  We present an adaptation of RNN sequence models to the problem of multi-label
classification for text, where the target is a set of labels, not a sequence.
Previous such RNN models define probabilities for sequences but not for sets;
attempts to obtain a set probability are after-thoughts of the network design,
including pre-specifying the label order, or relating the sequence probability
to the set probability in ad hoc ways.
  Our formulation is derived from a principled notion of set probability, as
the sum of probabilities of corresponding permutation sequences for the set. We
provide a new training objective that maximizes this set probability, and a new
prediction objective that finds the most probable set on a test document. These
new objectives are theoretically appealing because they give the RNN model
freedom to discover the best label order, which often is the natural one (but
different among documents).
  We develop efficient procedures to tackle the computation difficulties
involved in training and prediction. Experiments on benchmark datasets
demonstrate that we outperform state-of-the-art methods for this task.
