  In learning from label proportions (LLP), the instances are grouped into
bags, and the task is to learn an instance classifier given relative class
proportions in training bags. LLP is useful when obtaining individual instance
labels is impossible or costly.
  In this work, we focus on the case of small bags, which allows to design an
algorithm that explicitly considers all consistent instance label combinations.
In particular, we propose an EM algorithm alternating between optimizing a
general neural network instance classifier and incorporating bag-level
annotations. Using two different image datasets, we experimentally compare this
method with an approach based on normal approximation and two existing LLP
methods. The results show that our approach converges faster to a comparable or
better solution.
