We present the Sequential Ensemble Transform (SET) method, an approach for
generating approximate samples from a Bayesian posterior distribution. The
method explores the posterior distribution by solving a sequence of discrete
optimal transport problems to produce a series of transport plans which map
prior samples to posterior samples. We prove that the sequence of Dirac mixture
distributions produced by the SET method converges weakly to the true posterior
as the sample size approaches infinity. Furthermore, our numerical results
indicate that, when compared to standard Sequential Monte Carlo (SMC) methods,
the SET approach is more robust to the choice of Markov mutation kernels and
requires less computational efforts to reach a similar accuracy when used to
explore complex posterior distributions. Finally, we describe adaptive schemes
that allow to completely automate the use of the SET method.

我们提出了顺序集成变换（SET）方法，这是一种从贝叶斯后验分布中生成近似样本的方法，该方法通过解决一系列离散最优传输问题，生成将先验样本映射到后验样本的一系列传输计划。我们证明了 SET 方法产生的 Dirac 混合分布序列在样本大小无限增大时弱收敛至真后验分布，并且数值结果表明，与标准的顺序蒙特卡罗（SMC）方法相比，SET 方法对于马尔科夫突变核的选择更加稳健，并且在探索复杂的后验分布时需要更少的计算量。最后，我们描述了自适应方案，可以完全自动化 SET 方法的使用。

贝叶斯反问题的序列集成变换

Sequential Ensemble Transform for Bayesian Inverse Problems

In this paper, we address the problem of estimating transport surplus (a.k.a.
matching affinity) in high dimensional optimal transport problems. Classical
optimal transport theory specifies the matching affinity and determines the
optimal joint distribution. In contrast, we study the inverse problem of
estimating matching affinity based on the observation of the joint
distribution, using an entropic regularization of the problem. To accommodate
high dimensionality of the data, we propose a novel method that incorporates a
nuclear norm regularization which effectively enforces a rank constraint on the
affinity matrix. The low-rank matrix estimated in this way reveals the main
factors which are relevant for matching.

本文针对高维运输问题中的运输剩余（又称匹配亲和力）估计问题提出了一种基于矩阵核范数正则化的新方法，旨在有效强制亲和力矩阵的秩约束，从而估计出低秩矩阵并揭示与匹配相关的主要因素。