Bounds and estimates for BP convergence on binary undirected graphical models

Belief Propagation (BP) has become a popular method for inference on graphical models. Accurate approximations for intractable quantities (e.g. single-node marginals) can be obtained within rather modest computation times. However, for large interaction strengths (i.e. potentials that are highly dependent on their arguments) or densely connected graphs, BP can fail to converge. This can be remedied by damping the iteration equations, using sequential update schemes or using entirely different algorithms such as double-loop algorithms, that directly minimize the Bethe free energy. However, the value of this approach is questionable, since there is empirical evidence that failure of convergence of BP often indicates low quality of the Bethe approximation.