  Curating labeled training data has become the primary bottleneck in machine
learning. Recent frameworks address this bottleneck with generative models to
synthesize labels at scale from weak supervision sources. The generative
model's dependency structure directly affects the quality of the estimated
labels, but selecting a structure automatically without any labeled data is a
distinct challenge. We propose a structure estimation method that maximizes the
$\ell_1$-regularized marginal pseudolikelihood of the observed data. Our
analysis shows that the amount of unlabeled data required to identify the true
structure scales sublinearly in the number of possible dependencies for a broad
class of models. Simulations show that our method is 100$\times$ faster than a
maximum likelihood approach and selects $1/4$ as many extraneous dependencies.
We also show that our method provides an average of 1.5 F1 points of
improvement over existing, user-developed information extraction applications
on real-world data such as PubMed journal abstracts.
