  Combining the outputs of multiple classifiers or experts into a single
probabilistic classification is a fundamental task in machine learning with
broad applications from classifier fusion to expert opinion pooling. Here we
present a hierarchical Bayesian model of probabilistic classifier fusion based
on a new correlated Dirichlet distribution. This distribution explicitly models
positive correlations between marginally Dirichlet-distributed random vectors
thereby allowing explicit modeling of correlations between base classifiers or
experts. The proposed model naturally accommodates the classic Independent
Opinion Pool and other independent fusion algorithms as special cases. It is
evaluated by uncertainty reduction and correctness of fusion on synthetic and
real-world data sets. We show that a change in performance of the fused
classifier due to uncertainty reduction can be Bayes optimal even for highly
correlated base classifiers.
