  Programmatic Weak Supervision (PWS) aggregates the source votes of multiple
weak supervision sources into probabilistic training labels, which are in turn
used to train an end model. With its increasing popularity, it is critical to
have some tool for users to understand the influence of each component (e.g.,
the source vote or training data) in the pipeline and interpret the end model
behavior. To achieve this, we build on Influence Function (IF) and propose
source-aware IF, which leverages the generation process of the probabilistic
labels to decompose the end model's training objective and then calculate the
influence associated with each (data, source, class) tuple. These primitive
influence score can then be used to estimate the influence of individual
component of PWS, such as source vote, supervision source, and training data.
On datasets of diverse domains, we demonstrate multiple use cases: (1)
interpreting incorrect predictions from multiple angles that reveals insights
for debugging the PWS pipeline, (2) identifying mislabeling of sources with a
gain of 9%-37% over baselines, and (3) improving the end model's generalization
performance by removing harmful components in the training objective (13%-24%
better than ordinary IF).
