Conformal prediction without knowledge of labeled calibration data

We extend the method of conformal prediction beyond the case relying on labeled calibration data. Replacing the calibration scores by suitable estimates, we identify conformity sets $C$ for classification and regression models that rely on unlabeled calibration data. Given a classification model with accuracy $1-\beta$, we prove that the conformity sets guarantee a coverage of $P(Y \in C) \geq 1-\alpha-\beta$ for an arbitrary parameter $\alpha \in (0,1)$. The same coverage guarantee also holds for regression models, if we replace the accuracy by a similar exactness measure. Finally, we describe how to use the theoretical results in practice.