On Parameterizing Optimal Transport with Elastic Costs

“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 regularize.” -M. Cuturi

Marco is a researcher in machine learning at Apple, working since 2022 in the Machine Learning Research team led by Samy Bengio. Marco is also affiliated as a Professor at ENSAE / IP Paris since 2016. Marco worked at Google Brain (2018~2022), Kyoto University (2010~2016), Princeton University (2009~2010), in finance (2007~2008) and at the Institute of Statistical Mathematics (Tokyo, 2006~2007). Marco received his Ph.D. in 2005 from Ecole des Mines de Paris. Marco’s research interests span optimal transport theory, its computations and impact to ML and natural sciences.