## Liste des séminaires MOKAPLAN 2019-2020

• Mardi 24 septembre: Julien FAGEOT
• Mercredi 25 septembre: Hongkai ZHAO
• Mercredi 2 octobre: Max FATHI
• Mercredi 16 octobre: Yue LU
• Mercredi 11 décembre: Bruno NAZARET
• Mercredi 15 janvier: Luigi DE PASCALE & Beni SOLLNER

## Mokameeting du 15 janvier: Luigi De Pascale et Beni Söllner

Le prochain Mokameeting aura lieu le mercredi 15 janvier 2020 à INRIA Paris (2 rue Simone Iff) en salle Jacques-Louis Lions à 10h30.

Nous aurons le plaisir d’écouter les exposés de Luigi De Pascale (Dipartimento di Matematica ed Informatica,  Firenze, Italy)   et Beni Söllner (Zentrum Mathematik, Technische Universität München, Germany).

#### Exposé de Luigi De Pascale

Titre : Relaxing the multi-marginal, Coulomb (repulsive) optimal transport cost.

Résumé : Motivated by some applications to Density Functional Theory for Coulomb Systems I will show the need to relax the multi-marginal, Coulomb optimal transport cost with respect to the weak convergence of measures.
I will then present a formula for the relaxed functional. This formula involves transport costs with smaller numbers of marginals. If time permits the problem of molecular dissociation in this setting will be discussed.

#### Exposé de Beni Söllner

Titre : An entropic regularized BDF2 method for the porous medium equation.

Résumé : Recently a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for time-discrete approximation of gradient flows in metric spaces has been introduced. On the other hand, entropic regularized optimal transport provides an efficient method for numerical solutions of the minimizing movement scheme.

This talk will be about the analysis of a scheme that combines BDF2 with entropic regularization. Specifically we study an implicit second order scheme for approximate solutions to the porous medium equation that allows for efficient numerical implementation. Our focus is on the convergence of the scheme.

## Mokameeting du 11 décembre : Bruno Nazaret

Le prochain séminaire de l’équipe Mokaplan aura lieu le mercredi 11 décembre à INRIA Paris (2 rue Simone Iff) en salle A415 à 14h30.
Nous aurons le plaisir d’écouter Bruno Nazaret (Université Paris I Panthéon / MOKAPLAN).

Titre : Métrisabilité des espaces métriques probabilisés

Résumé : Nous présentons ici la notion d’espace métrique probabilisé introduit initialement par Menger en 1942, où la notion classique de distance entre deux points comme nombre réel positif est remplacé par une fonction de répartition d’une variable aléatoire à valeurs positives. En étudiant l’espace des fonctions 1-Lipschitziennes dans ce cadre, nous montrerons notamment que la topologie naturelle sur ce type d’espace est métrisable sous une hypothèse généralisant un résultat obtenu par Schweizer, Sklar and Thorp en 1960.
Ce travail à été effectué en collaboration avec Mohammed Bachir.

## Mokameeting du 16 octobre 2019

Un Mokameeting aura lieu le mercredi 16 octobre à INRIA Paris (2 rue Simone Iff) en salle A415 à 15h00.
Nous aurons le plaisir d’écouter Yue Lu (Harvard University).
Titre :  Exploiting the Blessings of Dimensionality in Big Data
Résumé : The massive datasets being compiled by our society present new challenges and opportunities to the field of signal and information processing. The increasing dimensionality of modern datasets offers many benefits. In particular, the very high-dimensional settings allow one to develop and use powerful asymptotic methods in probability theory and statistical physics to obtain precise characterizations that would otherwise be intractable in moderate dimensions.

In this talk, I will present recent work where such blessings of dimensionality are exploited. In particular, I will show (1) the exact characterization of a widely-used spectral method for nonconvex statistical estimation; (2) the fundamental limits of solving the phase retrieval problem via linear programming; and (3) how to use scaling and mean-field limits to analyze nonconvex optimization algorithms for high-dimensional inference and learning. In these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with high-dimensional data, they also lead to optimal designs that significantly outperform heuristic choices commonly used in practice.

## Mokameeting du 2 octobre 2019

Le prochain séminaire de l’équipe Mokaplan aura lieu le mercredi 2 octobre à INRIA Paris (2 rue Simone Iff) en salle A415 à 11h00.
Nous aurons le plaisir d’écouter Max Fathi (Institut de Math. de Toulouse).
Titre :
Une preuve du théorème de Caffarelli via la régularisation entropique

Résumé :
Le théorème de contraction de Caffarelli (2001) énonce que le transport optimal de la mesure Gaussienne sur une mesure uniformément log-concave est globalement lipschitz. Dans cet exposé, je présenterai une nouvelle preuve, basée sur la régularisation entropique du transport optimal et une caractérisation variationnelle des transport lipschitz, dûe à Gozlan et Juillet. Travail en collaboration avec Nathael Gozlan et Maxime Prod’homme.

## Mokameeting du 24 septembre 2019: Julien Fageot

Ce séminaire a eu lieu en salle A415 à INRIA Paris le 24 septembre à 15h30. Nous avons eu le plaisir d’écouter Julien Fageot (Harvard University).
Titre : Analog Reconstruction from Discrete Measurements
Abstract : We present a general framework for the reconstruction of analog signals from finitely many linear measurements. The reconstruction task is formulated as an optimization problem, whose ill-posedness is removed via the use of regularization costs. A special attention will be devoted to comparing quadratic versus sparsity-promoting methods, the latter being achieved via the total variation norm. The main goal of the presentation is to introduce  to the growing and fascinating project of providing continuous-domain methods for the reconstruction of sparse signals.

## MOKAMEETING 25 SEPTEMBER 14H

MOKAMEETING 25 SEPTEMBER 14H . ROOM JLL INRIA PARIS

HongKai Zhao,  UC Irvine.

Title:  Instability of an inverse problem for the stationary radiative transport near the diffusion limit.
Abstract:  In this talk we study the instability of an inverse problem of radiative transport equation with angularly averaged measurement near the diffusion limit. We show the transition of stability by establishing the balance of two different regimes depending on the relative size of the mean free path and the perturbation in measurements. When the free mean path is sufficiently small, one obtains exponential instability, which stands for the diffusive regime, and otherwise one obtains Holder instability, which stands for the transport regime.

## Mokameeting, June 26th, 10:30, Sebastian Claici

Mokameeting, June 26th 10:30, Room A415
Sebastian Claici (MIT)
Title: Transportation Techniques for Constrained Learning Problems

Abstract: Optimal transport (OT) is a method of measuring distances between probability distributions that has found numerous applications in machine learning, computer graphics, image processing, and others. However, research has focused largely on computing transport distances quickly in great generality, and less on developing better algorithms for problems with inherent structure.

In this talk, I hope to provide perspective on how additional knowledge and constraints on the distributions or the underlying domain help in designing better algorithms. I will discuss two directions: (1) learning problems that have natural OT interpretations and lead to simple constraints and efficient algorithms, and (2) connections between the semi-discrete transport problem and classical learning problems.

## Mokameeting du 17 avril 2019 / Georgina HALL

Le prochain séminaire de l’équipe Mokaplan aura lieu le mercredi 17 avril à 10h30 à l’INRIA Paris (2 rue Simone Iff) en salle Jacques-Louis Lions 1.

Nous aurons le plaisir d’écouter Georgina HALL (INSEAD).

Venez nombreux!

Title: Sum of squares optimization: fundamentals, applications, and recent scalability developments

Abstract: The problem of optimizing over nonnegative polynomials, and its dual formulation – optimizing over the set of moments that have a representing measure – are optimization problems that naturally arise in a variety of applications. In the first part of this talk, we will review a number of these applications in control, statistics, and probability, among others. We will also discuss how these problems can be tackled using sum of squares optimization, a subclass of optimization problems whose computational backbone is semidefinite programming. In the second part of this talk, we will focus on a major challenge that has limited the dissemination of sum of squares optimization within more applied fields: scalability. We will briefly review a few methods that have been developed to curb this issue, focusing on methods that replace the underlying semidefinite program with cheaper conic programs.

## Mokameeting du 13 mars 2019

Le prochain séminaire de l’équipe Mokaplan aura lieu le mercredi 13 mars à 10h30 à l’université Paris-Dauphine (Place du Maréchal de Lattre de Tassigny), en salle B207.

Nous aurons le plaisir d’écouter Daniela Vögler (TUM, Munich) et Simone di Marino (Indam, SNS, Pisa).

Exposé de Daniela Vögler:

Titre: Breaking the Curse of Dimension in Multi-Marginal Kantorovich Optimal Transport on Finite State Spaces
Résumé:  In this talk, I will present a new ansatz space for the general symmetric multi-marginal Kantorovich optimal transport problem on finite state spaces which reduces the number of unknowns from combinatorial in both N and  to (N+1), where  is the number of marginal states and N the number of marginals. These results were established in collaboration with Gero Friesecke.

Exposé de  Simone di Marino:

Titre: Duality in entropic optimal transport: a priori estimates and applications
Résumé: We want to explore a different approach to the duality in the entropic optimal transport, much more in the spirit of optimal transport, which is different from the usual techniques coming from the Schrodinger problem. This will result in consistent a priori estimates, which are consistent in the limit $\ep \to 0$. As a byproduct we prove that the IPFP algorithm is converging also in the multimarginal case.