Conditional Conformal Risk Adaptation

Uncertainty quantification is becoming increasingly important in image segmentation, especially for high-stakes applications like medical imaging. While conformal risk control generalizes conformal prediction beyond standard miscoverage to handle various loss functions such as false negative rate, its application to segmentation often yields inadequate conditional risk control: some images experience very high false negative rates while others have negligibly small ones. We develop Conformal Risk Adaptation (CRA), which introduces a new score function for creating adaptive prediction sets that significantly improve conditional risk control for segmentation tasks. We establish a novel theoretical framework that demonstrates a fundamental connection between conformal risk control and conformal prediction through a weighted quantile approach, applicable to any score function. To address the challenge of poorly calibrated probabilities in segmentation models, we introduce a specialized probability calibration framework that enhances the reliability of pixel-wise inclusion estimates. Using these calibrated probabilities, we propose Calibrated Conformal Risk Adaptation (CCRA) and a stratified variant (CCRA-S) that partitions images based on their characteristics and applies group-specific thresholds to further enhance conditional risk control. Our experiments on polyp segmentation demonstrate that all three methods (CRA, CCRA, and CCRA-S) provide valid marginal risk control and deliver more consistent conditional risk control across diverse images compared to standard approaches, offering a principled approach to uncertainty quantification that is particularly valuable for high-stakes and personalized segmentation applications.