Standard conformal prediction (CP) procedures are typically formulated in terms of p-values, but reliance on p-values alone limits flexibility, for example, when combining dependent evidence across models or data splits. Recent work has explored e-value formulations for conformal inference, yet a direct connection between p- and e-value formulations in CP has been missing, especially regarding their statistical efficiency. We first identify limitations of classical p-to-e calibrators in the CP setting, showing that they are not set-preserving and can lead to overly conservative prediction sets. To address this, we propose a novel P2E calibrator that converts conformal p-values into e-values without altering the prediction set induced by the original conformal p-value. We establish both theoretically and empirically that our calibrator can yield significant efficiency gains over existing p-to-e calibrators. This e-value formulation enables principled use of recent advances in e-value merging and randomization, where we demonstrate its impact in two applications: cross-conformal prediction (CCP), whose variants typically provide only approximate $1-2α$ coverage, and conformal aggregation (CA). In both cases, our e-value-based methods satisfy the desired $1-α$ coverage guarantee while improving efficiency over standard baselines. More broadly, our approach expands the flexibility of CP and opens new directions for efficient, distribution-free uncertainty quantification.

翻译：标准共形预测（CP）过程通常以p值形式表述，但仅依赖p值限制了灵活性，例如在跨模型或数据分割合并依赖证据时尤为明显。近期研究探索了共形推断的e值表述，然而CP中p值与e值表述之间的直接联系仍未被建立，尤其在统计效率方面。我们首先识别了经典p到e校准器在CP框架中的局限性，证明它们无法保持集合不变，且可能导致过度保守的预测集。为此，我们提出一种新型P2E校准器，可将共形p值转换为e值，且不改变原始共形p值诱导的预测集。我们从理论和实证两个层面证明，该校准器相比现有p到e校准器可获得显著效率提升。这种e值表述使共形方法能够原理性地应用e值合并与随机化的最新进展，我们在两个应用中展示其影响：交叉共形预测（CCP，其变体通常仅能提供近似$1-2α$覆盖）和共形聚合（CA）。在这两种情况下，基于e值的方法在满足理想$1-α$覆盖保证的同时，相较标准基线提升了效率。更广泛地看，我们的方法扩展了CP的灵活性，为高效、无分布假设的不确定性量化开辟了新方向。