Identify when combining WCP and NexCP weighting is useful

Determine problem settings in which combining the weighting mechanisms of weighted conformal prediction (likelihood-ratio weights addressing distribution shift) and nonexchangeable conformal prediction (index-swapping weights addressing nonexchangeability) would be useful for constructing conformal prediction sets.

Background

The paper presents a unified framework that encompasses several conformal prediction methods, including weighted conformal prediction (WCP) for known distribution shift and nonexchangeable conformal prediction (NexCP) for robustness under nonexchangeability. Although both are weighted approaches, they differ in their assumptions and technical motivations.

The authors note that their unified perspective suggests the potential to integrate these two weighting strategies. However, it remains unclear in which applications or data-generating scenarios such a combined approach would be advantageous. The explicit open question seeks to pinpoint those problem settings.