  While conformal predictors reap the benefits of rigorous statistical
guarantees on their error frequency, the size of their corresponding prediction
sets is critical to their practical utility. Unfortunately, there is currently
a lack of finite-sample analysis and guarantees for their prediction set sizes.
To address this shortfall, we theoretically quantify the expected size of the
prediction sets under the split conformal prediction framework. As this precise
formulation cannot usually be calculated directly, we further derive point
estimates and high-probability interval bounds that can be empirically
computed, providing a practical method for characterizing the expected set
size. We corroborate the efficacy of our results with experiments on real-world
datasets for both regression and classification problems.
