  This paper addresses the task of set prediction using deep learning. This is
important because the output of many computer vision tasks, including image
tagging and object detection, are naturally expressed as sets of entities
rather than vectors. As opposed to a vector, the size of a set is not fixed in
advance, and it is invariant to the ordering of entities within it. We define a
likelihood for a set distribution and learn its parameters using a deep neural
network. We also derive a loss for predicting a discrete distribution
corresponding to set cardinality. Set prediction is demonstrated on the problem
of multi-class image classification. Moreover, we show that the proposed
cardinality loss can also trivially be applied to the tasks of object counting
and pedestrian detection. Our approach outperforms existing methods in all
three cases on standard datasets.
