Multi-Marginal Optimal Transport and Probabilistic Graphical Models | IEEE Journals & Magazine | IEEE Xplore

Multi-Marginal Optimal Transport and Probabilistic Graphical Models


Abstract:

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlyin...Show More

Abstract:

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.
Published in: IEEE Transactions on Information Theory ( Volume: 67, Issue: 7, July 2021)
Page(s): 4647 - 4668
Date of Publication: 04 May 2021

ISSN Information:

Funding Agency:


Contact IEEE to Subscribe

References

References is not available for this document.