Universality of conformal prediction under the assumption of randomness

Vladimir Vovk

Keywords: Conformal prediction, train-invariant randomness prediction, exchangeability, randomness, p-values, e-values.

TL;DR: Conformal prediction does not lose much by not using the full strength of the assumption of IID data and only using data exchangeability.

Abstract: Conformal predictors provide set or functional predictions that are valid under the assumption of randomness, i.e., under the assumption of independent and identically distributed data. The question asked in this paper is whether there are predictors that are valid in the same sense under the assumption of randomness and that are more efficient than conformal predictors. The answer is that the class of conformal predictors is universal in that only limited gains in predictive efficiency are possible. The previous work in this area has relied on the algorithmic theory of randomness and so involved unspecified constants, whereas this paper's results are much more practical. They are also shown to be optimal in some respects.

Submission Number: 27