Differentially Private Wasserstein Barycenters
This addresses privacy concerns for applications in machine learning, statistics, and computer graphics that rely on sensitive data, representing a novel contribution rather than an incremental improvement.
The paper tackles the problem of computing Wasserstein barycenters from sensitive datasets by introducing the first differentially private algorithms, achieving high-quality private barycenters with strong accuracy-privacy tradeoffs on synthetic data, MNIST, and U.S. population datasets.
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.