Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic inference and influence diagrams
Operations Research
Probabilistic reasoning in expert systems: theory and algorithms
Probabilistic reasoning in expert systems: theory and algorithms
The topological fusion of Bayes nets
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
Methods for combining experts' probability assessments
Neural Computation
Introduction to Bayesian Networks
Introduction to Bayesian Networks
Directed reduction algorithms and decomposable graphs
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
A Theory of Frame Transformations for Belief Combination
Annals of Mathematics and Artificial Intelligence
Graphical Models for Groups: Belief Aggregation and Risk Sharing
Decision Analysis
An application of formal argumentation: Fusing Bayesian networks in multi-agent systems
Artificial Intelligence
Journal of Biomedical Informatics
Parallel BMDA with an aggregation of probability models
CEC'09 Proceedings of the Eleventh conference on Congress on Evolutionary Computation
Compact securities markets for pareto optimal reallocation of risk
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Aggregating learned probabilistic beliefs
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
Finding consensus Bayesian network structures
Journal of Artificial Intelligence Research
DemocraticOP: A Democratic way of aggregating Bayesian network parameters
International Journal of Approximate Reasoning
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Graphical models based on conditional independence support concise encodings of the subjective belief of a single agent. A natural question is whether the consensus belief of a group of agents can be represented with equal parsimony. We prove, under relatively mild assumptions, that even if everyone agrees on a common graph topology, no method of combining beliefs can maintain that structure. Even weaker conditions rule out local aggregation within conditional probability tables. On a more positive note, we show that if probabilities are combined with the logarithmic opinion pool (LogOP), then commonly held Markov independencies are maintained. This suggests a straightforward procedure for constructing a consensus Markov network. We describe an algorithm for computing the LogOP with time complexity comparable to that of exact Bayesian inference.