论文标题
均质不平衡的正规化最佳运输模型，并应用于边界的最佳运输
An Homogeneous Unbalanced Regularized Optimal Transport model with applications to Optimal Transport with Boundary
论文作者
论文摘要
这项工作研究了不平衡的最佳运输（OT）模型中熵正则项的引入如何改变其相对于输入度量的同质性。我们观察到，在常见的环境中（包括平衡的OT和不平衡的OT，与边际的kullback-Leibler不同），尽管最佳运输成本本身不是同质的，但最佳的运输计划和所谓的Sinkhorn差异确实是同质的。但是，均匀性并不存在于更一般的不平衡正则最佳运输（UROT）模型，例如使用总变化作为边际差异的模型。我们建议修改熵正则化项，以检索一个均匀模型，同时保留标准urrot模型的大多数属性。我们展示了使用我们的均匀尿素模型（Hurot）模型的重要性，该模型在与边界的最佳运输方面进行正规化，这是一种传输模型，涉及在空间上与边际差异变化的运输模型，标准（不均匀）UROT模型将产生不适当的行为。
This work studies how the introduction of the entropic regularization term in unbalanced Optimal Transport (OT) models may alter their homogeneity with respect to the input measures. We observe that in common settings (including balanced OT and unbalanced OT with Kullback-Leibler divergence to the marginals), although the optimal transport cost itself is not homogeneous, optimal transport plans and the so-called Sinkhorn divergences are indeed homogeneous. However, homogeneity does not hold in more general Unbalanced Regularized Optimal Transport (UROT) models, for instance those using the Total Variation as divergence to the marginals. We propose to modify the entropic regularization term to retrieve an UROT model that is homogeneous while preserving most properties of the standard UROT model. We showcase the importance of using our Homogeneous UROT (HUROT) model when it comes to regularize Optimal Transport with Boundary, a transportation model involving a spatially varying divergence to the marginals for which the standard (inhomogeneous) UROT model would yield inappropriate behavior.
