论文标题
多界限最佳运输和概率图形模型
Multi-marginal optimal transport and probabilistic graphical models
论文作者
论文摘要
我们从概率图形模型的角度研究了多界定最佳运输问题。我们指出，当最佳运输的基本成本允许图形结构时，两者之间的连接优雅。特别是，对于概率图形模型而言，熵正规化的多 - 边界最佳运输等同于贝叶斯边际推断问题，并要求指定某些边际分布的其他要求。一方面，这种关系扩展了最佳传输以及概率图形模型理论，另一方面，通过利用贝叶斯推论的良好发达的算法，导致了多 - 边界最佳最佳传输的快速算法。提供了几个数值示例以突出结果。
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.
