Universality of conformal prediction under the assumption of randomness
This work addresses the theoretical foundations of conformal prediction for researchers in machine learning, offering practical and optimal results, though it is incremental in refining existing theory.
The paper tackles the problem of whether more efficient predictors than conformal predictors exist under the randomness assumption, finding that conformal predictors are nearly optimal with only limited efficiency gains possible, and it provides practical results without unspecified constants.
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.