Tropical Optimal Transport and Wasserstein Distances in Phylogenetic Tree Space

13 Nov 2019 Wonjun Lee Wuchen Li Bo Lin Anthea Monod

We study the problem of optimal transport on phylogenetic tree space from the perspective of tropical geometry, and thus define the Wasserstein-$p$ distances for probability measures in this continuous metric measure space setting. With respect to the tropical metric---a combinatorial metric on the space of phylogenetic trees---the cases of $p=1,2$ are treated in detail, which give an efficient way to compute geodesics and also provide theoretical foundations for geometric insight a statistical framework on tree space... (read more)

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