The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
On the generation of alternative explanations with implications for belief revision
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
Complexity classes defined by counting quantifiers
Journal of the ACM (JACM)
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Cost-based abduction and MAP explanation
Artificial Intelligence
Simple characterizations of P(#P) and complete problems
Journal of Computer and System Sciences
Finding MAPs for belief networks is NP-hard
Artificial Intelligence
Approximating MAPs for belief networks is NP-hard and other theorems
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Stochastic Boolean Satisfiability
Journal of Automated Reasoning
Seabreeze Prediction Using Bayesian Networks
PAKDD '01 Proceedings of the 5th Pacific-Asia Conference on Knowledge Discovery and Data Mining
What is the most likely diagnosis?
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
A review of explanation methods for Bayesian networks
The Knowledge Engineering Review
Monotonicity in Bayesian networks
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Inference and Learning in Multi-dimensional Bayesian Network Classifiers
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Bayesian Networks and Decision Graphs
Bayesian Networks and Decision Graphs
Complexity results and approximation strategies for MAP explanations
Journal of Artificial Intelligence Research
The computational complexity of probabilistic planning
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
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
Reasoning MPE to multiply connected belief networks using message passing
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
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
Multi-dimensional classification with Bayesian networks
International Journal of Approximate Reasoning
Defining explanation in probabilistic systems
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Probabilities for a probabilistic network: a case study in oesophageal cancer
Artificial Intelligence in Medicine
New complexity results for MAP in Bayesian networks
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
Parameterized Complexity in Cognitive Modeling
The Computer Journal
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Structure approximation of most probable explanations in bayesian networks
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Energy distribution view for monotonic dual decomposition
International Journal of Approximate Reasoning
| Hi-index | 0.00 |
One of the key computational problems in Bayesian networks is computing the maximal posterior probability of a set of variables in the network, given an observation of the values of another set of variables. In its most simple form, this problem is known as the MPE-problem. In this paper, we give an overview of the computational complexity of many problem variants, including enumeration variants, parameterized problems, and approximation strategies to the MPE-problem with and without additional (neither observed nor explained) variables. Many of these complexity results appear elsewhere in the literature; other results have not been published yet. The paper aims to provide a fairly exhaustive overview of both the known and new results.