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. Supplementary material to reproduce the experiments is available online.

翻译：基于采样的算法是进行逆问题贝叶斯推断的经典方法。它们能够提供估计量及相关的置信区间，以量化估计量的不确定性。尽管这些方法难以扩展到高维问题，但近期已与优化技术（如近端方法和分裂方法）相结合以解决此问题。这类方法为分布式采样器开辟了道路，通过拆分计算使推断更具可扩展性和更快速度。我们提出一种分布式分裂吉布斯采样器，用以高效求解涉及多个与线性算子组合的光滑和非光滑函数分布的问题。所提方法借鉴了近期类似原始-对偶优化方法的近似增广技术，并进一步与块坐标法相结合，将原始变量和对偶变量拆分为多个块，从而形成分布式块坐标分裂吉布斯采样器。该算法利用所涉及线性算子的超图结构，在可控通信成本下将变量高效分配至多个工作节点，并支持多种分布式架构（如单程序多数据架构和客户端-服务器架构）。在大型图像去模糊问题上的实验表明，所提方法能够在短时间内产生具有置信区间的高质量估计结果。提供可在线获取的补充材料以复现实验。