This note discusses a simple modification of cross-conformal prediction inspired by recent work on e-values. The precursor of conformal prediction developed in the 1990s by Gammerman, Vapnik, and Vovk was also based on e-values and is called conformal e-prediction in this note. Replacing e-values by p-values led to conformal prediction, which has important advantages over conformal e-prediction without obvious disadvantages. The situation with cross-conformal prediction is, however, different: whereas for cross-conformal prediction validity is only an empirical fact (and can be broken with excessive randomization), this note draws the reader's attention to the obvious fact that cross-conformal e-prediction enjoys a guaranteed property of validity.

翻译：本笔记讨论了一种受近期e值研究启发的交叉共形预测的简单改进。由Gammerman、Vapnik和Vovk于1990年代发展的共形预测前身同样基于e值，本文将其称为共形e预测。将e值替换为p值催生了共形预测方法，该方法相较于共形e预测具有显著优势且无明显缺陷。然而交叉共形预测的情况有所不同：尽管交叉共形预测的有效性仅是经验事实（可能因过度随机化而失效），本笔记提请读者注意一个明显事实——交叉共形e预测具备可保证的有效性特性。