  Supervised machine learning assumes the availability of fully-labeled data,
but in many cases, such as low-resource languages, the only data available is
partially annotated. We study the problem of Named Entity Recognition (NER)
with partially annotated training data in which a fraction of the named
entities are labeled, and all other tokens, entities or otherwise, are labeled
as non-entity by default. In order to train on this noisy dataset, we need to
distinguish between the true and false negatives. To this end, we introduce a
constraint-driven iterative algorithm that learns to detect false negatives in
the noisy set and downweigh them, resulting in a weighted training set. With
this set, we train a weighted NER model. We evaluate our algorithm with
weighted variants of neural and non-neural NER models on data in 8 languages
from several language and script families, showing strong ability to learn from
partial data. Finally, to show real-world efficacy, we evaluate on a Bengali
NER corpus annotated by non-speakers, outperforming the prior state-of-the-art
by over 5 points F1.
