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Communication Dans Un Congrès Année : 2023

Tree-Based Diffusion Schrödinger Bridge with Applications to Wasserstein Barycenters

Résumé

Multi-marginal Optimal Transport (mOT), a generalization of OT, aims at minimizing the integral of a cost function with respect to a distribution with some prescribed marginals. In this paper, we consider an entropic version of mOT with a tree-structured quadratic cost, i.e., a function that can be written as a sum of pairwise cost functions between the nodes of a tree. To address this problem, we develop Tree-based Diffusion Schrödinger Bridge (TreeDSB), an extension of the Diffusion Schrödinger Bridge (DSB) algorithm. TreeDSB corresponds to a dynamic and continuous state-space counterpart of the multi-marginal Sinkhorn algorithm. A notable use case of our methodology is to compute Wasserstein barycenters which can be recast as the solution of a mOT problem on a star-shaped tree. We demonstrate that our methodology can be applied in high-dimensional settings such as image interpolation and Bayesian fusion.
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Dates et versions

hal-04402356 , version 1 (18-01-2024)

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Maxence Noble, Valentin de Bortoli, Arnaud Doucet, Alain Durmus. Tree-Based Diffusion Schrödinger Bridge with Applications to Wasserstein Barycenters. 37th Conference on Neural Information Processing Systems, 2023, New Orleans (LA), United States. ⟨hal-04402356⟩
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