Set-Preserving Calibration from Conformal P-Values to E-Values

• URL: http://arxiv.org/abs/2606.03600v1
• Date: Tue, 02 Jun 2026 13:06:01 GMT
• Title: Set-Preserving Calibration from Conformal P-Values to E-Values
• Abstract summary: 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.<n>This e-value formulation enables principled use of recent advances in e-value merging and randomization.
• Score: 6.673032375204486
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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