  Large Language Models have demonstrated remarkable few-shot performance, but
the performance can be sensitive to the selection of few-shot instances. We
propose PATRON, a new method that uses prompt-based uncertainty estimation for
data selection for pre-trained language model fine-tuning under cold-start
scenarios, i.e., no initial labeled data are available. In PATRON, we design
(1) a prompt-based uncertainty propagation approach to estimate the importance
of data points and (2) a partition-then-rewrite (PTR) strategy to promote
sample diversity when querying for annotations. Experiments on six text
classification datasets show that PATRON outperforms the strongest cold-start
data selection baselines by up to 6.9%. Besides, with 128 labels only, PATRON
achieves 91.0% and 92.1% of the fully supervised performance based on vanilla
fine-tuning and prompt-based learning respectively. Our implementation of
PATRON is available at \url{https://github.com/yueyu1030/Patron}.
