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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.

[1] C. Berzuini, R. Bellazzi, and S. Quaglini, "Temporal reasoning with probabilities," inProc. 1989 Workshop Uncertainty Artificial Intell.(Windsor, Canada), 1989, pp. 14-21.
[2] A. Broder, "How hard is it to marry at random? (On the approximation of the permanent)," inProc. Eighteenth ACM Symp. Theory Comput., 1986, pp. 50-58.
[3] R. Chavez, "Architectures and approximation algorithms for probabilistic expert systems," Ph.D. thesis, Medical Comput. Sci. Group, Stanford Univ., Stanford, CA, 1990.
[4] R. Chavez and G. Cooper, "A randomized approximation algorithm for probabilistic inference on Bayesian belief networks,"Networks, vol. 20, pp. 661-685, 1990.
[5] R. Chavez and G. Cooper, "A randomized approximation analysis of logic sampling," inProc. Sixth Conf. Uncertainty Artificial Intell.(Cambridge, MA), 1990, pp. 130-135.
[6] G. F. Cooper, "The computational complexity of probabilistic inference using Bayesian belief networks,"Artificial Intell., vol. 42, nos. 2-3, pp. 393-405, 1990.
[7] P. Dagum and E. Horvitz, "Reformulating inference problems through selective conditioning," inProc. Eighth Conf. Uncertainty Artificial Intell.(Stanford, CA), 1992, pp. 49-54.
[8] P. Dagum and E. Horvitz, "An analysis of Monte-Carlo algorithms for probabilistic inference," Tech. Rep. KSL-91-67, Knowledge Syst. Lab., Stanford Univ., Stanford, CA, 1991.
[9] P. Dagum and M. Luby, "Approximating probabilistic inference in Bayesian belief networks is NP-hard," Tech. Rep. KSL-91-51, Knowledge Syst. Lab., Stanford Univ., Stanford, CA, 1991.
[10] R. Fung and K. -C. Chang, "Weighing and integrating evidence for stochastic simulation in Bayesian networks," inUncertainty in Artificial Intelligence5. Amsterdam: Elsevier, 1990, pp. 209-219.
[11] M. Henrion, "Propagating uncertainty in Bayesian networks by probabilistic logic sampling," inUncertainty in Artificial Intelligence2. Amsterdam: North-Holland, 1988, pp. 149-163.
[12] M. Jerrum and A. Sinclair, "Approximating the permanent,"SIAM J. Comput., vol. 18, no. 6, pp. 1149-1178, 1989.
[13] M. Jerrum, L. Valiant, and V. Vazirani, "Random generation of combinatorial structures from a uniform distribution,"Theoretical Comput. Sci., vol. 43, pp. 169-188, 1986.
[14] R. Karp, M. Luby, and N. Madras, "Monte-Carlo approximation algorithms for enumeration problems,"J. Algorithms, vol. 10, pp. 429-448, 1989.
[15] J. Pearl, "Addendum: Evidential reasoning using stochastic simulation of causal models,"Artificial Intell., vol. 33, pp. 131, 1987.
[16] J. Pearl, "Evidential reasoning using stochastic simulation of causal models,"Artificial Intell., vol. 32, pp. 245-257, 1987.
[17] J. Pearl,Probabilistic Reasoning in Intelligent Systems. San Mateo, CA: Morgan Kaufmann, 1988.
[18] R. Shachter and M. Peot, "Evidential reasoning using likelihood weighting," to be published inArtificial Intell.
[19] R. D. Shachter and M. A. Peot, "Simulation approaches to general probabilistic inference on belief networks," inProc. Fifth Workshop Uncertainty Artificial Intell.(Los Altos, CA), 1989, pp. 311-318.
[20] A. Sinclair and M. Jerrum, "Approximate counting, uniform generation, and rapidly mixing Markov chains,"Inform. Comput., vol. 82, pp. 93-133, 1989.
[21] L. Valiant, "The complexity of computing the permanent,"Theoretical Comput. Sci., vol. 8, pp. 189-201, 1979.

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
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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