Archive for inverse problems
many folks for manifolds [computational methods for probability distributions on manifolds workshop]
Posted in pictures, Travel, University life with tags bootstrap, experimental design, France, generative model, Gromov-Wasserstein, group picture, IHP, Institut Henri Poincaré, inverse problems, kernel Stein discrepancy descent, manifold, manifold exploration, MCMC, mixture models, Paris, workshop on May 27, 2026 by xi'an
computational methods for probability distributions on manifolds (11-13 May, IHP, Paris)
Posted in Books, pictures, Statistics, Travel, University life with tags bootstrap, experimental design, generative model, Gromov-Wasserstein, IHP, Institut Henri Poincaré, inverse problems, kernel Stein discrepancy descent, manifold, manifold exploration, MCMC, mixture models, Paris, workshop on May 12, 2026 by xi'an
This week, we are running a small workshop on Computational methods for probability distributions on manifolds, whose size was dictated by the corresponding surface of the Institut Henri room allotted to us by the IHP administration. Very exciting theme and very exciting program, which more than make up for the unseasonal weather in Paris.
May 11
Guillaume Pouliot – MCMC on Manifolds in Economics
Alessandro Barp – Kernel and Stein discrepancies between distributions, à la Schwartz
Robin Ryder – Coupling MCMC on manifolds
Chang-Han Rhee – Experimental Design on Manifolds
May 12
Gilles Vilmart – High-order sampling of the invariant distribution of ergodic stochastic dynamics: preconditioning and postprocessing
Paul Breiding – Sampling from or near nonlinear algebraic varieties
Nick Whiteley – Statistical exploration of the Manifold Hypothesis
Judith Rousseau – Denoising diffusion Models under the Manifold Hypothesis : A dimension free convergence rate
Manon Michel – Convergence of non-reversible Markov processes via lifting and Flow Poincaré inequality
Tobias Grafke – Sampling Conditioned Diffusions via Pathspace Projected Monte Carlo
Miranda Holmes-Cerfon – Simulating sticky Brownian motion
Agnès Desolneux – Distances “à la Gromov-Wasserstein” for Gaussian Mixture Models
May 13
Giovanni Samaey – Multilevel interacting particle methods for sampling Bayesian inverse problems
Marylou Gabrié – Revisiting enhanced sampling driven by collective variables using generative models
Chris Walker – A Bayesian Perspective on the Maximum Score Problem
Lulu Kang – Active Learning for Manifold Gaussian Process Regression
mostly Monte Carlo [20/02]
Posted in Statistics with tags #ERCSyG, École Polytechnique, ERC, federated learning, generative prior, Gibbs sampling, inverse problems, machine learning model, MCMC, Ocean, Palaiseau, Paris, PariSanté campus, privacy, Scaffold algorithm, seminar, stochastic gradient on February 16, 2026 by xi'an
A new episode of our mostly Monte Carlo seminar, very soon coming near you (if in Paris):
On Friday 20/02/26, from 3-5pm at PariSanté Campus
15h: Paul Mangold (École Polytechnique, Palaiseau)
Convergence and Linear Speed-Up in Stochastic Federated Learning
In federated learning, multiple users collaboratively train a machine learning model without sharing local data. To reduce communication, users perform multiple local stochastic gradient steps that are then aggregated by a central server. However, due to data heterogeneity, local training introduces bias. In this talk, I will present a novel interpretation of the Federated Averaging algorithm, establishing its convergence to a stationary distribution. By analyzing this distribution, we show that the bias consists of two components: one due to heterogeneity and another due to gradient stochasticity. I will then extend this analysis to the Scaffold algorithm, demonstrating that it effectively mitigates heterogeneity bias but not stochasticity bias. Finally, we show that both algorithms achieve linear speed-up in the number of agents, a key property in federated stochastic optimization.
16h: Alain Durmus (École Polytechnique, Palaiseau)
A Mixture-based Framework for Guiding Diffusion Models
Inverse problems—such as image restoration from noisy or incomplete measurements and musical source separation—are ill-posed, making Bayesian approaches with learned generative priors especially appealing. Diffusion models provide powerful priors, but existing posterior sampling methods often rely on crude likelihood-gradient approximations and heavy task-specific tuning. In this talk, I will introduce a novel principled approach specifically designed to overcome these limitations. The core contribution of this approach is the construction of a mixture approximation of intermediate posterior distributions defined by the diffusion model. The sampling is carried out sequentially via Gibbs sampling, a Markov Chain Monte Carlo method, using a careful data augmentation scheme. Gibbs sampling is employed here due to its simplicity and theoretical guarantees, allowing for exact conditional updates at each iteration, thus ensuring stability and efficiency. One key advantage of the presented algorithm is its flexibility: it adapts to varying levels of computational resources by adjusting the number of Gibbs iterations. Consequently, substantial performance gains can be achieved by increasing inference-time computational effort. I will present extensive experimental results demonstrating empirical performance across diverse image restoration tasks, involving both pixel-space and latent-space diffusion models, and showcase its successful application in musical source separation.
Advances in MCMC Methods [10-12 Dec, EURANDOM]
Posted in Statistics, Travel, University life with tags ABC-MCMC, computational physics, Eindhoven, Eurandom, inverse problems, machine learning, Markov chain Monte Carlo algorithm, Monte Carlo Statistical Methods, the Netherlands, workshop on September 28, 2025 by xi'an
Irène Waldspurger, CNRS bronze medal
Posted in Statistics with tags bois de Boulogne, CNRS, CNRS Bronze Medal, inverse problems, La Défense, machine learning, Université Paris Dauphine on February 14, 2020 by xi'an
My colleague at Paris Dauphine, Irène Waldspurger, got one of the prestigious CNRS bronze medals this year. Irène is working on inverse problems and machine learning, with applications to sensing and imaging. Congrats!
