# Density-Reweighted Entropic Optimal Transport: Decoupling Geometry from Sampling Density

arXiv: https://arxiv.org/abs/2608.16506 · HTML: https://mlsanity.com/paper/2608.16506/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 17 Aug 2026.

## Builds on (most cited first, 15 of 15)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Robust Optimal Transport with Applications in Generative Modeling and Domain Adaptation](https://mlsanity.com/paper/2010.05862/) (2020)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Sinkhorn Divergences for Unbalanced Optimal Transport](https://mlsanity.com/paper/1910.12958/) (2019)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Accurate Point Cloud Registration with Robust Optimal Transport](https://mlsanity.com/paper/2111.00648/) (2021)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [Faster Unbalanced Optimal Transport: Translation invariant Sinkhorn and 1-D Frank-Wolfe](https://mlsanity.com/paper/2201.00730/) (2022)
- [Light Unbalanced Optimal Transport](https://mlsanity.com/paper/2303.07988/) (2023)
- [Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets](https://mlsanity.com/paper/2407.01718/) (2024)

## Abstract (arXiv)

Dataset alignment is a central step in data analysis across science and engineering, where the goal is to match observations between datasets. Entropic Optimal Transport (EOT) offers a computationally tractable framework for this task by encoding cross-dataset affinities in a transport plan. However, when two datasets are sampled from geometrically similar low-dimensional structures with substantially different sampling densities, the EOT plan may match points by relative sampling density rather than geometric proximity, yielding geometrically misleading correspondences. To address this issue, we propose a density-reweighted EOT framework in which the influence of sampling density on the transport plan can be discounted to a desired degree, ranging from standard EOT to alignment driven purely by underlying geometry. Under suitable regularity conditions, we establish convergence of the reweighted EOT plan to a family of population-level plans whose dependence on sampling density is made explicit. Through simulations, we show that our approach recovers geometrically faithful correspondences, improving over related EOT-based frameworks when datasets exhibit substantial sampling density disparity.