Year: 2013
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Pennock, David M., Wellman, Michael P.
Institution: University of Michigan
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G177218894
OpenAlex ID: W1601753016