2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
On the Average Number of Maxima in a Set of Vectors and Applications
Journal of the ACM (JACM)
Artificial Intelligence
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Hill-climbing and branch-and-bound algorithms for exact and approximate inference in credal networks
International Journal of Approximate Reasoning
Safe Reduction Rules for Weighted Treewidth
Algorithmica
Semiring induced valuation algebras: Exact and approximate local computation algorithms
Artificial Intelligence
International Journal of Approximate Reasoning
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 in credal networks: branch-and-bound methods and the A/R+ algorithm
International Journal of Approximate Reasoning
Generalized loopy 2U: A new algorithm for approximate inference in credal networks
International Journal of Approximate Reasoning
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Approximating credal network inferences by linear programming
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Approximation algorithms for max-sum-product problems
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Credal networks relax the precise probability requirement of Bayesian networks, enabling a richer representation of uncertainty in the form of closed convex sets of probability measures. The increase in expressiveness comes at the expense of higher computational costs. In this paper, we present a new variable elimination algorithm for exactly computing posterior inferences in extensively specified credal networks, which is empirically shown to outperform a state-of-the-art algorithm. The algorithm is then turned into a provably good approximation scheme, that is, a procedure that for any input is guaranteed to return a solution not worse than the optimum by a given factor. Remarkably, we show that when the networks have bounded treewidth and bounded number of states per variable the approximation algorithm runs in time polynomial in the input size and in the inverse of the error factor, thus being the first known fully polynomial-time approximation scheme for inference in credal networks.