Abstract

In machine learning and computer vision, optimal transport (OT) has had significant success in learning generative models and defining metrics between structured and stochastic data objects, that can be cast as probability measures. The key element of optimal transport is the so called lifting of an \emph{exact} cost (distance) function, defined on the sample space, to a cost (distance) between probability measures over the sample space. This is carried out by minimizing the total transportation cost between two measures, resulting in the OT plan.

However, in many real life applications the cost is stochastic: for example, an unpredictable traffic flow affects the cost of transportation between a factory and an outlet. In this talk, we devise a Bayesian approach for inferring a distribution over the OT plans in such random settings.