Decentralized Algorithms for Wasserstein Barycenters

We consider the Wasserstein barycenter problem from the computantional and statistical sides in two scenarios: (i) the measures are given and we need to compute their Wasserstein barycenter, and (ii) the measures are generated from a probability distribution and we need to calculate the population barycenter of the distribution defined by the notion of Fréchet mean. The statistical issues are estimating the sample size and the question of regularization. The computantional issues are developing decentralized algorithms to calculate the barycenters.