Publications

Apprentissage

Private Quantiles Estimation in the Presence of Atoms

Clément Lalanne, Clément Gastaud, Nicolas Grislain, Aurélien Garivier, Rémi Gribonval

Probability

Sticky nonlinear SDEs and convergence of McKean-Vlasov equations without confinement

We develop a new approach to study the long time behaviour of solutions to nonlinear stochastic differential equations in the sense of McKean, as well as propagation of chaos for the corresponding mean-field particle system approximations. Our…

Arnaud Guillin, Alain Durmus, Andreas Eberle, Katharina Schuh

Dynamical Systems

Flow Redirection for Epidemic Reaction-DIffusion Control

We show we can control an epidemic reaction-diffusion on a directed, and heterogeneous, network by redirecting the flows, thanks to the optimisation of well-designed loss functions, in particular the basic reproduction number of the model. We…

Pierre-Yves Massé, Quentin Laborde, Maria Cherifa, Jules Olayé, Laurent Oudre

Santé publique et épidémiologie

Epidemic Models for Personalised COVID-19 Isolation and Exit Policies Using Clinical Risk Predictions

In mid April 2020, with more than 2.5 billion people in the world following social distancing measures due to COVID-19, governments are considering relaxing lock-down. We combined individual clinical risk predictions with epidemic modelling to…

Theodoros Evgeniou, Mathilde Fekom, Anton Ovchinnikov, Raphaël Porcher, Camille Pouchol, Nicolas Vayatis

Image Processing

Gromov-Wasserstein Distances between Gaussian Distributions

The Gromov-Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative to the Wasserstein distances for comparing probability measures living…

Antoine Salmona, Julie Delon, Agnès Desolneux

Journal of Applied Probability - 2022

Statistics Theory

Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie

Since the seminal work of Venkatakrishnan et al. [82] in 2013, Plug & Play (PnP) methods have become ubiquitous in Bayesian imaging. These methods derive estimators for inverse problems in imaging by combining an explicit likelihood function…

Rémi Laumont, Valentin de Bortoli, Andrés Almansa, Julie Delon, Alain Durmus, Marcelo Pereyra

SIAM Journal on Imaging Sciences - 2022

Analysis of PDEs

A linear finite-difference scheme for approximating Randers distances on Cartesian grids

Randers distances are an asymmetric generalization of Riemannian distances, and arise in optimal control problems subject to a drift term, among other applications. We show that Randers eikonal equation can be approximated by a logarithmic…

Frédéric Bonnans, Guillaume Bonnet, Jean-Marie Mirebeau

ESAIM: Control, Optimisation and Calculus of Variations - 2022

Analysis of PDEs

Monotone discretization of the Monge-Ampère equation of optimal transport

We design a monotone finite difference discretization of the second boundary value problem for the Monge-Ampère equation, whose main application is optimal transport. We prove the existence of solutions to a class of monotone numerical schemes for…

Guillaume Bonnet, Jean-Marie Mirebeau

Statistics

A 3D Mathematical Breast Texture Model with Parameters Automatically Inferred from Clinical Breast CT Images

Zhijin Li, Ann-Katherine Carton, Serge Muller, Thomas Almecija, Pablo Milioni de Carvalho, Agnès Desolneux

IEEE Transactions on Medical Imaging - 2022

Signal and Image processing

Multivariate analysis with tensors and graphs – application to neuroscience

How to extract knowledge from multivariate data has emerged as a fundamental question in recent years. Indeed, their increasing availability has highlighted the limitations of standard models and the need to move towards more versatile methods. The…

Pierre Humbert