Year: 2021
Type: preprint
Abstract: Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure. We introduce novel order constraints into the optimal transport formulation to allow for the incorporation of structure. We define an efficient method for obtaining explainable solutions to the new formulation that scales far better than standard approaches. The theoretical properties of the method are provided. We demonstrate experimentally that order constraints improve explainability using the e-SNLI (Stanford Natural Language Inference) dataset that includes human-annotated rationales as well as on several image color transfer examples.
Source: arXiv (Cornell University)
Authors: Lim, Fabian, Wynter, Laura, Lim, Shiau Hong
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3206688697