Team seminars are called MokaMeetings. They are organized on a monthly basis.
The list of past seminars is available here.
- Mokameeting du 27 octobre 2021 : Ting-Kam Leonard Wong
Le prochain Mokameeting aura lieu le mercredi 27 octobre 2021 sur Discord à 15h00.
Nous aurons le plaisir d’écouter un exposé de Leonard Wong (University of Toronto).
Titre : Logarithmic divergences: optimal transport, geometry and applications
Résumé : Divergences such as Bregman and KL-divergences are fundamental in probability, statistics and machine learning. In the first part of the talk, we explain how divergences arise naturally from the geometry of optimal transport. Then, we study a family of logarithmic costs which may be regarded as a canonical deformation of the negative dot product in Euclidean quadratic transport. It induces a logarithmic divergence which has remarkable probabilistic and geometric properties. We illustrate its usefulness in statistics and machine learning with several applications.
- Mokameeting du 24 novembre 2021 : Michael Goldman et Bernhard Schmitzer
Un Mokameeting aura lieu le mercredi 24 novembre 2021 à 14h00.
Nous aurons le plaisir d’écouter deux exposés, l’un de Michael Goldman (LJLL, Paris 7), l’autre de Bernhard Schmitzer (Université de Göttingen).
Exposé de Michael Goldman
Titre : On recent progress on the optimal matching problem
Résumé : The optimal matching problem is a classical random combinatorial problem which may be interpreted as an optimal transport problem between random measures. Recent years have seen a renewed interest for this problem thanks to the PDE ansatz proposed in the physics literature by Caracciolo and al. and partially rigorously justified by Ambrosio-Stra-Trevisan. In this talk I will show how this ansatz combined with subadditivity may be used to give information both on the optimal cost and on the structure of the optimal transport map at various scales. This is based on joint works with L. Ambrosio, M. Huesmann, F. Otto and D. Trevisan.
Exposé de Bernhard Schmitzer
Titre : Domain decomposition for optimal transport
Résumé : Large optimal transport problems can be approached in a distributed way via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Benamou proved convergence to the global minimizer in the setting of Brenier’s theorem under suitable regularity assumptions on the decomposition. We show that with entropic regularization global convergence becomes much easier to prove and present a corresponding computationally efficient algorithm. To obtain a better understanding of the method we also discuss its limit behaviour in the regime of infinitesimally small decompositions.