Title: Maintaining Set Integrity: Calibrating Conformal P-Values to E-Values

Abstract:

While standard conformal prediction (CP) frameworks are traditionally grounded in p-values, depending exclusively on them restricts flexibility, particularly when synthesizing dependent evidence across different models or data partitions. Although recent studies have investigated e-value approaches for conformal inference, a direct link between p-value and e-value formulations in CP—especially concerning statistical efficiency—has remained elusive. In this work, we highlight the shortcomings of classical p-to-e calibrators within the CP context, demonstrating that they fail to be set-preserving and often result in prediction sets that are excessively conservative. To resolve these issues, we introduce a new P2E calibrator designed to transform conformal p-values into e-values while ensuring the induced prediction set remains unchanged relative to the original p-value. Through both theoretical analysis and empirical testing, we prove that our method achieves substantial efficiency improvements compared to existing p-to-e calibration techniques. This e-value-based framework facilitates the rigorous application of recent developments in e-value merging and randomization. We illustrate its effectiveness in two key areas: cross-conformal prediction (CCP), where variants usually offer only approximate $1-2\alpha$ coverage, and conformal aggregation (CA). In both scenarios, our e-value-driven methods adhere to the required $1-\alpha$ coverage guarantee while outperforming standard baselines in efficiency. Ultimately, this approach enhances the adaptability of CP and paves the way for novel avenues in efficient, distribution-free uncertainty quantification.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC