Isotonic Conformal Prediction

• URL: http://arxiv.org/abs/2607.16675v1
• Date: Sat, 18 Jul 2026 07:11:05 GMT
• Title: Isotonic Conformal Prediction
• Abstract summary: We consider two objectives for reliable uncertainty quantification: self-calibration and prediction-conditional validity.<n>Self-Calibrating Conformal Prediction attains both objectives exactly in finite samples, but requires refitting its calibrator for every candidate outcome.<n>We propose Isotonic Conformal Prediction (ICP), a framework that decouples calibration from prediction-set construction.
• Score: 1.0499611180329804
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: A point prediction that is well calibrated on average can still be systematically biased conditional on its own value, undermining its use in downstream decision-making. We consider two objectives for reliable uncertainty quantification: self-calibration, requiring a point prediction to be unbiased conditional on its own value, and prediction-conditional validity, requiring a prediction interval to attain nominal coverage conditional on the prediction. Self-Calibrating Conformal Prediction (SC-CP) attains both objectives exactly in finite samples, but requires refitting its calibrator for every candidate outcome, which is computationally prohibitive for continuous outcomes. We propose Isotonic Conformal Prediction (ICP), a framework that decouples calibration from prediction-set construction by fitting a single isotonic recalibration map and constructing prediction intervals within strata of similar recalibrated predictions. Within this framework we develop two procedures. Split Isotonic Conformal Prediction (SICP) attains prediction-conditional validity in finite samples and self-calibration asymptotically, at the computational cost of split conformal prediction. Transductive Isotonic Conformal Prediction (TICP) attains both objectives exactly in finite samples through a per-test-point inner loop that avoids refitting the isotonic calibrator. On synthetic heteroscedastic regression problems and a real-world healthcare-utilization dataset, both procedures match the coverage of SC-CP at substantially lower computational cost.

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