  Training deep neural networks (DNNs) with limited supervision has been a
popular research topic as it can significantly alleviate the annotation burden.
Self-training has been successfully applied in semi-supervised learning tasks,
but one drawback of self-training is that it is vulnerable to the label noise
from incorrect pseudo labels. Inspired by the fact that samples with similar
labels tend to share similar representations, we develop a neighborhood-based
sample selection approach to tackle the issue of noisy pseudo labels. We
further stabilize self-training via aggregating the predictions from different
rounds during sample selection. Experiments on eight tasks show that our
proposed method outperforms the strongest self-training baseline with 1.83% and
2.51% performance gain for text and graph datasets on average. Our further
analysis demonstrates that our proposed data selection strategy reduces the
noise of pseudo labels by 36.8% and saves 57.3% of the time when compared with
the best baseline. Our code and appendices will be uploaded to
https://github.com/ritaranx/NeST.
