Set-Preserving Calibration from Conformal P-Values to E-Values
2026-06-02 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a technique called conformal prediction, which helps make reliable predictions with guaranteed accuracy. They point out that the usual way of doing this relies on p-values, but using e-values can be more flexible in some situations. They introduce a new method to convert p-values to e-values without losing accuracy or making predictions too cautious, improving efficiency. They show this method works well in combining predictions and ensures correct coverage guarantees. Overall, their work makes conformal prediction more adaptable and efficient for uncertainty quantification.
conformal predictionp-valuese-valuescalibrationprediction setscross-conformal predictionstatistical coverageuncertainty quantificationaggregationrandomization
Authors
Nabil Alami, Jad Zakharia, Souhaib Ben Taieb
Abstract
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.