Efficient Conformal Prediction for Regression Models under Label Noise

In high-stakes scenarios, such as medical imaging applications, it is critical to equip the predictions of a regression model with reliable confidence intervals. Recently, Conformal Prediction (CP) has emerged as a powerful statistical framework that, based on a labeled calibration set, generates intervals that include the true labels with a pre-specified probability. In this paper, we address the problem of applying CP for regression models when the calibration set contains noisy labels. We begin by establishing a mathematically grounded procedure for estimating the noise-free CP threshold. Then, we turn it into a practical algorithm that overcomes the challenges arising from the continuous nature of the regression problem. We evaluate the proposed method on two medical imaging regression datasets with Gaussian label noise. Our method significantly outperforms the existing alternative, achieving performance close to the clean-label setting.