In classification, every confidence predictor that is valid under IID data can be transformed into a conformal predictor with an explicit, constant-free bound on the loss of efficiency.
Inductive randomness predictors: beyond conformal
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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.
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Randomness, exchangeability, and conformal prediction
In classification, every confidence predictor that is valid under IID data can be transformed into a conformal predictor with an explicit, constant-free bound on the loss of efficiency.