# On the potential benefits of entropic regularization for smoothing Wasserstein estimators

arXiv: https://arxiv.org/abs/2210.06934 · HTML: https://mlsanity.com/paper/2210.06934/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 13 Oct 2022.

## Builds on (most cited first, 14 of 14)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Statistical Aspects of Wasserstein Distances](https://mlsanity.com/paper/1806.05500/) (2018)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [On the Convergence and Robustness of Training GANs with Regularized Optimal Transport](https://mlsanity.com/paper/1802.08249/) (2018)
- [Some Theoretical Insights into Wasserstein GANs](https://mlsanity.com/paper/2006.02682/) (2020)
- [Stochastic Optimization for Regularized Wasserstein Estimators](https://mlsanity.com/paper/2002.08695/) (2020)
- [Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration](https://mlsanity.com/paper/1804.08962/) (2018)
- [Entropy-regularized Optimal Transport Generative Models](https://mlsanity.com/paper/1811.06763/) (2018)

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

- [Label Shift Quantification with Robustness Guarantees via Distribution Feature Matching](https://mlsanity.com/paper/2306.04376/) (2023)

## Abstract (arXiv)

This paper is focused on the study of entropic regularization in optimal transport as a smoothing method for Wasserstein estimators, through the prism of the classical tradeoff between approximation and estimation errors in statistics. Wasserstein estimators are defined as solutions of variational problems whose objective function involves the use of an optimal transport cost between probability measures. Such estimators can be regularized by replacing the optimal transport cost by its regularized version using an entropy penalty on the transport plan. The use of such a regularization has a potentially significant smoothing effect on the resulting estimators. In this work, we investigate its potential benefits on the approximation and estimation properties of regularized Wasserstein estimators. Our main contribution is to discuss how entropic regularization may reach, at a lower computational cost, statistical performances that are comparable to those of un-regularized Wasserstein estimators in statistical learning problems involving distributional data analysis. To this end, we present new theoretical results on the convergence of regularized Wasserstein estimators. We also study their numerical performances using simulated and real data in the supervised learning problem of proportions estimation in mixture models using optimal transport.