论文标题
Markov内核通过扩展C-Cyclic单调性进行最佳运输
Markov Kernels in Optimal Transport via Extending c-Cyclic Monotonicity
论文作者
论文摘要
在本文中，我们表明我们可以将Markov内核作为最佳运输模型。这个新框架可以轻松地转化为最佳运输的标准耦合公式，我们表明我们可以将耦合用作马尔可夫内核来解决许多最佳运输问题。使用内核使我们能够将最佳运输扩展到签名的措施，并将措施的支持视为显着特征。这种方法揭示了一维签名的最佳运输的其他结构。
In this paper we show that we can use Markov kernels as a model for optimal transport. This new framework can be easily translated into the standard coupling formulation of optimal transport, and we show that we can use a coupling as a Markov kernel for many optimal transport problems. Using kernels allows us to extend optimal transport to signed measures and treats the support of the measure as the salient feature. This approach reveals additional structure for one-dimensional signed optimal transport.
