Order Constraints in Optimal Transport
This work addresses the need for more interpretable optimal transport solutions in fields like natural language processing and image processing, though it appears incremental as it builds on existing structured optimal transport methods.
The paper tackles the problem of incorporating structure into optimal transport plans by introducing novel order constraints, and demonstrates experimentally that these constraints improve explainability on the e-SNLI dataset and image color transfer examples.
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.