Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Expert Systems and Probabiistic Network Models
Expert Systems and Probabiistic Network Models
Parametric Structure of Probabilities in Bayesian Networks
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Simulation Approaches to General Probabilistic Inference on Belief Networks
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Weighing and Integrating Evidence for Stochastic Simulation in Bayesian Networks
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
A new characterization of probabilities in Bayesian networks
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
A differential approach to inference in Bayesian networks
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
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The paper presents an efficient goal oriented algorithm for symbolic propagation in Bayesian networks. The proposed algorithm performs symbolic propagation using numerical methods. It first takes advantage of the independence relationships among the variables and produce a reduced graph which contains only the relevant nodes and parameters required to compute the desired propagation. Then, the symbolic expression of the solution is obtained by performing numerical propagations associated with specific values of the symbolic parameters. These specific values are called the canonical components. Substantial savings are obtained with this new algorithm. Furthermore, the canonical components allow us to obtain lower and upper bounds for the symbolic expressions resulting from the propagation. An example is used to illustrate the proposed methodology.