A Unified Approach to Count-Based Weakly Supervised Learning

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 weakly-labeled data, which we call *count-based weakly-supervised learning*. At the heart of our approach is the ability to compute the probability of exactly k out of n outputs being set to true. This computation is differentiable, exact, and efficient.