Randomness, exchangeability, and conformal prediction

This paper continues development of the functional theory of randomness, a modification of the algorithmic theory of randomness getting rid of unspecified additive constants. It introduces new kinds of confidence predictors, including randomness predictors (the most general confidence predictors based on the assumption of IID observations) and exchangeability predictors (the most general confidence predictors based on the assumption of exchangeable observations). The main result implies that both are close to conformal predictors and quantifies the difference between randomness prediction and conformal prediction.