Partial abductive inference in Bayesian belief networks using a genetic algorithm
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Mini-buckets: A general scheme for bounded inference
Journal of the ACM (JACM)
Approximating MAP using Local Search
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
MAP complexity results and approximation methods
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Bucket elimination: a unifying framework for probabilistic inference
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Probabilistic maximum error modeling for unreliable logic circuits
Proceedings of the 17th ACM Great Lakes symposium on VLSI
On probabilistic inference by weighted model counting
Artificial Intelligence
Solving MAP exactly by searching on compiled arithmetic circuits
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Solving factored MDPs with hybrid state and action variables
Journal of Artificial Intelligence Research
Dynamic weighting A* search-based MAP algorithm for Bayesian networks
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
A new d-DNNF-based bound computation algorithm for functional E-MAJSAT
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Efficient computation of jointree bounds for systematic MAP search
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Abductive inference in bayesian networks: finding a partition of the explanation space
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Approximation algorithms for max-sum-product problems
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given some partial evidence about the complement of that set. Unlike posterior probabilities, or MPE (a special case of MAP), the time and space complexity of structure-based algorithms for MAP are not only exponential in the network treewidth, but in a larger parameter known as the constrained treewidth. In practice, this means that computing MAP can be orders of magnitude more expensive than computing posterior probabilities or MPE. We introduce in this paper a new, simple upper bound on the probability of a MAP solution, which is shown to be generally much tighter than existing bounds. We then use the proposed upper bound to develop a branch-andbound search algorithm for solving MAP exactly. Experimental results demonstrate that the search algorithm is able to solve many problems that are far beyond the reach of any structurebased method for MAP. For example, we show that the proposed algorithm can compute MAP exactly and efficiently for some networks whose constrained treewidth is more than 40.