A pivoting algorithm for convex hulls and vertex enumeration of arrangements and polyhedra
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Measures of uncertainty in expert systems
Artificial Intelligence
Artificial Intelligence
Decision making under uncertainty using imprecise probabilities
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
On the Credal Structure of Consistent Probabilities
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Modeling Unreliable Observations in Bayesian Networks by Credal Networks
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
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
Generalized loopy 2U: A new algorithm for approximate inference in credal networks
International Journal of Approximate Reasoning
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Credal sets are closed convex sets of probability mass functions. The lower probabilities specified by a credal set for each element of the power set can be used as constraints defining a second credal set. This simple procedure produces an outer approximation, with a bounded number of extreme points, for general credal sets. The approximation is optimal in the sense that no other lower probabilities can specify smaller supersets of the original credal set. Notably, in order to be computed, the approximation does not need the extreme points of the credal set, but only its lower probabilities. This makes the approximation particularly suited for credal networks, which are a generalization of Bayesian networks based on credal sets. Although most of the algorithms for credal networks updating only return lower posterior probabilities, the suggested approximation can be used to evaluate (as an outer approximation of) the posterior credal set. This makes it possible to adopt more sophisticated decision making criteria, without having to replace existing algorithms. The quality of the approximation is investigated by numerical tests.