  Conformal prediction has shown impressive capacity in constructing
statistically rigorous prediction sets for machine learning models with
exchangeable data samples. The siloed datasets, coupled with the escalating
privacy concerns related to local data sharing, have inspired recent
innovations extending conformal prediction into federated environments with
distributed data samples. However, this framework for distributed uncertainty
quantification is susceptible to Byzantine failures. A minor subset of
malicious clients can significantly compromise the practicality of coverage
guarantees. To address this vulnerability, we introduce a novel framework
Rob-FCP, which executes robust federated conformal prediction, effectively
countering malicious clients capable of reporting arbitrary statistics with the
conformal calibration process. We theoretically provide the conformal coverage
bound of Rob-FCP in the Byzantine setting and show that the coverage of Rob-FCP
is asymptotically close to the desired coverage level. We also propose a
malicious client number estimator to tackle a more challenging setting where
the number of malicious clients is unknown to the defender and theoretically
shows its effectiveness. We empirically demonstrate the robustness of Rob-FCP
against diverse proportions of malicious clients under a variety of Byzantine
attacks on five standard benchmark and real-world healthcare datasets.
