Adaptive Probabilistic Networks with Hidden Variables
Machine Learning - Special issue on learning with probabilistic representations
2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
Hill-climbing and branch-and-bound algorithms for exact and approximate inference in credal networks
International Journal of Approximate Reasoning
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 in polytrees with sets of probabilities
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
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
Updating credal networks is approximable in polynomial time
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
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Credal networks generalize Bayesian networks by relaxing the requirement of precision of probabilities. Credal networks are considerably more expressive than Bayesian networks, but this makes belief updating NP-hard even on polytrees. We develop a new efficient algorithm for approximate belief updating in credal networks. The algorithm is based on an important representation result we prove for general credal networks: that any credal network can be equivalently reformulated as a credal network with binary variables; moreover, the transformation, which is considerably more complex than in the Bayesian case, can be implemented in polynomial time. The equivalent binary credal network is then updated by L2U, a loopy approximate algorithm for binary credal networks. Overall, we generalize L2U to non-binary credal networks, obtaining a scalable algorithm for the general case, which is approximate only because of its loopy nature. The accuracy of the inferences with respect to other state-of-the-art algorithms is evaluated by extensive numerical tests.