发表机构
Imperial College London（伦敦帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出Hierarchy-GBP（H-GBP）框架，通过抽象与恢复两阶段加速高斯信念传播（GBP）的因子图推理，解决全局误差并细化局部误差，显著提升收敛速度，并在位姿图优化和光束法平差中实现最先进性能。
AI 中文摘要
高斯信念传播（GBP）是一种分布式推理算法，通过在图形模型中传递消息，使其成为可扩展空间智能的有吸引力的选择。然而，我们发现GBP在局部最为有效：它能快速平滑在相邻变量之间急剧变化的消息误差，但通过长距离消息传播来逐步纠正跨远距离图区域的全局误差。我们提出Hierarchy-GBP（H-GBP），一种迭代的两阶段框架，通过首先使用粗粒度图近似（抽象）解决这些全局误差，并将结果投影回原始图（恢复），然后用GBP细化剩余的局部误差，从而加速GBP。我们通过推导抽象和恢复步骤的组合矩阵算子并分析其谱半径，证明了H-GBP收敛到最优解。在线性稀疏图上的实验表明，H-GBP的收敛速度从根本上快于标准GBP。此外，我们在两个重要的空间问题上验证了H-GBP：位姿图优化（PGO）和光束法平差（BA）。H-GBP显著加速了大规模PGO，并在所有测试的BA规模上实现了最先进的运行时间。
英文摘要
Gaussian Belief Propagation (GBP) is a distributed inference algorithm that passes messages in graphical models, making it attractive for scalable spatial intelligence. However, we find GBP most effective locally: it rapidly smooths message errors that vary sharply between neighbor variables, but corrects global errors across distant graph regions incrementally through long-range message propagations. We propose Hierarchy-GBP (H-GBP), an iterative, two-stage framework that accelerates GBP by first solving these global errors with a coarse graph approximation (abstraction) and projecting the results back to the original graph (recovery), then refining the remaining local errors with GBP. We prove H-GBP convergence to the optimum by deriving the combined matrix operator of our abstraction and recovery steps and analyzing its spectral radius. Experiments on linear sparse graphs show that H-GBP converges fundamentally faster than standard GBP. Moreover, we validate H-GBP on two important spatial problems: Pose Graph Optimization (PGO) and Bundle Adjustment (BA). H-GBP markedly accelerates large-scale PGO and achieves state-of-the-art runtime across all tested BA scales.
Comments33 pages, 10 figures, including appendices
