The complexity of Markov decision processes
Mathematics of Operations Research
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
On the hardness of approximate reasoning
Artificial Intelligence
Initial experiments in stochastic satisfiability
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
Artificial Intelligence - special issue on computational tradeoffs under bounded resources
Stochastic Boolean Satisfiability
Journal of Automated Reasoning
Approximating MAP using Local Search
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
The computational complexity of probabilistic planning
Journal of Artificial Intelligence Research
Loopy belief propagation for approximate inference: an empirical study
UAI'99 Proceedings of the Fifteenth 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
Mini-buckets: A general scheme for bounded inference
Journal of the ACM (JACM)
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
Complexity of probabilistic reasoning in directed-path singly-connected Bayes networks
Artificial Intelligence
A differential semantics for jointree algorithms
Artificial Intelligence
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Monotonicity in Bayesian networks
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Force deployment analysis with generalized grammar
Information Fusion
Towards efficient sampling: exploiting random walk strategies
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
A general framework for generating multivariate explanations in Bayesian networks
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
From sampling to model counting
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Dynamic weighting A* search-based MAP algorithm for Bayesian networks
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
The inferential complexity of Bayesian and credal networks
IJCAI'05 Proceedings of the 19th international joint conference on 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
Leveraging belief propagation, backtrack search, and statistics for model counting
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Solving MAP exactly using systematic search
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Argumentation in bayesian belief networks
ArgMAS'04 Proceedings of the First international conference on Argumentation in Multi-Agent Systems
On the combination of logical and probabilistic models for information analysis
Applied Intelligence
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MAP is the problem of nding a most probable instantiation of a set of variables in a Bayesian network, given some evidence. MAP appears to be a signi cantly harder problem than the related problems of computing the probability of evidence (Pr), or MPE (a special case of MAP). Because of the complexity of MAP, and the lack of viable algorithms to approximate it, MAP computations are generally avoided by practitioners. This paper investigates the complexity of MAP. We show that MAP is complete for NPPP. We also provide negative complexity results for elimination based algorithms. It turns out that MAP remains hard even when MPE, and Pr are easy. We show that MAP is NP-complete when the networks are restricted to polytrees, and even then can not be e ectively approximated. Because there is no approximation algorithm with guaranteed results, we investigate best effort approximations. We introduce a generic MAP approximation framework. As one instantiation of it, we implement local search coupled with belief propagation (BP) to approximate MAP. We show how to extract approximate evidence retraction information from belief propagation which allows us to perform e cient local search. This allows MAP approximation even on networks that are too complex to even exactly solve the easier problems of computing Pr or MPE. Experimental results indicate that using BP and local search provides accurate MAP estimates in many cases.