  Training deep neural networks requires many training samples, but in practice
training labels are expensive to obtain and may be of varying quality, as some
may be from trusted expert labelers while others might be from heuristics or
other sources of weak supervision such as crowd-sourcing. This creates a
fundamental quality versus-quantity trade-off in the learning process. Do we
learn from the small amount of high-quality data or the potentially large
amount of weakly-labeled data? We argue that if the learner could somehow know
and take the label-quality into account when learning the data representation,
we could get the best of both worlds. To this end, we propose
"fidelity-weighted learning" (FWL), a semi-supervised student-teacher approach
for training deep neural networks using weakly-labeled data. FWL modulates the
parameter updates to a student network (trained on the task we care about) on a
per-sample basis according to the posterior confidence of its label-quality
estimated by a teacher (who has access to the high-quality labels). Both
student and teacher are learned from the data. We evaluate FWL on two tasks in
information retrieval and natural language processing where we outperform
state-of-the-art alternative semi-supervised methods, indicating that our
approach makes better use of strong and weak labels, and leads to better
task-dependent data representations.
