Continuous Regularized Wasserstein Barycenters

Understand

Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport.

• They are difficult to compute in practice, however, leading previous work to restrict their supports to finite sets of points.
• Leveraging a new dual formulation for the regularized Wasserstein barycenter problem, we introduce a stochastic algorithm that constructs a continuous approximation of the barycenter.
• We establish strong duality and use the corresponding primal-dual relationship to parametrize the barycenter implicitly using the dual potentials of regularized transport problems.