Conditional Conformal Risk Adaptation

TL;DR

This work addresses uncertain segmentation in high-stakes domains by extending conformal risk control to image segmentation through Conformal Risk Adaptation (CRA), which builds adaptive prediction sets that align with image-specific probability distributions. A weighted-quantile framework links conformal risk control and conformal prediction, enabling efficient, threshold-free risk management across score functions. The authors introduce probability calibration (CCRA) and a stratified variant (CCRA-S) to improve pixelwise probability estimates and achieve more consistent conditional risk across diverse images. Empirical results on polyp segmentation demonstrate valid marginal risk control with tighter conditional guarantees than traditional CRC, highlighting practical implications for reliable uncertainty quantification in medical imaging. The methods provide a principled, distribution-free approach to uncertainty that adapts to image difficulty and polyp characteristics, with potential broader impact on personalized segmentation tasks.

Abstract

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.

Figures (4)

• Figure 1: Left: Distribution of probability mass proportion required to achieve $(1-\alpha)$ coverage before and after calibration. For each sample $X_i$, we compute the minimum proportion of total probability mass ($\sum \hat{p}_j(X_i)$) needed to include at least $(1-\alpha)$ of the true positive pixels $Y_i$. Right: Calibration curve showing predicted vs. calibrated probabilities. The red curve shows our isotonic regression calibration function, correcting for overconfidence in mid-range probabilities.
• Figure 2: Left: Coverage gap distribution for all methods at significance level $\alpha = 0.1$ (target coverage 90%). The boxplots show the distribution of absolute differences between achieved coverage and target coverage across 100 experimental trials. Lower values indicate better conformity to the target coverage. Our proposed CCRA and CCRA-S methods demonstrate smaller coverage gaps and less variance compared to the baseline CRC, indicating more reliable uncertainty quantification. Right: Coverage distribution for all methods at significance level $\alpha = 0.1$. The histogram shows the density of coverage values achieved across all test samples in all experimental trials. The vertical red dashed line indicates the target coverage of 90%. Our proposed methods, especially CCRA-S, produce distributions more tightly centered around the target coverage, demonstrating better calibration compared to the baseline CRC method, which shows a wider, more dispersed distribution.
• Figure 3: Coverage gap versus significance level $\alpha$ for all methods. The plot shows how the mean coverage gap (with standard deviation error bars) varies with different values of $\alpha$ from 0.01 to 0.20. Our proposed methods consistently achieve smaller coverage gaps than the baseline CRC across the entire range of significance levels, with CCRA-S demonstrating the optimal performance. This indicates that our conditional approaches provide more reliable uncertainty quantification regardless of the desired confidence level.
• Figure 4: Qualitative comparison of CRC and CCRA-S prediction sets at significance level $\alpha = 0.1$. Each column pair shows examples at specific CRC coverage levels (from left to right: 85%, 90%, 95%, 99%, and 99.5%), while CCRA-S coverage remains approximately 90% across all samples. The top row displays original polyp images, the middle row shows CRC prediction sets, and the bottom row presents CCRA-S prediction sets. White pixels indicate true positives, red pixels show false negatives, and teal pixels represent false positives. FNR values (False Negative Rate = 1 - coverage) are shown for each prediction. Note how CCRA-S maintains more consistent coverage and false negatives across different images, while CRC's performance varies substantially depending on image characteristics, demonstrating the advantage of our conditional risk control approaches.

Theorems & Definitions (6)

• Theorem 1
• proof
• Theorem 2
• proof
• Remark
• Remark