Differentially Private Wasserstein Barycenters

Anming Gu, Sasidhar Kunapuli, Edward Chien, Mark Bun, Kristjan Greenewald

Keywords: Wasserstein barycenters, differential privacy

Abstract: A Wasserstein barycenter is the mean of a set of probability measures under the optimal transport metric, and it has numerous applications spanning machine learning, statistics, and computer graphics. In applications, the input measures are often empirical distributions formed from datasets, hence privatizing the output barycenter is desired if the input datasets contain sensitive records. We provide the first differentially private algorithms for approximate computation of Wasserstein barycenters between empirical distributions. Our algorithms essentially matches the approximation guarantees of any non-private algorithm for Wasserstein barycenters, while only incurring small additive errors.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

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Submission Number: 14531