4 papers
Sobolev--Ricci Curvature
Kyoichi Iwasaki, Tam Le, Hideitsu Hino
Ricci curvature is a fundamental concept in differential geometry for encoding local geometric structure, and its graph-based analogues have recently gained prominence as practical…
Generalized Sobolev IPM for Graph-Based Measures
Tam Le, Truyen Nguyen, Hideitsu Hino +1
We study the Sobolev IPM problem for measures supported on a graph metric space, where critic function is constrained to lie within the unit ball defined by Sobolev norm. While Le…
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…