# Sampling From the Wasserstein Barycenter

arXiv: https://arxiv.org/abs/2105.01706 · HTML: https://mlsanity.com/paper/2105.01706/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 4 May 2021.

## Builds on (most cited first, 12 of 12)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence](https://mlsanity.com/paper/2006.02509/) (2020)
- [Scalable Bayes via Barycenter in Wasserstein Space](https://mlsanity.com/paper/1508.05880/) (2015)
- [Exponential ergodicity of mirror-Langevin diffusions](https://mlsanity.com/paper/2005.09669/) (2020)
- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [Sinkhorn Barycenters with Free Support via Frank-Wolfe Algorithm](https://mlsanity.com/paper/1905.13194/) (2019)
- [Fast Optimal Transport Averaging of Neuroimaging Data](https://mlsanity.com/paper/1503.08596/) (2015)
- [Sinkhorn Barycenter via Functional Gradient Descent](https://mlsanity.com/paper/2007.10449/) (2020)
- [Averaging Atmospheric Gas Concentration Data using Wasserstein Barycenters](https://mlsanity.com/paper/2010.02762/) (2020)

## Built on by (most cited first, 5 of 5)

- [Wasserstein Iterative Networks for Barycenter Estimation](https://mlsanity.com/paper/2201.12245/) (2022)
- [Doubly Regularized Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2303.11844/) (2023)
- [Variational Wasserstein Barycenters with c-Cyclical Monotonicity](https://mlsanity.com/paper/2110.11707/) (2021)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [Computational Guarantees for Doubly Entropic Wasserstein Barycenters via Damped Sinkhorn Iterations](https://mlsanity.com/paper/2307.13370/) (2023)

## Abstract (arXiv)

This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive penalization to account for the marginal constraints. We prove that the minimum of this penalized multimarginal formulation is achieved for a coupling that is close to the Wasserstein barycenter. The performances of the algorithm are showcased in several settings.