Graphical Optimal Transport and Its Applications
summary
Presents algorithms that exploit pairwise graphical structure in multi-marginal optimal transport by combining Sinkhorn with junction-tree/belief-propagation to make the costly projection step scale linearly in number of marginals for tree costs, with much smaller dependence on label dimension. Extends entropy-regularized Schrödinger bridge to account for particle killing and mean-field interactions, solves it with proximal/Sinkhorn-style iterations, demonstrates particle-based variational transport for infinite-dimensional objectives, and introduces a diffusion normalizing flow with trajectory-space matching and low-dimensional examples.
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chapters (10)
- 0:00Intro
- 1:01Discrete optimal transport
- 1:17Multi-marginal optimal transport
- 2:18Graphical optimal transport
- 3:46Wasserstein spline
- 5:09Schrödinger bridge with unbalanced marginals
- 7:01Density control of interacting particle system
- 8:57Variational transport
- 10:46Diffusion normalizing flow
- 12:09Farlier work
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