Inductive randomness predictors: beyond conformal
This is an incremental theoretical contribution for researchers in machine learning, specifically in conformal prediction and statistical learning theory.
The paper tackles the problem of improving inductive conformal predictors by introducing inductive randomness predictors, which strictly dominate them but only offer at most a factor of e (≈2.72) improvement in e-prediction, with the result being that the improvement is rare and not recommended for replacement.
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.