Multi-Marginal Optimal Transport and Probabilistic Graphical Models
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 e...
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| Veröffentlicht in: | IEEE transactions on information theory 2021-07, Vol.67 (7), p.4647-4668 |
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| creator | Haasler, Isabel Singh, Rahul Zhang, Qinsheng Karlsson, Johan Chen, Yongxin |
| description | 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. |
| doi_str_mv | 10.1109/TIT.2021.3077465 |
| format | Article |
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| subjects | Algorithms Bayesian analysis Bayesian inference belief propagation Entropy Graphical models Heuristic algorithms Inference algorithms iterative scaling Machine learning algorithms norm-product Optimal transport probabilistic graphical models Probabilistic inference Probabilistic logic Statistical inference |
| title | Multi-Marginal Optimal Transport and Probabilistic Graphical Models |
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