Graphical Representations of Consensus Belief

01/23/2013 ∙ by David M. Pennock, et al. ∙ 0

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.



There are no comments yet.


page 1

page 2

page 3

page 4

page 5

page 8

page 9

page 10

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.