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Uncertainty Estimation by Density Aware Evidential Deep Learning
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Proposes DAEDL, which multiplies EDL logits by a GDA-based normalized feature-space density and uses an exponential activation with no "1" prior term, improving OOD detection, classification, and calibration.
Problem
Evidential deep learning (EDL) fails to reflect distance from training data when quantifying uncertainty, hurting OOD detection, and its parameterization limits classification accuracy.
Approach
Integrate a normalized Gaussian discriminant analysis feature-space density of the test example with EDL logits at prediction time, and replace the conventional parameterization (alpha = 1 + ReLU(logits)) with alpha = exp(logits), which removes the uniform prior term and aligns expected class probabilities with softmax; spectral normalization is added to keep feature distances meaningful.
Key results
- On CIFAR-10, DAEDL reaches 91.11% test accuracy versus 89.20% for the runner-up I-EDL and a Brier score of 14.27 versus 22.84 for PostNet.
- OOD detection AUPR on CIFAR-10 to SVHN is 85.50 for DAEDL versus 83.26 for I-EDL, a gain of 2.24.
- On distribution shift detection (MNIST-C), DAEDL achieves 92.43 AUPR, outperforming the runner-up MSP by 6.37.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DAEDL instead of I-EDL | OOD detection · MNIST → KMNIST and MNIST → FMNIST | AUPR: improvements of 1.56, 1.59, 0.94, and 1.01 | Helped |
| Use DAEDL instead of I-EDL | OOD detection · CIFAR-10 → SVHN and CIFAR-10 → CIFAR-100 | AUPR: improvements of 2.24, 2.58, 2.81, and 3.35 | Helped |
| Use DAEDL instead of the strongest baseline | CIFAR-10 classification and confidence calibration · CIFAR-10 | test accuracy, AUPR, and Brier score: 1.91; 0.36; 8.57 | Helped |
| Use DAEDL instead of MSP | distribution shift detection · MNIST-C | AUPR: +6.37 | Helped |
| Use DAEDL instead of MSP | distribution shift detection · CIFAR-10-C severity levels 1–5 | AUPR: +1.50, +1.35, +1.67, +2.30, and +2.73 | Helped |
| Add EXP (alternative exponential parameterization) to EDL (ablation) | EDL · CIFAR-10 | test accuracy: 83.55 $\pm$ 0.6 -> 88.59 $\pm$ 0.4 | Helped |
| Add EXP to EDL (ablation) | EDL · CIFAR-10 | AUPR (misclassified image detection): 97.86 $\pm$ 0.2 -> 98.42 $\pm$ 0.1 | Helped |
| Add feature-space density integration (DE) to EXP (ablation) | DAEDL without spectral normalization · CIFAR-10 | AUPR (misclassified image detection): 98.42 $\pm$ 0.1 -> 99.01 $\pm$ 0.0 | Helped |
| Add DE to EXP (ablation) | DAEDL without spectral normalization · CIFAR-10 → SVHN | AUPR (aleatoric): 80.39 $\pm$ 2.0 -> 85.02 $\pm$ 0.7 | Helped |
| Add spectral normalization (SN) to EXP (ablation) | DAEDL without density integration · CIFAR-10 | test accuracy: 88.59 $\pm$ 0.4 -> 91.11 $\pm$ 0.2 | Helped |
| Add SN to EXP (ablation) | DAEDL without density integration · CIFAR-10 → SVHN | AUPR (aleatoric): 80.39 $\pm$ 2.0 -> 84.53 $\pm$ 0.9 | Helped |
| Add DE to EXP + SN (ablation) | DAEDL · CIFAR-10 | test accuracy: 91.11 $\pm$ 0.2 -> 91.11 $\pm$ 0.2 | No clear effect |
Surprising findings
- EDL and I-EDL perform worse than the softmax-based MSP baseline on distribution shift detection.
Limitations
- In complex scenarios, EDL outputs and feature space density may not accurately capture uncertainty.
- Experiments limited to image classification benchmarks (MNIST, CIFAR-10) with small architectures.
- Regression extension left as future work.
Experimental setup
Datasets: MNIST CIFAR-10 FMNIST KMNIST SVHN CIFAR-100 MNIST-C CIFAR-10-C
Benchmarks: MNIST CIFAR-10 FMNIST KMNIST SVHN CIFAR-100 MNIST-C CIFAR-10-C
Metrics: AUPR AUROC test accuracy Brier score
Baselines: Dropout KL-PN RKL-PN PostNet EDL I-EDL MSP
Builds on: evidential deep learning posterior network I-EDL spectral normalization
Closest papers by meaning
- Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage? (NeurIPS 2024 · similarity 0.91)
- Uncertainty Estimation by Flexible Evidential Deep Learning (NeurIPS 2025 · similarity 0.91)
- Calibrating LLMs with Information-Theoretic Evidential Deep Learning (ICLR 2025 · similarity 0.87)
- ANEDL: Adaptive Negative Evidential Deep Learning for Open-Set Semi-supervised Learning (AAAI 2024 · similarity 0.87)
- Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods? (ICML 2024 · similarity 0.86)
- Uncertainty Regularized Evidential Regression (AAAI 2024 · similarity 0.86)
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