When and How Mixup Improves Calibration

In many machine learning applications, it is important for the model to provide confidence scores that accurately captures its prediction uncertainty. Although modern learning methods have achieved great success in predictive accuracy, generating calibrated confidence scores remains a major challenge. Mixup, a popular yet simple data augmentation technique based on taking convex combinations of pairs of training examples, has been empirically found to significantly improve confidence calibration across diverse applications. However, when and how Mixup helps calibration is still mysterious. In this paper, we theoretically prove that Mixup improves calibration in high-dimensional settings by investigating two natural data models on classification and regression. Interestingly, the calibration benefit of Mixup increases as the model capacity increases. We support our theories with experiments on common architectures and data sets. In addition, we study how Mixup improves calibration in semi-supervised learning. While incorporating unlabeled data can sometimes make the model less calibrated, adding Mixup training mitigates this issue and provably improves calibration. Our analysis provides new insights and a framework to understand Mixup and calibration.