IEEE Transactions on Systems, Man and Cybernetics - Special issue on artificial intelligence
On the generation of alternative explanations with implications for belief revision
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
Fusion and propagation with multiple observations in belief networks
Artificial Intelligence
Coping with uncertainty in a control system for navigation and exploration
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 2
A probabilistic model of plan recognition
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
Most probable explanations in Bayesian networks: Complexity and tractability
International Journal of Approximate Reasoning
Efficient enumeration of instantiations in Bayesian networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
An efficient approach for finding the MPE in belief networks
UAI'93 Proceedings of the Ninth international conference on Uncertainty in artificial intelligence
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Finding the l Most Probable Explanations (MPE) of a given evidence, Se, in a Bayesian belief network is a process to identify and order a set of composite hypotheses, HiS, of which the posterior probabilities are the l largest; i.e., Pr(H1|Se) ≥ Pr(H2|Se) ≥ ... ≥ Pr(Hl|Se). A composite hypothesis is defined as an instantiation of all the non-evidence variables in the network. It could be shown that finding all the probable explanations is a NP-hard problem. Previously, only the first two best explanations (i.e., l = 2) in a singly connected Bayesian network could be efficiently derived without restrictions on network topologies and probability distributions. This paper presents an efficient algorithm for finding l (≥ 2) MPE in singly-connected networks and the extension of this algorithm for multiply-connected networks. This algorithm is based on a message passing scheme and has a time complexity O(lkn) for singly-connected networks; where l is the number of MPE to be derived, 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 the incoming/outgoing arcs of the node.