Year: 2026
Type: article
Abstract: We propose a localized consensus-based method for sampling from non-Gaussian distributions, a task that frequently arises when solving Bayesian inverse problems. Our method arises from an alternative derivation of consensus-based sampling (CBS). Starting from ensemble-preconditioned Langevin dynamics, we replace the potential by its Moreau envelope—a smoother approximation—in order to replace the gradient in the Langevin equation with a proximal operator. We then approximate this operator by a weighted mean. In the limit of infinitely smoothing the potential to a quadratic function, this procedure recovers the standard CBS dynamics. In addition, outside this limit, we retrieve a refined variant of polarized CBS. We call the resulting algorithm localized CBS , since particles interact more with nearby particles than with faraway ones. Our method is affine-invariant, exact for Gaussian targets in the mean-field limit, and demonstrates improved robustness over polarized CBS in numerical experiments. Like other consensus-based methods, localized CBS is gradient-free and easily parallelizable.
Source: Inverse Problems
Institution: KU Leuven
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2630444842, Design and analysis of multilevel interacting-particle methods with surrogate models for efficient Bayesian inversion, G3742396460, Learning to optimize nonconvex problems: provably and efficiently, Taming Nonconvexity in Structured Low-Rank Optimization., From model-based to data-driven: signal processing and control engineering for nonlinear systems
OpenAlex ID: W4414858782
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