  We present a novel analysis of the expected risk of weighted majority vote in
multiclass classification. The analysis takes correlation of predictions by
ensemble members into account and provides a bound that is amenable to
efficient minimization, which yields improved weighting for the majority vote.
We also provide a specialized version of our bound for binary classification,
which allows to exploit additional unlabeled data for tighter risk estimation.
In experiments, we apply the bound to improve weighting of trees in random
forests and show that, in contrast to the commonly used first order bound,
minimization of the new bound typically does not lead to degradation of the
test error of the ensemble.
