Fast learning from label proportions with small bags.

In learning from label proportions (LLP), the instances are grouped into bags, compared with supervised learning 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 designing more efficient algorithms by explicitly considering all consistent label combinations. In particular, we propose an EM algorithm alternating between optimizing a general neural network instance classifier and incorporating bag-level annotations. In comparison to existing deep LLP methods, our approach converges faster to a comparable or better solution. Several experiments were performed on two different datasets.