  Belief Propagation (BP) is a simple probabilistic inference algorithm,
consisting of passing messages between nodes of a graph representing a
probability distribution. Its analogy with a neural network suggests that it
could have far-ranging applications for neuroscience and artificial
intelligence. Unfortunately, it is only exact when applied to cycle-free
graphs, which restricts the potential of the algorithm. In this paper, we
propose Circular Belief Propagation (CBP), an extension of BP which limits the
detrimental effects of message reverberation caused by cycles by learning to
detect and cancel spurious correlations and belief amplifications. We show in
numerical experiments involving binary probabilistic graphs that CBP far
outperforms BP and reaches good performance compared to that of previously
proposed algorithms.
