Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A linear time algorithm for finding tree-decompositions of small treewidth
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Modeling and Reasoning with Bayesian Networks
Modeling and Reasoning with Bayesian Networks
Complexity results and approximation strategies for MAP explanations
Journal of Artificial Intelligence Research
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Artificial Intelligence
Most probable explanations in Bayesian networks: Complexity and tractability
International Journal of Approximate Reasoning
Solving limited memory influence diagrams
Journal of Artificial Intelligence Research
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
Variational algorithms for marginal MAP
The Journal of Machine Learning Research
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This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.