Exchangeability, Conformal Prediction, and Rank Tests

Although these two concepts are very closely related, the fact that exchangeability allows for a specific type of dependence between the random variables leads to numerous implications/applications of this concept. One of the most important implications of exchangeability is that the indexing of random variables is immaterial. In technical words, this means that the ranks of real-valued exchangeable random variables are uniform over the set of all permutations. Just this one implication has pioneered two very different fields in statistics and machine learning, namely, nonparametric rank tests and conformal prediction. The main purpose of this article is to define exchangeability, discuss its implications (rigorously), and then exposit the uses of this concept for conformal prediction and rank tests. To our knowledge, conformal prediction (starting from Vovk et al. (2005)) is the first field to apply the full strength of exchangeability.