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
An optimal approximation algorithm for Bayesian inference
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
A differential approach to inference in Bayesian networks
Journal of the ACM (JACM)
Stochastic Greedy Search: Efficiently Computing a Most Probable Explanation in Bayesian Networks
Stochastic Greedy Search: Efficiently Computing a Most Probable Explanation in Bayesian Networks
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
Understanding the role of noise in stochastic local search: Analysis and experiments
Artificial Intelligence
An Intrusion Plan Recognition Algorithm Based on Max-1-Connected Causal Networks
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part IV: ICCS 2007
Learning Actions through Imitation and Exploration: Towards Humanoid Robots That Learn from Humans
Creating Brain-Like Intelligence
Mendelian error detection in complex pedigrees using weighted constraint satisfaction techniques
Proceedings of the 2007 conference on Artificial Intelligence Research and Development
Diagnosing faults in electrical power systems of spacecraft and aircraft
IAAI'08 Proceedings of the 20th national conference on Innovative applications of artificial intelligence - Volume 3
Optimal value of information in graphical models
Journal of Artificial Intelligence Research
The inferential complexity of Bayesian and credal networks
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
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
Understanding the scalability of Bayesian network inference using clique tree growth curves
Artificial Intelligence
Decision-theoretic Optimal Sampling in Hidden Markov Random Fields
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Probabilistic model-based diagnosis: an electrical power system case study
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans - Special issue on model-based diagnostics
Probabilistic graphical models in artificial intelligence
Applied Soft Computing
Journal of Automated Reasoning
The complexity of finding kth most probable explanations in probabilistic networks
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
On stopping evidence gathering for diagnostic Bayesian networks
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Most probable explanations in Bayesian networks: Complexity and tractability
International Journal of Approximate Reasoning
Most Relevant Explanation: computational complexity and approximation methods
Annals of Mathematics and Artificial Intelligence
Decomposition of multi-operator queries on semiring-based graphical models
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Abductive inference in bayesian networks: finding a partition of the explanation space
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
New complexity results for MAP in Bayesian networks
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Spectral learning for non-deterministic dependency parsing
EACL '12 Proceedings of the 13th Conference of the European Chapter of the Association for Computational Linguistics
Solving limited memory influence diagrams
Journal of Artificial Intelligence Research
The computational complexity of monotonicity in probabilistic networks
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
Same-decision probability: A confidence measure for threshold-based decisions
International Journal of Approximate Reasoning
A review on evolutionary algorithms in Bayesian network learning and inference tasks
Information Sciences: an International Journal
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
An ensemble of Bayesian networks for multilabel classification
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
An exact algorithm for computing the same-decision probability
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Software health management with Bayesian networks
Innovations in Systems and Software Engineering
Variational algorithms for marginal MAP
The Journal of Machine Learning Research
Hi-index | 0.00 |
MAP is the problem of finding a most probable instantiation of a set of variables given evidence. MAP has always been perceived to be significantly harder than the related problems of computing the probability of a variable instantiation (Pr), or the problem of computing the most probable explanation (MPE). This paper investigates the complexity of MAP in Bayesian networks. Specifically, we show that MAP is complete for NPPP and provide further negative complexity results for algorithms based on variable elimination. We also show that MAP remains hard even when MPE and Pr become easy. For example, we show that MAP is NP-complete when the networks are restricted to polytrees, and even then can not be effectively approximated. Given the difficulty of computing MAP exactly, and the difficulty of approximating MAP while providing useful guarantees on the resulting approximation, we investigate best effort approximations. We introduce a generic MAP approximation framework. We provide two instantiations of the framework; one for networks which are amenable to exact inference (Pr), and one for networks for which even exact inference is too hard. This allows MAP approximation on networks that are too complex to even exactly solve the easier problems, Pr and MPE. Experimental results indicate that using these approximation algorithms provides much better solutions than standard techniques, and provide accurate MAP estimates in many cases.