  A sufficient amount of annotated data is usually required to fine-tune
pre-trained language models for downstream tasks. Unfortunately, attaining
labeled data can be costly, especially for multiple language varieties and
dialects. We propose to self-train pre-trained language models in zero- and
few-shot scenarios to improve performance on data-scarce varieties using only
resources from data-rich ones. We demonstrate the utility of our approach in
the context of Arabic sequence labeling by using a language model fine-tuned on
Modern Standard Arabic (MSA) only to predict named entities (NE) and
part-of-speech (POS) tags on several dialectal Arabic (DA) varieties. We show
that self-training is indeed powerful, improving zero-shot MSA-to-DA transfer
by as large as \texttildelow 10\% F$_1$ (NER) and 2\% accuracy (POS tagging).
We acquire even better performance in few-shot scenarios with limited amounts
of labeled data. We conduct an ablation study and show that the performance
boost observed directly results from the unlabeled DA examples used for
self-training. Our work opens up opportunities for developing DA models
exploiting only MSA resources and it can be extended to other languages and
tasks. Our code and fine-tuned models can be accessed at
https://github.com/mohammadKhalifa/zero-shot-arabic-dialects.
