# Differentially Private Wasserstein Barycenters

arXiv: https://arxiv.org/abs/2510.03021 · HTML: https://mlsanity.com/paper/2510.03021/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 72 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Builds on (most cited first, 30 of 31)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Winning the NIST Contest: A scalable and general approach to differentially private synthetic data](https://mlsanity.com/paper/2108.04978/) (2021)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Performance of Johnson-Lindenstrauss Transform for k-Means and k-Medians Clustering](https://mlsanity.com/paper/1811.03195/) (2018)
- [Differentially Private Clustering: Tight Approximation Ratios](https://mlsanity.com/paper/2008.08007/) (2020)
- [LinkedIn's Audience Engagements API: A Privacy Preserving Data Analytics System at Scale](https://mlsanity.com/paper/2002.05839/) (2020)
- [Stochastic Wasserstein Barycenters](https://mlsanity.com/paper/1802.05757/) (2018)
- [Wasserstein barycenters can be computed in polynomial time in fixed dimension](https://mlsanity.com/paper/2006.08012/) (2020)
- [Differentially Private k-Means with Constant Multiplicative Error](https://mlsanity.com/paper/1804.08001/) (2018)
- [Differentially Private Release of Israel's National Registry of Live Births](https://mlsanity.com/paper/2405.00267/) (2024)
- [Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applications](https://mlsanity.com/paper/2101.04039/) (2021)
- [Improved Approximations for Euclidean k-means and k-median, via Nested Quasi-Independent Sets](https://mlsanity.com/paper/2204.04828/) (2022)
- [Dimensionality Reduction for Wasserstein Barycenter](https://mlsanity.com/paper/2110.08991/) (2021)
- [k-Variance: A Clustered Notion of Variance](https://mlsanity.com/paper/2012.06958/) (2020)
- [Algorithmically Effective Differentially Private Synthetic Data](https://mlsanity.com/paper/2302.05552/) (2023)
- [Differentially Private Clustering via Maximum Coverage](https://mlsanity.com/paper/2008.12388/) (2020)
- [Instance-Optimal Private Density Estimation in the Wasserstein Distance](https://mlsanity.com/paper/2406.19566/) (2024)
- [Differentially private k-means clustering via exponential mechanism and max cover](https://mlsanity.com/paper/2009.01220/) (2020)
- [Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples](https://mlsanity.com/paper/2103.00394/) (2021)
- [An Improved Local Search Algorithm for k-Median](https://mlsanity.com/paper/2111.04589/) (2021)
- [Private Query Release via the Johnson-Lindenstrauss Transform](https://mlsanity.com/paper/2208.07410/) (2022)
- [Multimarginal Wasserstein Barycenter for Stain Normalization and Augmentation](https://mlsanity.com/paper/2006.14566/) (2020)
- [Randomized Dimensionality Reduction for Facility Location and Single-Linkage Clustering](https://mlsanity.com/paper/2107.01804/) (2021)

## Built on by (most cited first, 2 of 2)

- [Minimax optimal differentially private synthetic data for smooth queries](https://mlsanity.com/paper/2602.01607/) (2026)
- [Differentially Private Sampling from Distributions via Wasserstein Projection](https://mlsanity.com/paper/2605.10015/) (2026)

## Abstract (arXiv)

The Wasserstein barycenter is defined as the mean of a set of probability measures under the optimal transport metric, and has numerous applications spanning machine learning, statistics, and computer graphics. In practice these input measures are empirical distributions built from sensitive datasets, motivating a differentially private (DP) treatment. We present, to our knowledge, the first algorithms for computing Wasserstein barycenters under differential privacy. Empirically, on synthetic data, MNIST, and large-scale U.S. population datasets, our methods produce high-quality private barycenters with strong accuracy-privacy tradeoffs.