Multi-Marginal Optimal Transport and Probabilistic Graphical Models
Multi-Marginal Optimal Transport and Probabilistic Graphical Models
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DOI：
10.1109/tit.2021.3077465
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发表时间：
2021-07-01
影响因子：
2.5
通讯作者：
Chen, Yongxin
中科院分区：
文献类型：
--
作者：
Haasler, Isabel;Singh, Rahul;Chen, Yongxin
从概率图模型的角度研究了多边际最优运输问题。我们指出，当最优运输的潜在成本允许一个图结构时，两者之间有一个优雅的联系。特别地，一个熵正则化的多边际最优传输等价于一个概率图模型的贝叶斯边际推理问题，附加的要求是一些边际分布是指定的。这种关系一方面扩展了最优传输和概率图模型理论，另一方面利用贝叶斯推理中成熟的算法，导致了多边缘最优传输的快速算法。给出了几个数值例子来突出结果。
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular, an entropy regularized multi-marginal optimal transport is equivalent to a Bayesian marginal inference problem for probabilistic graphical models with the additional requirement that some of the marginal distributions are specified. This relation on the one hand extends the optimal transport as well as the probabilistic graphical model theories, and on the other hand leads to fast algorithms for multi-marginal optimal transport by leveraging the well-developed algorithms in Bayesian inference. Several numerical examples are provided to highlight the results.