4 papers
Metric Geometry of Lebesgue, Wasserstein, and Gromov-Wasserstein Spaces: Submetries, Curvature, and Geodesics
Martin Bauer, Facundo Mémoli, Tom Needham +1
A metric space gives rise to three natural classes of infinite-dimensional metric spaces associated to : -Wasserstein spaces of probability measures on , nonlinear Leb…
The Z-Gromov-Wasserstein Distance
Martin Bauer, Facundo Mémoli, Tom Needham +1
The Gromov-Wasserstein (GW) distance is a powerful tool for comparing metric measure spaces which has found broad applications in data science and machine learning. Driven by the n…
A Benamou-Brenier Proximal Splitting Method for Constrained Unbalanced Optimal Transport
Mao Nishino, Martin Bauer, Tom Needham +1
The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity…
Path constrained unbalanced optimal transport
Martin Bauer, Nicolas Charon, Tom Needham +1
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kin…