标题： 基于局部一致的采样算法 显示英文标题

标题： A localized consensus-based sampling algorithm

摘要： 我们开发了一种新颖的相互作用粒子方法，用于从非高斯分布中进行采样。 作为第一步，我们提出了一种新的方法来推导基于共识的采样（CBS）算法，从集合预条件朗之万扩散开始。 我们通过其莫拉维包络近似目标势能，使得朗之万方程中的梯度可以被近似算子代替。 然后我们通过加权均值近似近似算子，并最终假设初始分布和目标分布都是高斯分布，从而得到CBS动力学。 如果我们只保留那些在非高斯设置中可以证明的近似，结果是一种新的相互作用粒子采样方法，我们称之为局部基于共识的采样。 我们证明了我们的算法在平均场设置下对于高斯分布是仿射不变且精确的。 数值测试表明，在仿射不变性和对非高斯分布的性能方面，局部CBS优于其他方法。 显示英文摘要

摘要： We develop a novel interacting-particle method for sampling from non-Gaussian distributions. As a first step, we propose a new way to derive the consensus-based sampling (CBS) algorithm, starting from ensemble-preconditioned Langevin diffusions. We approximate the target potential by its Moreau envelope, such that the gradient in the Langevin equation can be replaced by a proximal operator. We then approximate the proximal operator by a weighted mean, and finally assume that the initial and target distributions are Gaussian, resulting in the CBS dynamics. If we keep only those approximations that can be justified in the non-Gaussian setting, the result is a new interacting-particle method for sampling, which we call localized consensus-based sampling. We prove that our algorithm is affine-invariant and exact for Gaussian distributions in the mean-field setting. Numerical tests illustrate that localized CBS compares favorably to alternative methods in terms of affine-invariance and performance on non-Gaussian distributions.