Abstract
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.
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Cite this article
APA 7
Cheng, Y., Yates, T., Alzugaray, I., Akarca, D., Mediano, P. A. M., & Davison, A. J. (2026). Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery. https://omanscience.com/en/articles/hierarchy-gbp-accelerating-factor-graph-inference-via-abstraction-and-recovery
MLA 9
Cheng, Yuzhou, et al. "Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery." https://omanscience.com/en/articles/hierarchy-gbp-accelerating-factor-graph-inference-via-abstraction-and-recovery.
Chicago (author–date)
Cheng, Yuzhou, Tom Yates, Ignacio Alzugaray, Danyal Akarca, Pedro A. M. Mediano, and Andrew J. Davison. 2026. "Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery." https://omanscience.com/en/articles/hierarchy-gbp-accelerating-factor-graph-inference-via-abstraction-and-recovery.
Harvard
Cheng, Y., Yates, T., Alzugaray, I., Akarca, D., Mediano, P. A. M. and Davison, A. J. (2026) 'Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery', Available at: https://omanscience.com/en/articles/hierarchy-gbp-accelerating-factor-graph-inference-via-abstraction-and-recovery.
Vancouver
Cheng Y, Yates T, Alzugaray I, Akarca D, Mediano PAM, Davison AJ. Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery. https://omanscience.com/en/articles/hierarchy-gbp-accelerating-factor-graph-inference-via-abstraction-and-recovery
IEEE
Y. Cheng, T. Yates, I. Alzugaray, D. Akarca, P. A. M. Mediano, and A. J. Davison, "Hierarchy-GBP: Accelerating Factor Graph Inference via Abstraction and Recovery," https://omanscience.com/en/articles/hierarchy-gbp-accelerating-factor-graph-inference-via-abstraction-and-recovery.