High-quality labels are often very scarce, whereas unlabeled data with inferred weak labels occurs more naturally. In many cases, these weak labels dictate the frequency of each respective class over a set of instances. In this paper, we develop a unified approach to learning from such weak supervision, which we call *count-based weakly supervised learning*. At the heart of our approach lies the ability to compute the probability of exactly k out of n outputs being set to true. This computation…