Statistical analysis with missing data
Statistical analysis with missing data
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Fundamental concepts of qualitative probabilistic networks
Artificial Intelligence
2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
Artificial Intelligence
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Strong Conditional Independence for Credal Sets
Annals of Mathematics and Artificial Intelligence
Equivalence and synthesis of causal models
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Updating beliefs with incomplete observations
Artificial Intelligence
Fast algorithms for robust classification with Bayesian nets
International Journal of Approximate Reasoning
Binarization Algorithms for Approximate Updating in Credal Nets
Proceedings of the 2006 conference on STAIRS 2006: Proceedings of the Third Starting AI Researchers' Symposium
The inferential complexity of Bayesian and credal networks
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Graphical models for imprecise probabilities
International Journal of Approximate Reasoning
Inference with separately specified sets of probabilities in credal networks
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Artificial Intelligence
Credal networks for military identification problems
International Journal of Approximate Reasoning
Modeling Unreliable Observations in Bayesian Networks by Credal Networks
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
Generalized loopy 2U: A new algorithm for approximate inference in credal networks
International Journal of Approximate Reasoning
Credal sets approximation by lower probabilities: application to credal networks
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Putting humans in the loop: Social computing for Water Resources Management
Environmental Modelling & Software
Updating credal networks is approximable in polynomial time
International Journal of Approximate Reasoning
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Credal networks are models that extend Bayesian nets to deal with imprecision in probability, and can actually be regarded as sets of Bayesian nets. Credal nets appear to be powerful means to represent and deal with many important and challenging problems in uncertain reasoning. We give examples to show that some of these problems can only be modeled by credal nets called non-separately specified. These, however, are still missing a graphical representation language and updating algorithms. The situation is quite the opposite with separately specified credal nets, which have been the subject of much study and algorithmic development. This paper gives two major contributions. First, it delivers a new graphical language to formulate any type of credal network, both separately and non-separately specified. Second, it shows that any non-separately specified net represented with the new language can be easily transformed into an equivalent separately specified net, defined over a larger domain. This result opens up a number of new outlooks and concrete outcomes: first of all, it immediately enables the existing algorithms for separately specified credal nets to be applied to non-separately specified ones. We explore this possibility for the 2U algorithm: an algorithm for exact updating of singly connected credal nets, which is extended by our results to a class of non-separately specified models. We also consider the problem of inference on Bayesian networks, when the reason that prevents some of the variables from being observed is unknown. The problem is first reformulated in the new graphical language, and then mapped into an equivalent problem on a separately specified net. This provides a first algorithmic approach to this kind of inference, which is also proved to be NP-hard by similar transformations based on our formalism.