  By adding entropic regularization, multi-marginal optimal transport problems
can be transformed into tensor scaling problems, which can be solved
numerically using the multi-marginal Sinkhorn algorithm. The main computational
bottleneck of this algorithm is the repeated evaluation of marginals. Recently,
it has been suggested that this evaluation can be accelerated when the
application features an underlying graphical model. In this work, we accelerate
the computation further by combining the tensor network dual of the graphical
model with additional low-rank approximations. We provide an example for the
color transfer between several images, in which these additional low-rank
approximations save more than 96% of the computation time.
