  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
introduce "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
document ranking where we outperform state-of-the-art alternative
semi-supervised methods.
