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Multi-Marginal Optimal Transport and Probabilistic Graphical Models
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2021-05-04 , DOI: 10.1109/tit.2021.3077465 Isabel Haasler , Rahul Singh , Qinsheng Zhang , Johan Karlsson , Yongxin Chen
IEEE Transactions on Information Theory ( IF 2.5 ) Pub Date : 2021-05-04 , DOI: 10.1109/tit.2021.3077465 Isabel Haasler , Rahul Singh , Qinsheng Zhang , Johan Karlsson , Yongxin Chen
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.
中文翻译:
多边际最优传输和概率图形模型
我们从概率图模型的角度研究多边际最优运输问题。当最佳传输的潜在成本允许图结构时,我们指出两者之间的优雅联系。特别是,熵正则化多边际最优传输等价于概率图形模型的贝叶斯边际推理问题,附加要求是指定一些边际分布。这种关系一方面扩展了最优传输以及概率图模型理论,另一方面通过利用贝叶斯推理中成熟的算法导致了多边际最优传输的快速算法。提供了几个数值例子来突出结果。
更新日期:2021-06-18
中文翻译:
多边际最优传输和概率图形模型
我们从概率图模型的角度研究多边际最优运输问题。当最佳传输的潜在成本允许图结构时,我们指出两者之间的优雅联系。特别是,熵正则化多边际最优传输等价于概率图形模型的贝叶斯边际推理问题,附加要求是指定一些边际分布。这种关系一方面扩展了最优传输以及概率图模型理论,另一方面通过利用贝叶斯推理中成熟的算法导致了多边际最优传输的快速算法。提供了几个数值例子来突出结果。