The optimal correlation structure in a multimarginal Schrödinger bridge is a minimum spanning tree whose edge weights are pairwise Schrödinger bridge costs plus endpoint entropies.
Multi-marginal optimal transport using partial information with applications in robust localization and sensor fusion,
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Optimal Multimarginal Schr\"odinger Bridge: Minimum Spanning Tree over Measure-valued Vertices
The optimal correlation structure in a multimarginal Schrödinger bridge is a minimum spanning tree whose edge weights are pairwise Schrödinger bridge costs plus endpoint entropies.