The safe integration of machine learning modules in decision-making processes
hinges on their ability to quantify uncertainty. A popular technique to achieve
this goal is conformal prediction (CP), which transforms an arbitrary base
predictor into a set predictor with coverage guarantees. While CP certifies the
predicted set to contain the target quantity with a user-defined tolerance, it
does not provide control over the average size of the predicted sets, i.e.,
over the informativeness of the prediction. In this work, a theoretical
connection is established between the generalization properties of the base
predictor and the informativeness of the resulting CP prediction sets. To this
end, an upper bound is derived on the expected size of the CP set predictor
that builds on generalization error bounds for the base predictor. The derived
upper bound provides insights into the dependence of the average size of the CP
set predictor on the amount of calibration data, the target reliability, and
the generalization performance of the base predictor. The theoretical insights
are validated using simple numerical regression and classification tasks.

通过建立基础预测器的泛化性能与条件概率预测集成信息量之间的理论连接，本研究推导了一个上界，以便理解条件概率预测集的平均大小对校准数据量、目标可靠性和基础预测器的泛化性能的依赖关系。通过简单的数值回归和分类任务验证了理论洞察的有效性。