On the Expected Size of Conformal Prediction Sets
This work addresses a critical gap for practitioners using conformal prediction by providing tools to quantify set sizes, though it is incremental as it builds on existing split conformal frameworks.
The paper tackled the lack of finite-sample analysis for the size of prediction sets in conformal prediction, deriving theoretical expected sizes and practical estimates with interval bounds, validated on real-world datasets.
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.