贝叶斯融合：分布式统计分析的可扩展统一
Bayesian Fusion: Scalable unification of distributed statistical analyses
摘要：
最近有相当大的兴趣在解决统一的分布式统计分析到一个单一的连贯推理的问题。这个问题在许多情况下自然会出现，包括在大数据环境中，在隐私约束下工作时，以及在贝叶斯模型选择中。大多数现有的方法依赖于方便的近似的分布式分析。虽然通常是计算效率高，并容易缩放相对于被统一的分析的数量，近似的方法可以有显着的缺点-推理的质量可以迅速降低与被统一的分析的数量，并可以基本上是有偏见的，即使在统一的少量的分析，不同意。相比之下，Dai等人（2019）最近的Fusion方法是一种拒绝抽样方案，该方案易于并行化且精确（避免除蒙特卡罗误差外的任何形式的近似），尽管其适用性有限，无法统一少量低维分析。在本文中，我们介绍了一个实用的贝叶斯融合方法。我们扩展了融合方法的理论基础，通过将其嵌入到序贯蒙特卡罗算法中，我们能够恢复正确的目标分布。通过对该方法实施的广泛指导，我们从理论上和经验上证明了贝叶斯融合对越来越多的分析具有鲁棒性，并且一致地统一了不一致的分析。这是实现的，而计算上的竞争力与近似方案。
英文摘要：
There has recently been considerable interest in addressing the problem of unifying distributed statistical analyses into a single coherent inference. This problem naturally arises in a number of situations, including in big-data settings, when working under privacy constraints, and in Bayesian model choice. The majority of existing approaches have relied upon convenient approximations of the distributed analyses. Although typically being computationally efficient, and readily scaling with respect to the number of analyses being unified, approximate approaches can have significant shortcomings -- the quality of the inference can degrade rapidly with the number of analyses being unified, and can be substantially biased even when unifying a small number of analyses that do not concur. In contrast, the recent Fusion approach of Dai et al. (2019) is a rejection sampling scheme which is readily parallelisable and is exact (avoiding any form of approximation other than Monte Carlo error), albeit limited in applicability to unifying a small number of low-dimensional analyses. In this paper we introduce a practical Bayesian Fusion approach. We extend the theory underpinning the Fusion methodology and, by embedding it within a sequential Monte Carlo algorithm, we are able to recover the correct target distribution. By means of extensive guidance on the implementation of the approach, we demonstrate theoretically and empirically that Bayesian Fusion is robust to increasing numbers of analyses, and coherently unifying analyses which do not concur. This is achieved while being computationally competitive with approximate schemes.
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。
