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Evaluating and Boosting Uncertainty Quantification in Classification
Xiaoyang Huang, Jiancheng Yang, Linguo Li, Haoran Deng, Bingbing Ni, Yi Xu
TL;DR
Classification UQ methods are difficult to compare because they lack a unified quantitative evaluation. The paper proposes CCC/AUCCC and a cascade that distills deep-ensemble confidence; UDist outperforms UQ baselines, with reported gains on ChestX-ray14.
Problem
Classification UQ methods are difficult to compare because evaluations lack a unified quantitative metric and may be qualitative or dependent on classifier performance.
Source: §1 · p. 2Method
The paper introduces CCC/AUCCC for evaluating classification UQ and UDist, a cascade model that distills confidence estimated by deep ensembles.
Source: §1 · p. 2Results
UDist outperforms all UQ baselines; on ChestX-ray14, its improvement margin is 0.7%, while deep ensemble provides 0.5% advancement over DenseNet.
Source: §4.2 · p. 7Takeaways & Limitations
CCC analysis unifies evaluation of in-distribution calibration and out-of-distribution generalization by treating out-of-distribution classifications as inaccurate.
Source: §2.2 · p. 4Over-confident training-set uncertainty estimates remain a challenge; on CIFAR-10, a base model’s AUCCC exceeds 0.99, much higher than on the test set.
Source: Over-confidence issue · p. 8
Abstract
from arXiv · showhide
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.
1 Introduction
Biomedical decision making motivates uncertainty quantification, but classification UQ methods are hard to compare without unified quantitative evaluation. The paper proposes CCC/AUCCC and UDist, which distills confidence estimated by deep ensembles.
1 Introduction
- UQ is important for safety-critical medical decisions because it can help clinicians intervene when automated decisions are uncertain.The paper frames UQ as an important capability for explainable AI.Source: §1 · p. 1
- Classification UQ examines calibration on in-distribution inputs and uncertainty on out-of-distribution inputs, separately from classification accuracy.The text notes that a classifier may be accurate yet miscalibrated, or the reverse.Source: §1 · pp. 1–2
- Classification UQ methods lack a unified quantitative evaluation, and existing evaluations can be qualitative or dependent on classifier performance.The proposed CCC analysis is intended to evaluate both in-distribution calibration and out-of-distribution generalization.Source: §1 · p. 2
- UDist is a cascade model that distills deep-ensemble confidence because uncertainty estimates generally lack ground-truth labels.The paper reports that experiments validate this scheme over deep ensembles on UQ.Source: §1 · p. 2
2 Evaluating Uncertainty Quantification
The paper frames UQ as distinguishing correct from incorrect classifications using confidence, then defines CCC analysis and AUCCC to evaluate that separation across confidence thresholds. CCC is designed to avoid sensitivity to small confidence perturbations and classifier performance.
2.1 A Discriminative View of Uncertainty Quantification
- A discriminative view treats UQ as separating accurate from inaccurate classifications by assigning them different confidence scores.The desired separation is orthogonal to how well the classifier itself performs.Source: §2.1 · p. 2
- Cross entropy and Brier score can rank equivalent UQ models differently after uniform confidence shifts or small endpoint perturbations.The text argues that a fair UQ metric should not be sensitive to such perturbations.Source: §2.1 · p. 3
2.2 Confidence-Classification Characteristic Analysis
- CCC maps each instance to a classification outcome and confidence-based accept/reject decision, then tracks correct-accept and correct-reject rates.Its curve plots CAccR against 1−CRejR as confidence thresholds vary.Source: Figure 1 · p. 3, §2.2 · p. 4
- AUCCC summarizes the CCC curve: random confidence has AUCCC 0.5, while perfect confidence separation is expected to yield 1.0.CCC treats out-of-distribution classifications as inaccurate, allowing the analysis to cover in-distribution calibration and out-of-distribution generalization.Source: §2.2 · p. 4
- CCC uses all confidence thresholds, is robust to score perturbations that preserve ordering, and is insensitive to classification performance.Unlike ROC, CCC evaluates accepted-prediction accuracy across confidence thresholds at a fixed classification threshold.Source: §2.2 · p. 4
3 Boosting UQ Performance via Uncertainty Distillation
UDist separates confidence estimation from classification by training a cascade to mimic softened deep-ensemble confidence. The confidence model receives both the image and the ensemble output.
3 Boosting UQ Performance via Uncertainty Distillation
- UDist uses knowledge distillation to distill uncertainty estimated by a deep ensemble, addressing the lack of ground truth needed to extract actual-class output at inference and effectively boosting UQ performance.Max softmax output is an alternative, but it is over-confident at inaccurate classification.Source: §3 · p. 5
- To reduce over-confidence from over-fitting, independently trained classifiers are averaged and temperature-scaled to soften their probability outputs.The paper calls training-set probabilities higher than test-set probabilities the over-confidence issue.Source: §3 · p. 5
- The softened ensemble probability assigned to the actual class, Pt, serves as the confidence target in a cross-entropy confidence loss.Pt is generally unavailable during inference because the actual class is unknown.Source: §3 · p. 5
- The confidence cascade takes both the input image and softened ensemble probabilities, since confidence depends jointly on the input and output.The ensemble's softened actual-class output supplies the confidence-loss target.Source: §3 · pp. 5–6, Figure 2 · p. 5
4 Experiments
Experiments evaluate UQ on CIFAR-10, ChestX-ray14, and out-of-distribution (OOD) samples. UDist outperforms baselines in UQ on the natural and medical image datasets and distinguishes OOD from in-distribution samples across settings.
4.1 CIFAR-10
- The experiments assess AUCCC on CIFAR-10 and ChestX-ray14, and report classification accuracy and AUCCC for CIFAR-10.CIFAR-10 uses VGG, DenseNet, deep ensembles, and UDist; the described models use small networks due to computation constraints.Source: §4 · p. 6, Experiment Settings · p. 6, Table 1 · p. 6
Experiment Settings
- On CIFAR-10, UDist further improves UQ over deep ensembles with temperature scaling, while DenseNet ensembles improve both AUROC and AUCCC over the reported baselines.The experiments use CIFAR-10 as the natural-image dataset; Table 1 covers classification and UQ performance.Source: Experiment Settings · pp. 6–7, Table 1 · p. 6
4.2 ChestX-ray14
- For ChestX-ray14, the experiments use 112,120 X-ray images from 30,805 patients, each labeled for 14 diseases.The multi-label confidence loss averages confidence loss across classes.Source: §4.2 · p. 7
- UDist outperforms all baselines in UQ on ChestX-ray14, with a 0.7% improvement margin compared with the 0.5% advancement of deep ensembles over DenseNet.The reported comparisons concern UQ performance on this multi-label medical image dataset.Source: §4.2 · p. 7, Table 2 · p. 7
4.3 On Out-of-Distribution Samples
- UDist effectively distinguishes OOD from in-distribution samples across settings; AUCCC is generally higher than I/O AUROC, while its improvement is more significant under I/O AUROC.The experiments compare CIFAR-10 with SVHN and ChestX-ray14 with OCT2017, using equal numbers of OOD and in-distribution samples.Source: §4.3 · p. 7, Results · p. 8, Table 3 · p. 8
5 Discussions
The discussion identifies over-confidence in training-set uncertainty estimates as a challenge for UDist and notes a limitation in how classification information enters its cascade.
5 Discussions
- Training-set over-confidence remains a challenge despite using ensemble and temperature-scaling techniques to alleviate it.On CIFAR-10, a base model's training-set AUCCC exceeds 0.99 and is much higher than its test-set AUCCC; independent uncertainty-estimation datasets are proposed for future work.Source: Over-confidence issue · p. 8
Over-confidence issue.
- In the cascade, classification information is concatenated with the image input, then decays through convolution and normalization layers, especially for multi-label classification.The discussion suggests conditional-generation techniques may help address this issue.Source: On the cascade inputs · p. 8
6 Conclusion
The conclusion presents CCC analysis and UDist as the paper's two contributions to uncertainty quantification.
6 Conclusion
- The paper proposes Confidence-Classification Characteristic analysis to unify in-distribution calibration and out-of-distribution generalization evaluation, and UDist to improve UQ over strong baselines.The conclusion identifies addressing over-confidence and simplifying the cascade as future work.Source: §6 · p. 8