  Learning from label proportions (LLP) is a weakly supervised setting for
classification in which unlabeled training instances are grouped into bags, and
each bag is annotated with the proportion of each class occurring in that bag.
Prior work on LLP has yet to establish a consistent learning procedure, nor
does there exist a theoretically justified, general purpose training criterion.
In this work we address these two issues by posing LLP in terms of mutual
contamination models (MCMs), which have recently been applied successfully to
study various other weak supervision settings. In the process, we establish
several novel technical results for MCMs, including unbiased losses and
generalization error bounds under non-iid sampling plans. We also point out the
limitations of a common experimental setting for LLP, and propose a new one
based on our MCM framework.
