  Weak supervision (WS) frameworks are a popular way to bypass hand-labeling
large datasets for training data-hungry models. These approaches synthesize
multiple noisy but cheaply-acquired estimates of labels into a set of
high-quality pseudolabels for downstream training. However, the synthesis
technique is specific to a particular kind of label, such as binary labels or
sequences, and each new label type requires manually designing a new synthesis
algorithm. Instead, we propose a universal technique that enables weak
supervision over any label type while still offering desirable properties,
including practical flexibility, computational efficiency, and theoretical
guarantees. We apply this technique to important problems previously not
tackled by WS frameworks including learning to rank, regression, and learning
in hyperbolic space. Theoretically, our synthesis approach produces a
consistent estimators for learning some challenging but important
generalizations of the exponential family model. Experimentally, we validate
our framework and show improvement over baselines in diverse settings including
real-world learning-to-rank and regression problems along with learning on
hyperbolic manifolds.
