [OTROPE: Optimal Transport-based Robust Off-policy Evaluation for Large Language Models](https://mlsanity.com/paper/2609.36264/) (2026)

## Abstract (arXiv)

Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second sample as the size of both samples goes to infinity. We study an optimal reweighting that minimizes the Wasserstein distance between the empirical measures of the two samples, and leads to an expression of the weights in terms of Nearest Neighbors. The consistency and some asymptotic convergence rates in terms of expected Wasserstein distance are derived, and do not need the assumption of absolute continuity of one random variable with respect to the other. These results have some application in Uncertainty Quantification for decoupled estimation and in the bound of the generalization error for the Nearest Neighbor Regression under covariate shift.