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Approximating Probabilistic Inference in Bayesian Belief Networks
March 1993 (vol. 15 no. 3)
pp. 246-255

A belief network comprises a graphical representation of dependencies between variables of a domain and a set of conditional probabilities associated with each dependency. Unless rho =NP, an efficient, exact algorithm does not exist to compute probabilistic inference in belief networks. Stochastic simulation methods, which often improve run times, provide an alternative to exact inference algorithms. Such a stochastic simulation algorithm, D-BNRAS, which is a randomized approximation scheme is presented. To analyze the run time, belief networks are parameterized, by the dependence value D/sub xi /, which is a measure of the cumulative strengths of the belief network dependencies given background evidence xi . This parameterization defines the class of f-dependence networks. The run time of D-BNRAS is polynomial when f is a polynomial function. Thus, the results prove the existence of a class of belief networks for which inference approximation is polynomial and, hence, provably faster than any exact algorithm.

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Index Terms:
probabilistic inference approximation; reasoning; Bayesian belief networks; conditional probabilities; stochastic simulation algorithm; D-BNRAS; polynomial; Bayes methods; belief maintenance; inference mechanisms; polynomials; probabilistic logic; uncertainty handling
Citation:
P. Dagum, R.M. Chavez, "Approximating Probabilistic Inference in Bayesian Belief Networks," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 3, pp. 246-255, March 1993, doi:10.1109/34.204906
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