5 papers
Orlicz-Sobolev with Musielak: An Efficient Regularization Approach for Graph-based IPM
Tam Le, Truyen Nguyen, Hideitsu Hino +1
We study the Sobolev IPM problem for probability measures supported on a graph metric space, where critic function is constrained to lie within the unit ball defined by Sobolev nor…
An Efficient Orlicz-Sobolev Approach for Transporting Unbalanced Measures on a Graph
Tam Le, Truyen Nguyen, Hideitsu Hino +1
We investigate optimal transport (OT) for measures on graph metric spaces with different total masses. To mitigate the limitations of traditional geometry, Orlicz-Wasserstein…
Scalable Sobolev IPM for Probability Measures on a Graph
Tam Le, Truyen Nguyen, Hideitsu Hino +1
We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and i…
Generalized Sobolev Transport for Probability Measures on a Graph
Tam Le, Truyen Nguyen, Kenji Fukumizu
We study the optimal transport (OT) problem for measures supported on a graph metric space. Recently, Le et al. (2022) leverage the graph structure and propose a variant of OT, nam…
Optimal Transport for Measures with Noisy Tree Metric
Tam Le, Truyen Nguyen, Kenji Fukumizu
We study optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-fo…