Inductive randomness predictors: beyond conformal

Abstract

This paper introduces inductive randomness predictors, which form a proper superset of inductive conformal predictors but have the same principal property of validity under the assumption of randomness (i.e., of IID data). It turns out that every non-trivial inductive conformal predictor is strictly dominated by an inductive randomness predictor, although the improvement is not great, at most a factor of $\mathrm{e}\approx2.72$ in the case of e-prediction. The dominating inductive randomness predictors are more complicated and more difficult to compute; besides, an improvement by a factor of $\mathrm{e}$ is rare. Therefore, this paper does not suggest replacing inductive conformal predictors by inductive randomness predictors and only calls for a more detailed study of the latter.