ReCIRC: Rectified Conformal Risk Control

2026-09-29

AI Summary

This study addresses the limitation of conventional conformal prediction, which relies on a global threshold and consequently yields uneven risk control across easy and hard samples. To overcome this, we propose an input-dependent risk budgeting framework that, for the first time, reformulates global calibration as conditional control. By reparameterizing the threshold through inversion of the local risk curve, our approach achieves approximate conditional risk control while preserving finite-sample marginal coverage guarantees. Empirical evaluations demonstrate that the proposed method significantly reduces worst-group risk across multi-class tasks while maintaining the target marginal coverage level. Ultimately, this work effectively reconciles distribution-free theoretical guarantees with conditional adaptivity, offering a principled solution for heterogeneous uncertainty quantification in predictive modeling.

Abstract

Many applications of black-box predictive models require controlling task-relevant error rates, such as missed lesion pixels in segmentation or missed labels in multilabel classification. Conformal risk control (CRC; Angelopoulos et al., arXiv:2208.02814) gives distribution-free guarantees for such losses, but it calibrates a single threshold shared by all inputs. Because conditional risk varies with the input, this marginal guarantee often overprotects easy cases and underprotects hard ones. We propose ReCIRC (Rectified Conformal Risk Control), which inverts each input's estimated local risk curve to reparameterize the calibrated threshold as a risk budget $a$ representing a common target conditional risk, and then applies CRC unchanged to the resulting family. ReCIRC retains CRC's finite-sample marginal guarantee regardless of the accuracy of the estimated curves, while accurate curves yield approximate conditional risk control and, under additional conditions, asymptotically exact conditional risk control; they also support a risk-calibration diagnostic. Across three synthetic and five real-data settings spanning segmentation, multilabel and multiclass classification, and regression, ReCIRC attained the lowest average worst-group risk and mean positive group excess in every setting, while maintaining marginal risk close to the target, whereas changes in prediction size were application-dependent.

Problem

• conformal risk control
• conditional risk
• black-box predictive models
• risk calibration

Innovation

• Conformal Risk Control
• Conditional Risk
• Risk Budget
• Distribution-free Guarantees
• Local Risk Curve