Knothe-Rosenblatt maps via soft-constrained optimal transport
speaker: Franca Hoffmann (Caltech )abstract: In the theory of optimal transport, Knothe-Rosenblatt maps provide an explicit and efficient way of finding a transport map between two measures, under minimal assumptions. Knothe-Rosenblatt maps have shown to be useful in many different realms of math, from proving inequalities to conditional sampling. It was shown in previous work that this map is the limit of a class of transport maps solving the optimal transport problem with a weighted quadratic cost. We show that one can obtain the Knothe-Rosenblatt map via a limit of maps that solve a weighted free target version of optimal transport (as is often done in practice), and we are in the process of expanding these results to dynamic optimal transport. This is ongoing work together with Ricardo Baptista, Minh Nguyen and Benjamin Zhang.
timetable:
Fri 6 Dec, 9:50 - 10:35, Aula Dini
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