Emergence of artificial intelligence techniques in biomedical applications urges the researchers to pay more attention on the uncertainty quantification (UQ) in machine-assisted medical decision making. For classification tasks, prior studies on UQ are difficult to compare with each other, due to the lack of a unified quantitative evaluation metric. Considering that well-performing UQ models ought to know when the classification models act incorrectly, we design a new evaluation metric, area under Confidence-Classification Characteristic curves (AUCCC), to quantitatively evaluate the performance of the UQ models. AUCCC is threshold-free, robust to perturbation, and insensitive to the classification performance. We evaluate several UQ methods (e.g., max softmax output) with AUCCC to validate its effectiveness. Furthermore, a simple scheme, named Uncertainty Distillation (UDist), is developed to boost the UQ performance, where a confidence model is distilling the confidence estimated by deep ensembles. The proposed method is easy to implement; it consistently outperforms strong baselines on natural and medical image datasets in our experiments.
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