  Consider a binary classification problem in which the learner is given a
labeled training set, an unlabeled test set, and is restricted to choosing
exactly $k$ test points to output as positive predictions. Problems of this
kind---{\it transductive precision@$k$}---arise in information retrieval,
digital advertising, and reserve design for endangered species. Previous
methods separate the training of the model from its use in scoring the test
points. This paper introduces a new approach, Transductive Top K (TTK), that
seeks to minimize the hinge loss over all training instances under the
constraint that exactly $k$ test instances are predicted as positive. The paper
presents two optimization methods for this challenging problem. Experiments and
analysis confirm the importance of incorporating the knowledge of $k$ into the
learning process. Experimental evaluations of the TTK approach show that the
performance of TTK matches or exceeds existing state-of-the-art methods on 7
UCI datasets and 3 reserve design problem instances.
