在朗之万动力学中与前向模型的相互作用较小
Less interaction with forward models in Langevin dynamics
摘要：
包围方法已经成为普遍存在的贝叶斯推理问题的解决方案。最先进的Langevin采样器，如Enhancement Kalman Sampler（EKS）、仿射不变Langevin Dynamics（ALDI）或其使用加权协方差估计的扩展依赖于前向模型或其梯度的连续评估。因此，这些方法的主要缺点是它们需要大量的前向调用，以及它们在更复杂的后验测量（例如多峰分布）的情况下可能缺乏收敛。本文的目的是在一定程度上解决这些挑战。首先，几种可能的自适应合奏富集策略，相继扩大粒子的数量在底层的朗之万动力学进行了讨论，反过来又导致显着减少的总数量的前向调用。其次，分析一致性保证的集合富集方法提供了线性正演模型。第三，为了解决更多涉及的目标分布，该方法是通过应用自适应朗之万动力学同伦形式主义的基础上，收敛性证明。最后，几个基准问题的数值研究说明了所提出的方法可能的收益，比较它的国家的最先进的朗之万采样器。
英文摘要：
Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted covariance estimates rely on successive evaluations of the forward model or its gradient. A main drawback of these methods hence is their vast number of required forward calls as well as their possible lack of convergence in the case of more involved posterior measures such as multimodal distributions. The goal of this paper is to address these challenges to some extend. First, several possible adaptive ensemble enrichment strategies that successively enlarge the number of particles in the underlying Langevin dynamics are discusses that in turn lead to a significant reduction of the total number of forward calls. Second, analytical consistency guarantees of the ensemble enrichment method are provided for linear forward models. Third, to address more involved target distributions, the method is extended by applying adapted Langevin dynamics based on a homotopy formalism for which convergence is proved. Finally, numerical investigations of several benchmark problems illustrates the possible gain of the proposed method, comparing it to state-of-the-art Langevin samplers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
