Hierarchy-GBP
A hierarchical abstraction-based acceleration algorithm for Gaussian Belief Propagation. It operates in two stages: constructing a coarse-grained graph approximation to resolve global errors, then reprojecting onto the original graph where GBP corrects local errors. The algorithm provides formal convergence guarantees.
Timeline (last 90 days)
Hierarchy-GBP (H-GBP) is an iterative two-phase framework whose core ideas are abstraction and recovery.
In the abstraction phase, H-GBP first constructs a coarse-grained graph approximation, transforming global errors that would otherwise need to propagate across a large number of nodes into problems solvable over short distances.
In the recovery phase, H-GBP projects the global solution from the coarse graph back onto the original fine-grained graph, then uses standard GBP to refine the remaining local errors.
H-GBP provides a rigorous convergence proof by deriving the combined matrix operator of the abstraction and recovery steps and analyzing its spectral radius to prove convergence to the optimal solution.
The coarse-graph solve in H-GBP eliminates components corresponding to low-frequency modes, making the spectral radius of the combined operator significantly smaller than that of the original GBP operator, thereby theoretically guaranteeing faster convergence.
H-GBP significantly accelerates the solution of large-scale pose graph optimization (PGO).
H-GBP achieves state-of-the-art runtime on bundle adjustment (BA) at all tested scales.
H-GBP's spectral radius analysis framework is highly consistent in approach with the smoothness analysis in multigrid methods.
H-GBP introduces multigrid-style hierarchical thinking into the belief propagation framework while preserving the distributed and parallelizable properties of GBP.
All Facts (9)
Hierarchy-GBP (H-GBP) is an iterative two-phase framework whose core ideas are abstraction and recovery.
50%UnverifiedIn the abstraction phase, H-GBP first constructs a coarse-grained graph approximation, transforming global errors that would otherwise need to propagate across a large number of nodes into problems solvable over short distances.
50%UnverifiedIn the recovery phase, H-GBP projects the global solution from the coarse graph back onto the original fine-grained graph, then uses standard GBP to refine the remaining local errors.
50%UnverifiedH-GBP provides a rigorous convergence proof by deriving the combined matrix operator of the abstraction and recovery steps and analyzing its spectral radius to prove convergence to the optimal solution.
50%UnverifiedThe coarse-graph solve in H-GBP eliminates components corresponding to low-frequency modes, making the spectral radius of the combined operator significantly smaller than that of the original GBP operator, thereby theoretically guaranteeing faster convergence.
50%UnverifiedH-GBP significantly accelerates the solution of large-scale pose graph optimization (PGO).
50%UnverifiedH-GBP achieves state-of-the-art runtime on bundle adjustment (BA) at all tested scales.
50%UnverifiedH-GBP's spectral radius analysis framework is highly consistent in approach with the smoothness analysis in multigrid methods.
50%UnverifiedH-GBP introduces multigrid-style hierarchical thinking into the belief propagation framework while preserving the distributed and parallelizable properties of GBP.
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