On Parameterizing Optimal Transport with Elastic Costs

Abstract: 

I will present in this talk an overview of the computations of optimal transport, focusing in particular on the challenge of computing OT maps using two samples from high-dimensional probability measures. After reviewing a few of the popular methods that have been explored for this task recently, including those leveraging neural architectures, I will introduce our recent work on parameterising OT problems with elastic costs, i.e. ground costs that mix the classic squared Euclidean distance with a regularizer (e.g. L1 norm). After highlighting the properties of OT maps that follow such costs, I will present a method to compute ground truth OT maps with elastic costs and also a method to learn the parameters, adaptively, of such a regularizer.