  A popular approach to decrease the need for costly manual annotation of large
data sets is weak supervision, which introduces problems of noisy labels,
coverage and bias. Methods for overcoming these problems have either relied on
discriminative models, trained with cost functions specific to weak
supervision, and more recently, generative models, trying to model the output
of the automatic annotation process. In this work, we explore a novel direction
of generative modeling for weak supervision: Instead of modeling the output of
the annotation process (the labeling function matches), we generatively model
the input-side data distributions (the feature space) covered by labeling
functions. Specifically, we estimate a density for each weak labeling source,
or labeling function, by using normalizing flows. An integral part of our
method is the flow-based modeling of multiple simultaneously matching labeling
functions, and therefore phenomena such as labeling function overlap and
correlations are captured. We analyze the effectiveness and modeling
capabilities on various commonly used weak supervision data sets, and show that
weakly supervised normalizing flows compare favorably to standard weak
supervision baselines.
