Isotonic Conformal Prediction

2026-07-18

AI Summary

This work addresses the issue that point predictions, even when globally well-calibrated, may exhibit systematic local biases that undermine the reliability of downstream decisions. To mitigate this, the authors propose a framework that decouples calibration from prediction set construction: first, a single isotonic regression mapping is fitted for recalibration; then, prediction intervals are constructed within subsets of data points whose recalibrated values are similar. Building on this framework, they introduce both Split and Transductive variants of isotonic conformal prediction, which achieve conditional coverage validity while substantially reducing computational overhead by avoiding repeated recalibration for each candidate output. Experiments on synthetic heteroscedastic regression tasks and real-world medical datasets demonstrate that the proposed methods attain coverage comparable to self-calibrated conformal prediction at significantly lower computational cost.

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.

Problem

• self-calibration
• prediction-conditional validity
• conformal prediction
• uncertainty quantification
• isotonic regression

Innovation

• Isotonic Conformal Prediction
• Self-calibration
• Prediction-conditional validity
• Conformal prediction
• Recalibration