Displacement-Reshaped Optimal Transport for Distribution Shifts
A new approach called ReshapeOT has been introduced by researchers, which modifies the ground metric in optimal transport by incorporating observed displacements of samples. This technique substitutes the traditional Euclidean metric with a Mahalanobis distance derived from the second moments of displacement, facilitating the formation of expressways in the input space for improved alignment with actual changes. ReshapeOT is computationally efficient, works seamlessly with any optimal transport solver that utilizes a cost matrix, and has the potential for kernelization. Its effectiveness has been validated through experiments conducted on both synthetic and real-world datasets.
Key facts
- ReshapeOT reshapes the ground metric using observed sample displacements.
- It replaces Euclidean metric with Mahalanobis distance from displacement second moments.
- The method is computationally lightweight and integrates into any OT solver.
- It can be kernelized for further flexibility.
- Experiments on synthetic and real-world data show effectiveness.
- The approach invites transport solutions that align with observed displacements.
- It carves expressways through input space.
- The work is published on arXiv (2605.04965).
Entities
Institutions
- arXiv