On Wasserstein Gaussian Barycenters


In this report, we study the problem of averaging gaussian probabilistic models through Wasserstein Barycenters. We compare the approach to the standard moment matching technique, and prove that the Wasserstein Barycenter of gaussian distributions produce lower entropy averages, hinting at its applicability in averaging distributions with latent bias. We analyze the currently used fixed point approximation solution to the problem, and offer the first closed-form solution by drawing connections to Optimal Control theory. Through preliminary experiments we demonstrate the usefulness of the approach and hint at a phase transition point where the Wasserstein Barycenter becomes more accurate as a method of inference over standard moment matching.

Technical Report written at Invenia Labs