Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Bayesian networks for pattern classification, data compression, and channel coding
Bayesian networks for pattern classification, data compression, and channel coding
Correctness of Local Probability Propagation in Graphical Models with Loops
Neural Computation
On the Convergence of Loopy Belief Propagation Algorithm for Different Update Rules
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Loopy belief propagation and Gibbs measures
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
Active tuples-based scheme for bounding posterior beliefs
Journal of Artificial Intelligence Research
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Belief propagation (BP) algorithm has been becoming increasingly a popular method for probabilistic inference on general graphical models. When networks have loops, it may not converge and, even if converges, beliefs, i.e., the result of the algorithm, may not be equal to exact marginal probabilities. When networks have loops, the algorithm is called Loopy BP (LBP). Tatikonda and Jordan applied Gibbs measures theory to LBP algorithm and derived a sufficient convergence condition. In this paper, we utilize Gibbs measure theory to investigate the discrepancy between a marginal probability and the corresponding belief. Consequently, in particular, we obtain an error bound if the algorithm converges under a certain condition. It is a general result for the accuracy of the algorithm. We also perform numerical experiments to see the effectiveness of the result.