Le prochain Mokameeting aura lieu le mercredi 16 décembre 2020 sur Discord à 14h00.

Nous aurons le plaisir d’écouter un exposé joint de Bruno Loureiro (EPFL) et Antoine Maillard (ENS Paris).

Titre : Statistical physics and machine learning: a bird’s eye view

Résumé : In the first part of this talk we will give an overview of how tools originally developed to  study disordered physical systems gained a new life in the analysis of high-dimensional inference and learning problems. In the second part, we will have a closer look at a specific example: the phase retrieval problem. We will show the how these methods can be used to derive the statistical and algorithmic limitations of phase reconstruction for a large class of measurement matrix ensembles and discuss how they can be translated into rigorous mathematical results.

Le prochain Mokameeting aura lieu le mercredi 25 novembre 2020 sur Discord à 14h00.

Nous aurons le plaisir d’écouter un exposé de Rob Tovey (Mokaplan).

Titre : An introduction; past, present and future.

Résumé : This talk will be an overview of my research from the start of my PhD up until today. This will cover a brief introduction to inverse problems, the physics of electron microscopy, and optimisation. I will then discuss my current work in ‘off-the-grid’ optimisation, which first brought me to Paris. Finally, I will conclude with an introduction to the topic which Vincent and I hope to explore during the next two years.

Le prochain Mokameeting aura lieu le mercredi 4 novembre 2020 sur Discord à 14h00.

Nous aurons le plaisir d’écouter un exposé de Grégoire Loeper (BNP Paribas).

Titre : Joint Modelling and Calibration of SPX and VIX by Optimal Transport

Résumé : This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE formulation along with its dual counterpart. The solution, a calibrated dif- fusion process, can be represented via the solutions of Hamilton–Jacobi–Bellman equations arising from the dual formulation. The method is tested on both simulated data and market data. Numerical examples show that the model can be accurately calibrated to SPX options, VIX options and VIX futures simultaneously.

Le prochain Mokameeting aura lieu le mercredi 26 février 2020 à INRIA Paris (2 rue Simone Iff) en salle Jacques-Louis Lions 1 à 14h00.

Nous aurons le plaisir d’écouter un exposé de Tim Kunisky (Courant Institute, New York University).

Titre : The low-degree method for identifying statistical-to-computational gaps

Résumé : I will give a pedagogical introduction to a technique for studying statistical-to-computational gaps, certain regimes in statistical inference problems where inference is, in principle, possible with unbounded computational resources, but various evidence suggests that efficient algorithms for inference do not exist. A recent and strikingly simple method for identifying those regimes analyzes when inference or hypothesis testing can be performed using low-degree polynomials. I will outline how to apply this technique to various problems, giving the ingredients of a simple “back-of-the-envelope” calculation that correctly predicts the difficulty of tasks ranging from principal component analysis in matrices and tensors to community detection in structured graphs.

Based loosely on a recent survey paper with Alex Wein and Afonso Bandeira:
https://arxiv.org/abs/1907.11636

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.

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.

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 25 SEPTEMBER 14H . ROOM JLL INRIA PARIS

HongKai Zhao,  UC Irvine.