  Wasserstein Barycenter is a principled approach to represent the weighted
mean of a given set of probability distributions, utilizing the geometry
induced by optimal transport. In this work, we present a novel scalable
algorithm to approximate the Wasserstein Barycenters aiming at high-dimensional
applications in machine learning. Our proposed algorithm is based on the
Kantorovich dual formulation of the Wasserstein-2 distance as well as a recent
neural network architecture, input convex neural network, that is known to
parametrize convex functions. The distinguishing features of our method are: i)
it only requires samples from the marginal distributions; ii) unlike the
existing approaches, it represents the Barycenter with a generative model and
can thus generate infinite samples from the barycenter without querying the
marginal distributions; iii) it works similar to Generative Adversarial Model
in one marginal case. We demonstrate the efficacy of our algorithm by comparing
it with the state-of-art methods in multiple experiments.
