  We consider training probabilistic classifiers in the case of a large number
of classes. The number of classes is assumed too large to perform exact
normalisation over all classes. To account for this we consider a simple
approach that directly approximates the likelihood. We show that this simple
approach works well on toy problems and is competitive with recently introduced
alternative non-likelihood based approximations. Furthermore, we relate this
approach to a simple ranking objective. This leads us to suggest a specific
setting for the optimal threshold in the ranking objective.
