Adaptive conformal classification with noisy labels

This paper develops novel conformal prediction methods for classification tasks that can automatically adapt to random label contamination in the calibration sample, enabling more informative prediction sets with stronger coverage guarantees compared to state-of-the-art approaches. This is made possible by a precise theoretical characterization of the effective coverage inflation (or deflation) suffered by standard conformal inferences in the presence of label contamination, which is then made actionable through new calibration algorithms. Our solution is flexible and can leverage different modeling assumptions about the label contamination process, while requiring no knowledge about the data distribution or the inner workings of the machine-learning classifier. The advantages of the proposed methods are demonstrated through extensive simulations and an application to object classification with the CIFAR-10H image data set.