Fusion, propagation, and structuring in belief networks
Artificial Intelligence
IEEE Transactions on Systems, Man and Cybernetics - Special issue on artificial intelligence
Distributed revision of composite beliefs
Artificial Intelligence
Decision theory in expert systems and artificial intelligence
International Journal of Approximate Reasoning
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Qualitative probabilistic networks for planning under uncertainty
Readings in uncertain reasoning
Probabilistic inference in multiply connected belief networks using loop cutsets
International Journal of Approximate Reasoning
Fundamental concepts of qualitative probabilistic networks
Artificial Intelligence
An Introduction to Algorithms for Inference in Belief Nets
UAI '89 Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence
Qualitative reasoning of Bayesian belief using meta-knowledge
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Symbolic probabilistic inference in belief networks
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
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Finding the l Most Probable Explanations (MPE) of a given evidence, S"e, in a Bayesian belief network can be formulated as identifying and ordering a set of composite hypotheses, H"is, of which the posterior probabilities are the l largest; ie, Pr(H"1|S"e) = ... = Pr(H"1|S"e). When an order includes all the composite hypotheses in the network in order to find all the probable explanations, it becomes a total order and the derivation of such an order has an exponential complexity. The focus of this paper is on the derivation of a partial order, with length l, for finding the l most probable composite hypotheses; where l typically is much smaller than the total number of composite hypotheses in a network. Previously, only the partial order of length two (ie, l = 2) in a singly connected Bayesian network could be efficiently derived without further restriction on network topologies and the increase in spatial complexity. This paper discusses an efficient algorithm for the derivation of the partial ordering of the composite hypotheses in a singly connected network with arbitrary order length. This algorithm is based on the propagation of quantitative vector streams in a feed-forward manner to a designated ''root'' node in a network. The time complexity of the algorithm is in the order of O(lkn); where l is the length of a partial order, k the length of the longest path in a network, and n the maximum number of node states-defined as the product of the size of the conditional probability table of a node and the number of incoming messages towards the node.