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Daily Overview |
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OT2: Optimal Transport: Theory and Applications Location: G227 Session Chair: Stephan Eckstein Session Chair: Johannes Wiesel | |
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Graph Causal Optimal Transport University of Oxford, United Kingdom Graph causal optimal transport is a recent generalisation of both classical and causal optimal transport in which the allowed couplings satisfy causal restrictions given by a directed graph. Inspired by applications to structural causal models, it was originally introduced in Eckstein and Cheridito (2023). We study fundamental properties of graph causal optimal transport, with a particular focus on its induced Wasserstein distance. Our main result is a full characterisation of the directed graphs for which this graph causal Wasserstein distance is indeed a metric, an open problem in the original paper. We study the topology of the new metric and prove continuity of a class of stochastic team problems with respect to it. Furthermore, we fully characterise the gluing properties of graph causal couplings, prove denseness of Monge maps, and provide a dynamic programming principle. Based on joint work with Jan Obloj. | |
