Circular Belief Propagation for Approximate Probabilistic Inference

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.