The risk-controlling prediction sets (RCPS) framework is a general tool for transforming the output of any machine learning model to design a predictive rule with rigorous error rate control. The key idea behind this framework is to use labeled hold-out calibration data to tune a hyper-parameter that affects the error rate of the resulting prediction rule. However, the limitation of such a calibration scheme is that with limited hold-out data, the tuned hyper-parameter becomes noisy and leads to a prediction rule with an error rate that is often unnecessarily conservative. To overcome this sample-size barrier, we introduce a semi-supervised calibration procedure that leverages unlabeled data to rigorously tune the hyper-parameter without compromising statistical validity. Our procedure builds upon the prediction-powered inference framework, carefully tailoring it to risk-controlling tasks. We demonstrate the benefits and validity of our proposal through two real-data experiments: few-shot image classification and early time series classification.

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 whenever the noise is dispersive and increases variability. In other adversarial 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.

Deep neural networks are powerful tools to detect hidden patterns in data and leverage them to make predictions, but they are not designed to understand uncertainty and estimate reliable probabilities. In particular, they tend to be overconfident. We begin to address this problem in the context of multi-class classification by developing a novel training algorithm producing models with more dependable uncertainty estimates, without sacrificing predictive power. The idea is to mitigate overconfidence by minimizing a loss function, inspired by advances in conformal inference, that quantifies model uncertainty by carefully leveraging hold-out data. Experiments with synthetic and real data demonstrate this method can lead to smaller conformal prediction sets with higher conditional coverage, after exact calibration with hold-out data, compared to state-of-the-art alternatives.