  Out-of-distribution (OOD) generalization has attracted increasing research
attention in recent years, due to its promising experimental results in
real-world applications. In this paper,we study the confidence set prediction
problem in the OOD generalization setting. Split conformal prediction (SCP) is
an efficient framework for handling the confidence set prediction problem.
However, the validity of SCP requires the examples to be exchangeable, which is
violated in the OOD setting. Empirically, we show that trivially applying SCP
results in a failure to maintain the marginal coverage when the unseen target
domain is different from the source domain. To address this issue, we develop a
method for forming confident prediction sets in the OOD setting and
theoretically prove the validity of our method. Finally, we conduct experiments
on simulated data to empirically verify the correctness of our theory and the
validity of our proposed method.
