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arXiv · 2510.03021

Differentially Private Wasserstein Barycenters

Anming Gu·Sasidhar Kunapuli·Mark Bun·Edward Chien·Kristjan Greenewald
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Abstract

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.

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Anming Gu, Sasidhar Kunapuli, Mark Bun, Edward Chien, Kristjan Greenewald. 2025-10-03. Differentially Private Wasserstein Barycenters. https://arxiv.org/abs/2510.03021

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