Partial abductive inference in Bayesian belief networks using a genetic algorithm
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
Approximating MAP using Local Search
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Performing Bayesian inference by weighted model counting
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
Exploiting causal independence in Bayesian network inference
Journal of Artificial Intelligence Research
Compiling Bayesian networks with local structure
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Context-specific independence in Bayesian networks
UAI'96 Proceedings of the Twelfth international 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
Solving MAP exactly using systematic search
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial 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
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The MAP (maximum a posteriori hypothesis) problem in Bayesian networks is to find the most likely states of a set of variabls given partial evidence on the complement of that set. Standard structure-based inference methods for finding exact solutions to MAP, such as variable elimination and join-tree algorithms, have complexities that are exponential in the constrained treewidth of the network. A more recent algorithm, proposed by Park and Darwiche, is exponential only in the treewidth and has been shown to handle networks whose constrained treewidth is quite high. In this paper we present a new algorithm for exact MAP that is not necessarily limited in scalability even by the treewidth. This is achieved by leveraging recent advances in compilation of Bayesian networks into arithmetic circuits, which can circumvent treewidth-imposed limits by exploiting the local structure present in the network. Specifically, we implement a branch-and-bound search where the bounds are computed using linear-time operations on the compiled arithmetic circuit. On networks with local structure, we observe orders-of-magnitude improvements over the algorithm of Park and Darwiche. In particular, we are able to efficiently solve many problems where the latter algorithm runs out of memory because of high treewidth.