Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
Artificial Intelligence
Updating beliefs with incomplete observations
Artificial Intelligence
Graphoid properties of epistemic irrelevance and independence
Annals of Mathematics and Artificial Intelligence
Epistemic irrelevance on sets of desirable gambles
Annals of Mathematics and Artificial Intelligence
Computing lower and upper expectations under epistemic independence
International Journal of Approximate Reasoning
Notes on conditional previsions
International Journal of Approximate Reasoning
Decision making under uncertainty using imprecise probabilities
International Journal of Approximate Reasoning
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
A survey of the theory of coherent lower previsions
International Journal of Approximate Reasoning
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
Learning Reliable Classifiers From Small or Incomplete Data Sets: The Naive Credal Classifier 2
The Journal of Machine Learning Research
Artificial Intelligence
Updating coherent previsions on finite spaces
Fuzzy Sets and Systems
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
Imprecise markov chains and their limit behavior
Probability in the Engineering and Informational Sciences
The inferential complexity of Bayesian and credal networks
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
International Journal of Approximate Reasoning
Artificial Intelligence
Updating credal networks is approximable in polynomial time
International Journal of Approximate Reasoning
Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research
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We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm's operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.