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SUMMARY:Tree-Based Diffusion Schrödinger Bridge with Applications to Wass
 erstein Barycenters - Maxence Noble-Bourillot (Ecole Polytechnique Paris)
DTSTART:20230623T090000Z
DTEND:20230623T100000Z
UID:TALK201562@talks.cam.ac.uk
DESCRIPTION:Multi-marginal Optimal Transport (mOT)\, a generalization of O
 T\, aims at minimizing the integral of a cost function with respect to a d
 istribution 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 t
 he nodes of a tree. To address this problem\, we develop Tree-based Diffus
 ion Schr&ouml\;dinger Bridge (TreeDSB)\, an extension of the Diffusion Sch
 r&ouml\;dinger Bridge (DSB) algorithm. TreeDSB corresponds to a dynamic an
 d continuous state-space counterpart of the multimarginal Sinkhorn algorit
 hm. A notable use case of our methodology is to compute Wasserstein baryce
 nters which can be recast as the solution of a mOT problem on a star-shape
 d tree. We demonstrate that our methodology can be applied in high-dimensi
 onal settings such as image interpolation and Bayesian fusion.\n&nbsp\;\nC
 o-authors: Valentin de Bortoli (ENS Ulm)\, Arnaud Doucet (Oxford Universit
 y)\, Alain Durmus (Ecole polytechnique)
LOCATION:Seminar Room 2\, Newton Institute
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