  Weak supervision is a popular method for building machine learning models
without relying on ground truth annotations. Instead, it generates
probabilistic training labels by estimating the accuracies of multiple noisy
labeling sources (e.g., heuristics, crowd workers). Existing approaches use
latent variable estimation to model the noisy sources, but these methods can be
computationally expensive, scaling superlinearly in the data. In this work, we
show that, for a class of latent variable models highly applicable to weak
supervision, we can find a closed-form solution to model parameters, obviating
the need for iterative solutions like stochastic gradient descent (SGD). We use
this insight to build FlyingSquid, a weak supervision framework that runs
orders of magnitude faster than previous weak supervision approaches and
requires fewer assumptions. In particular, we prove bounds on generalization
error without assuming that the latent variable model can exactly parameterize
the underlying data distribution. Empirically, we validate FlyingSquid on
benchmark weak supervision datasets and find that it achieves the same or
higher quality compared to previous approaches without the need to tune an SGD
procedure, recovers model parameters 170 times faster on average, and enables
new video analysis and online learning applications.
