Ensemble Kalman Sampler: mean-field limit and convergence analysis

Ensemble Kalman Sampler (EKS) is a method to find approximately \(i.i.d.\) samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The continuous version of the algorithm is a set of coupled stochastic differential equations (SDEs). In this pa...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Ding, Zhiyan, Li, Qin
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 21.08.2020
Subjects
Algorithms
Convergence
Fokker-Planck equation
Sampling
Online AccessGet full text

Cover

More Information
Summary:Ensemble Kalman Sampler (EKS) is a method to find approximately \(i.i.d.\) samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The continuous version of the algorithm is a set of coupled stochastic differential equations (SDEs). In this paper, we prove the wellposedness of the SDE system, justify its mean-field limit is a Fokker-Planck equation, whose long time equilibrium is the target distribution. We further demonstrate that the convergence rate is near-optimal (\(J^{-1/2}\), with \(J\) being the number of particles). These results, combined with the in-time convergence of the Fokker-Planck equation to its equilibrium, justify the validity of EKS, and provide the convergence rate as a sampling method.
ISSN:2331-8422