While conformal predictors reap the benefits of rigorous statistical guarantees for 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 set under the split conformal prediction framework. As this precise formulation cannot usually be calculated directly, we further derive point estimates and high probability intervals that can be easily computed, providing a practical method for characterizing the expected prediction set size across different possible realizations of the test and calibration data. Additionally, we corroborate the efficacy of our results with experiments on real-world datasets, for both regression and classification problems.

本文旨在解决当前对于确保错误频率的合规性统计保证，且相应预测集的大小对其实用性至关重要，但预测集大小缺乏有限样本分析和保证的问题，通过量化拆分一致性预测框架下预测集的期望大小来解决此不足，并提供一种实用的方法来表示测试和校准数据的不同可能实现的预期预测集大小。实验结果表明，对于回归和分类问题的现实世界数据集，本文的结果的功效得到了验证。

关于适应性预测集大小的预期尺寸