Sampling-based algorithms are classical approaches to perform Bayesian inference in inverse problems. They provide estimators with the associated credibility intervals to quantify the uncertainty on the estimators. Although these methods hardly scale to high dimensional problems, they have recently been paired with optimization techniques, such as proximal and splitting approaches, to address this issue. Such approaches pave the way to distributed samplers, splitting computations to make inference more scalable and faster. We introduce a distributed Split Gibbs sampler (SGS) to efficiently solve such problems involving distributions with multiple smooth and non-smooth functions composed with linear operators. The proposed approach leverages a recent approximate augmentation technique reminiscent of primal-dual optimization methods. It is further combined with a block-coordinate approach to split the primal and dual variables into blocks, leading to a distributed block-coordinate SGS. The resulting algorithm exploits the hypergraph structure of the involved linear operators to efficiently distribute the variables over multiple workers under controlled communication costs. It accommodates several distributed architectures, such as the Single Program Multiple Data and client-server architectures. Experiments on a large image deblurring problem show the performance of the proposed approach to produce high quality estimates with credibility intervals in a small amount of time. Codes to reproduce the experiments are available online.

翻译：基于采样的算法是贝叶斯逆问题推理中的经典方法。这类方法能提供估计器及其相关的置信区间，以量化估计的不确定性。尽管这些方法难以扩展至高维问题，近年来研究者通过结合近端算子与分裂方法等优化技术来应对这一挑战。此类方法为分布式采样器开辟了路径——通过拆分计算任务来提升推理的可扩展性与速度。我们提出一种分布式分裂吉布斯采样器，用于高效求解涉及多个由线性算子组合的平滑与非平滑函数分布的逆问题。该方法借鉴了近期在原始-对偶优化方法中使用的近似增广技术，并进一步结合块坐标法将原始变量与对偶变量划分为块结构，从而形成分布式块坐标分裂吉布斯采样器。最终算法利用线性算子的超图结构，在受控通信成本下将变量高效分配给多个工作节点。该方案兼容多种分布式架构，如单程序多数据流架构与客户端-服务器架构。在大型图像去模糊问题上的实验表明，所提方法能在短时间内生成具有置信区间的高质量估计。实验复现代码已开放获取。