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17 April 2008 Convergence study of message passing in arbitrary continuous Bayesian networks
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Abstract
Pearl's traditional message passing algorithm developed in 1980s is the first exact inference algorithm for Bayesian networks (BNs). Although it originally was developed for discrete polytree networks only, it has been used widely in networks with loops by providing approximate solutions. In such case, messages propagated in the loops are not exact and this method is called loopy belief propagation. Loopy propagation usually converges and when it converges, it provides good approximate solutions. However, when dealing with arbitrary continuous Bayesian networks, message representations and manipulations need special cares because continuous vairables may have arbitrary distributions and their dependency relationships could be nonlinear. In this paper, we propose a loopy message passing mechanism for arbitrary continuous Bayesian networks called Unscented Message Passing (UMP-BN). UMP-BN combines Pearl's algorithm and an efficient nonlinear transformation technique called Unscented Transformation to provide estimates of the first two moments of the posterior distributions for any hidden continuous variable. We study its convergence properties by investigating various typical situations with different networks. The numerical experiments show promising results.
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Wei Sun and K. C. Chang "Convergence study of message passing in arbitrary continuous Bayesian networks", Proc. SPIE 6968, Signal Processing, Sensor Fusion, and Target Recognition XVII, 69680Z (17 April 2008); https://doi.org/10.1117/12.780626
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