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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. 246255, March, 1993.  
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@article{ 10.1109/34.204906, author = {P. Dagum and R.M. Chavez}, title = {Approximating Probabilistic Inference in Bayesian Belief Networks}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {15}, number = {3}, issn = {01628828}, year = {1993}, pages = {246255}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.204906}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Approximating Probabilistic Inference in Bayesian Belief Networks IS  3 SN  01628828 SP246 EP255 EPD  246255 A1  P. Dagum, A1  R.M. Chavez, PY  1993 KW  probabilistic inference approximation; reasoning; Bayesian belief networks; conditional probabilities; stochastic simulation algorithm; DBNRAS; polynomial; Bayes methods; belief maintenance; inference mechanisms; polynomials; probabilistic logic; uncertainty handling VL  15 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
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, DBNRAS, 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 fdependence networks. The run time of DBNRAS 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. 1421.
[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. 5058.
[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. 661685, 1990.
[5] R. Chavez and G. Cooper, "A randomized approximation analysis of logic sampling," inProc. Sixth Conf. Uncertainty Artificial Intell.(Cambridge, MA), 1990, pp. 130135.
[6] G. F. Cooper, "The computational complexity of probabilistic inference using Bayesian belief networks,"Artificial Intell., vol. 42, nos. 23, pp. 393405, 1990.
[7] P. Dagum and E. Horvitz, "Reformulating inference problems through selective conditioning," inProc. Eighth Conf. Uncertainty Artificial Intell.(Stanford, CA), 1992, pp. 4954.
[8] P. Dagum and E. Horvitz, "An analysis of MonteCarlo algorithms for probabilistic inference," Tech. Rep. KSL9167, Knowledge Syst. Lab., Stanford Univ., Stanford, CA, 1991.
[9] P. Dagum and M. Luby, "Approximating probabilistic inference in Bayesian belief networks is NPhard," Tech. Rep. KSL9151, 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. 209219.
[11] M. Henrion, "Propagating uncertainty in Bayesian networks by probabilistic logic sampling," inUncertainty in Artificial Intelligence2. Amsterdam: NorthHolland, 1988, pp. 149163.
[12] M. Jerrum and A. Sinclair, "Approximating the permanent,"SIAM J. Comput., vol. 18, no. 6, pp. 11491178, 1989.
[13] M. Jerrum, L. Valiant, and V. Vazirani, "Random generation of combinatorial structures from a uniform distribution,"Theoretical Comput. Sci., vol. 43, pp. 169188, 1986.
[14] R. Karp, M. Luby, and N. Madras, "MonteCarlo approximation algorithms for enumeration problems,"J. Algorithms, vol. 10, pp. 429448, 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. 245257, 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. 311318.
[20] A. Sinclair and M. Jerrum, "Approximate counting, uniform generation, and rapidly mixing Markov chains,"Inform. Comput., vol. 82, pp. 93133, 1989.
[21] L. Valiant, "The complexity of computing the permanent,"Theoretical Comput. Sci., vol. 8, pp. 189201, 1979.