Orateur
Description
Interacting particle systems have attracted increasing interest for
sampling and Bayesian inference. They are appealing because they are
well suited to parallel implementation and, in several cases, provide
derivative-free approximations. In this talk, I focus on the Ensemble
Kalman Sampler (EKS), an interacting particle system for sampling that
enjoys a property of invariance with respect to affine transformations.
EKS evolves an ensemble of particles interacting through the empirical
covariance, which acts as an adaptive preconditioner.
Although the mean field limit of EKS is relatively well understood, the
long-time behavior of the finite particle system remains largely open.
We address this gap in the Gaussian setting by first establishing
uniform-in-time quantitative bounds on the distance between the finite
particle system and its mean field limit. We then derive new estimates
on the long-time behavior of the finite particle system, showing that
the distance to the target distribution decreases faster with the number
of particles than might be expected from the mean field limit alone.