Unifying different theories of conformal prediction

This paper establishes a unified framework for understanding the methodology and theory behind several different methods in the conformal prediction literature, which includes standard conformal prediction (CP), weighted conformal prediction (WCP), nonexchangeable conformal prediction (NexCP), and randomly-localized conformal prediction (RLCP), among others. At the crux of our framework is the idea that conformal methods are based on revealing partial information about the data at hand, and positing a conditional distribution for the data given the partial information. Different methods arise from different choices of partial information, and of the corresponding (approximate) conditional distribution. In addition to recovering and unifying existing results, our framework leads to both new theoretical guarantees for existing methods, and new extensions of the conformal methodology.