# The statistical effect of entropic regularization in optimal transportation

arXiv: https://arxiv.org/abs/2006.05199 · HTML: https://mlsanity.com/paper/2006.05199/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jun 2020.

## Built on by (most cited first, 14 of 14)

- [The Schr"odinger Bridge between Gaussian Measures has a Closed Form](https://mlsanity.com/paper/2202.05722/) (2022)
- [Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent](https://mlsanity.com/paper/2106.08502/) (2021)
- [An improved central limit theorem and fast convergence rates for entropic transportation costs](https://mlsanity.com/paper/2204.09105/) (2022)
- [Lower Complexity Adaptation for Empirical Entropic Optimal Transport](https://mlsanity.com/paper/2306.13580/) (2023)
- [Energy-Guided Continuous Entropic Barycenter Estimation for General Costs](https://mlsanity.com/paper/2310.01105/) (2023)
- [Doubly Regularized Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2303.11844/) (2023)
- [Entropy Regularized Optimal Transport Independence Criterion](https://mlsanity.com/paper/2112.15265/) (2021)
- [Convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings](https://mlsanity.com/paper/2101.01429/) (2021)
- [Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean space](https://mlsanity.com/paper/2507.01709/) (2025)
- [Estimating 2-Sinkhorn Divergence between Gaussian Processes from Finite-Dimensional Marginals](https://mlsanity.com/paper/2102.03267/) (2021)
- [Finite sample approximations of exact and entropic Wasserstein distances between covariance operators and Gaussian processes](https://mlsanity.com/paper/2104.12368/) (2021)
- [Estimation of Stationary Optimal Transport Plans](https://mlsanity.com/paper/2107.11858/) (2021)
- [Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations](https://mlsanity.com/paper/2307.13370/) (2023)
- [Optimal Transport with Heterogeneously Missing Data](https://mlsanity.com/paper/2505.17291/) (2025)

## Abstract (arXiv)

We propose to tackle the problem of understanding the effect of regularization in Sinkhorn algotihms. In the case of Gaussian distributions we provide a closed form for the regularized optimal transport which enables to provide a better understanding of the effect of the regularization from a statistical framework.