What "Form'' of Uncertainty Does Conformal Prediction Quantify?

Conformal prediction (CP) is a post-hoc calibration method that returns prediction sets with distribution-free coverage guarantees, and the size of the output set is often interpreted as a notion of uncertainty. We show that the difference in set size between full and split CP is directly connected to Bayesian posterior variance, which is the epistemic uncertainty of the model. Essentially, this difference in set size is an aggregation of two opposite effects: (1) better model accuracy and therefore smaller set size achieved by training over extra calibration points, and (2) the "formability" of the model at test point towards every possible label. The latter effect vanishes with stronger models or more calibration data (as epistemic uncertainty is known for that behavior). It turns out that the model's formability itself (without the quantization effect of prediction sets, and through estimating the posterior variance) is a useful tool to quantify the epistemic uncertainty. In our empirical evaluation it performs on par with the state of the art in many setups.