Loopy Belief Propagation for Approximate Inference: An Empirical Study

Recently, researchers have demonstrated that "loopy belief propagation" -- the use of Pearl's polytree algorithm in a Bayesian network with loops -- can perform well in the context of error-correcting codes. The most dramatic instance of this is the near Shannon-limit performance of "Turbo Codes" -- codes whose decoding algorithm is equivalent to loopy belief propagation in a chain-structured Bayesian network. In this paper we ask: is there something special about the error-correcting code context, or does loopy propagation work as an approximate inference scheme in a more general setting? We compare the marginals computed using loopy propagation to the exact ones in four Bayesian network architectures, including two real-world networks: ALARM and QMR. We find that the loopy beliefs often converge and when they do, they give a good approximation to the correct marginals. However, on the QMR network, the loopy beliefs oscillated and had no obvious relationship to the correct posteriors. We present some initial investigations into the cause of these oscillations, and show that some simple methods of preventing them lead to the wrong results.