Wasserstein barycenters from the computational perspective

In this talk we give an overview of several works devoted to numerical methods for the Wasserstein barycenter problem. Wasserstein barycenter allows to generalize the notion of average object to the space of probability measures and has a number of applications in machine learning and data analysis. We discuss the complexity of this problem in the discrete-discrete setting as well as efficient algorithms, in particular distributed optimization methods that allow one to scale up the computations.