Graphical Representations of Consensus Belief
David Pennock, Michael Wellman
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.
Keywords: combination of models, consensus Bayesian networks,
Markov networks, opinion pools,
PS Link: http://www.eecs.umich.edu/~dpennock/homepage/papers/consensus-bn-final.ps
PDF Link: /papers/99/p531-pennock.pdf
AUTHOR = "David Pennock
and Michael Wellman",
TITLE = "Graphical Representations of Consensus Belief",
BOOKTITLE = "Proceedings of the Fifteenth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-99)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1999",
PAGES = "531--540"