Finding MAPs for belief networks is NP-hard
Artificial Intelligence
On the hardness of approximate reasoning
Artificial Intelligence
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Partial abductive inference in Bayesian belief networks using a genetic algorithm
Pattern Recognition Letters - Special issue on pattern recognition in practice VI
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
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Solving MAP exactly by searching on compiled arithmetic circuits
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Dynamic weighting A* search-based MAP algorithm for Bayesian networks
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Compiling Bayesian networks with local structure
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
MAP complexity results and approximation methods
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Solving MAP exactly using systematic search
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
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The MAP (maximum a posteriori assignment) problem in Bayesian networks is the problem of finding the most probable instantiation of a set of variables given partial evidence for the remaining variables. The state-of-the-art exact solution method is depth-first branch-and-bound search using dynamic variable ordering and a jointree upper bound proposed by Park and Darwiche [2003]. Since almost all search time is spent computing the jointree bounds, we introduce an efficient method for computing these bounds incrementally. We point out that, using a static variable ordering, it is only necessary to compute relevant upper bounds at each search step, and it is also possible to cache potentials of the jointree for efficient backtracking. Since the jointree computation typically produces bounds for joint configurations of groups of variables, our method also instantiates multiple variables at each search step, instead of a single variable, in order to reduce the number of times that upper bounds need to be computed. Experiments show that this approach leads to orders of magnitude reduction in search time.