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.

[1] https://arxiv.org/abs/2106.02519
 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Organizer(s):
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)