Belief Propagation (BP) is a powerful algorithm for distributed inference in probabilistic graphical models, however it quickly becomes infeasible for practical compute and memory budgets. Many efficient, non-parametric forms of BP have been developed, but the most popular is Gaussian Belief Propagation (GBP), a variant that assumes all distributions are locally Gaussian. GBP is widely used due to its efficiency and empirically strong performance in applications like computer vision or sensor networks - even when modelling non-Gaussian problems. In this paper, we seek to provide a theoretical guarantee for when Gaussian approximations are valid in highly non-Gaussian, sparsely-connected factor graphs performing BP (common in spatial AI). We leverage the Central Limit Theorem (CLT) to prove mathematically that variables' beliefs under BP converge to a Gaussian distribution in complex, loopy factor graphs obeying our 4 key assumptions. We then confirm experimentally that variable beliefs become increasingly Gaussian after just a few BP iterations in a stereo depth estimation task.

翻译：置信传播（BP）是一种用于概率图模型中分布式推理的强大算法，然而其计算与内存需求在实际预算下迅速变得不可行。目前已发展出多种高效的非参数化BP形式，其中最流行的是高斯置信传播（GBP），该变体假设所有分布均为局部高斯分布。GBP因其高效性及在计算机视觉或传感器网络等应用中的经验性强性能而被广泛使用——即使在对非高斯问题进行建模时亦是如此。本文旨在为高度非高斯、稀疏连接的因子图（常见于空间人工智能）执行BP时高斯近似的有效性提供理论保证。我们利用中心极限定理（CLT）从数学上证明：在满足我们提出的四项关键假设的复杂带环因子图中，BP作用下变量的置信度会收敛于高斯分布。随后通过立体深度估计任务的实验验证，变量置信度在仅数次BP迭代后即逐渐趋近高斯分布。