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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Tree-Based Diffusion Schrödinger Bridge with Applications to Wasserstein Barycenters

## Tree-Based Diffusion Schrödinger Bridge with Applications to Wasserstein BarycentersAdd to your list(s) Download to your calendar using vCal - Maxence Noble-Bourillot (Ecole Polytechnique Paris)
- Friday 23 June 2023, 10:00-11:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. DDE - The mathematical and statistical foundation of future data-driven engineering 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 multimarginal 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. Co-authors: Valentin de Bortoli (ENS Ulm), Arnaud Doucet (Oxford University), Alain Durmus (Ecole polytechnique) This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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