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.
翻译:最佳运输是比较措施的一个框架,根据这些措施,一种措施的运输成本会发生,另一种措施是最佳运输。最近的工作旨在通过采用各种形式的结构改进最佳运输计划。我们将新的秩序限制引入最佳运输方式,以便纳入结构。我们界定了一种有效的方法,为新配方找到可解释的解决办法,这种新配方的规模远远超过标准方法。提供了该方法的理论特性。我们实验性地证明,按秩序限制提高了使用电子SNLI(斯坦福德自然语言推断)数据集的解释性,该数据集包括人类附加说明的理由以及若干图像颜色转换实例。