Universality of conformal prediction under the assumption of randomness

TL;DR

This paper investigates the efficiency of conformal predictors under the assumption of randomness, demonstrating their near-optimality and universality in providing valid predictions with limited potential for improvement.

Contribution

It proves that conformal predictors are essentially optimal under randomness assumptions, offering a practical and rigorous analysis of their universality and efficiency.

Findings

Conformal predictors are nearly optimal under randomness.

Limited gains are possible beyond conformal predictors.

Results are more practical and less reliant on unspecified constants.

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.