Graph Causal Optimal Transport and Wasserstein Distances
chaumian · x · 2026-08-18
This paper studies the graph causal optimal transport problem, a generalization of the classical optimal transport problem where allowed couplings satisfy causal restrictions prescribed by a directed graph. The authors fully characterize the directed acyclic graphs for which the associated graph causal Wasserstein discrepancy is a metric and show the induced topology agrees with other natural adapted topologies. The paper also characterizes gluing properties, proves denseness of Monge couplings, and obtains a dynamic programming principle.
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