Finding MAPs for belief networks is NP-hard
Artificial Intelligence
Decision-theoretic troubleshooting
Communications of the ACM
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)
A Comparison of Annealing Techniques for Academic Course Scheduling
PATAT '97 Selected papers from the Second International Conference on Practice and Theory of Automated Timetabling II
Relevance-Based Sequential Evidence Processing in Bayesian Networks
Proceedings of the Eleventh International Florida Artificial Intelligence Research Society Conference
Approximating MAP using Local Search
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in 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
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
A general framework for generating multivariate explanations in Bayesian networks
AAAI'08 Proceedings of the 23rd 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
An MCMC approach to solving hybrid factored MDPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Efficient computation of jointree bounds for systematic MAP search
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Large-scale cross-document coreference using distributed inference and hierarchical models
HLT '11 Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies - Volume 1
Most Relevant Explanation: computational complexity and approximation methods
Annals of Mathematics and Artificial Intelligence
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Variational algorithms for marginal MAP
The Journal of Machine Learning Research
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Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22], even for constrained networks, such as polytrees [18]. Hence, previous approaches often fail to yield any results for MAP problems in large complex Bayesian networks. To address this problem, we propose ANNEALEDMAP algorithm, a simulated annealing-based MAP algorithm. The ANNEALEDMAP algorithm simulates a non-homogeneous Markov chain whose invariant function is a probability density that concentrates itself on the modes of the target density. We tested this algorithm on several real Bayesian networks. The results show that, while maintaining good quality of the MAP solutions, the ANNEALEDMAP algorithm is also able to solve many problems that are beyond the reach of previous approaches.