Consensus-based sampling

Urbain Vaes (INRIA Paris)

May 19. 2022, 09:15 — 10:00

In the first part of this talk, I will present background material on Bayesian inverse problems, the associated challenges at the numerical level, and gradient-free sampling and optimization approaches for solving them. In the second part, I will present recent work [1] on a novel gradient-free sampling method that is well suited for Bayesian inverse problems. The method is inspired by consensus-based methods in optimization and based on a stochastic interacting particle system. We demonstrate its potential in regimes where the target distribution is unimodal and close to Gaussian. More precisely, we prove that consensus-based sampling enables to recover a Laplace approximation of the measure in certain parametric regimes and provide numerical evidence that this Laplace approximation attracts a large set of initial conditions in a number of examples.


Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)