We studied multi-marginal optimal transport problems from a probabilistic graphical model perspective. We pointed 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 equiv- alent 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.

List of Publications:

  1. Inference With Aggregate Data in Probabilistic Graphical Models: An Optimal Transport Approach,
    Rahul Singh, Isabel Haasler, Qinsheng Zhang, Johan Karlsson, and Yongxin Chen
    IEEE Transactions on Automatic Control, 2022.