Set and functional prediction: randomness, exchangeability, and conformal

Conformal prediction is usually presented as a method of set prediction [10, Part I], i.e., as a way of producing prediction sets (rather than pointpredictions). Another way to look at a conformal predictor is as a way of producin g a p-value function (discussed, in a slightly different context, in, e.g., [4]), which is a function mapping each possible label y of a test object to the corresponding conformal p-value. In analogy with "prediction sets", we will call su ch p-value functions "prediction functions".