  We study the robustness of conformal prediction, a powerful tool for
uncertainty quantification, to label noise. Our analysis tackles both
regression and classification problems, characterizing when and how it is
possible to construct uncertainty sets that correctly cover the unobserved
noiseless ground truth labels. We further extend our theory and formulate the
requirements for correctly controlling a general loss function, such as the
false negative proportion, with noisy labels. Our theory and experiments
suggest that conformal prediction and risk-controlling techniques with noisy
labels attain conservative risk over the clean ground truth labels except in
adversarial cases. In such cases, we can also correct for noise of bounded size
in the conformal prediction algorithm in order to ensure achieving the correct
risk of the ground truth labels without score or data regularity.
