  In this paper, we introduce a conformal prediction method to construct
prediction sets in a oneshot federated learning setting. More specifically, we
define a quantile-of-quantiles estimator and prove that for any distribution,
it is possible to output prediction sets with desired coverage in only one
round of communication. To mitigate privacy issues, we also describe a locally
differentially private version of our estimator. Finally, over a wide range of
experiments, we show that our method returns prediction sets with coverage and
length very similar to those obtained in a centralized setting. Overall, these
results demonstrate that our method is particularly well-suited to perform
conformal predictions in a one-shot federated learning setting.
