Tree-Based Diffusion Schrödinger Bridge with Applications to Wasserstein Barycenters

Add 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
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 2, Newton Institute
• bld31

Note that ex-directory lists are not shown.