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Uncertainty Estimation by Flexible Evidential Deep Learning
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Proposes flexible evidential deep learning (F-EDL), which replaces the Dirichlet over class probabilities in EDL with a flexible Dirichlet distribution to improve uncertainty quantification in classical, long-tailed, and noisy in-distribution settings while keeping single-forward-pass efficiency.
Problem
Evidential deep learning's restrictive Dirichlet assumption over class probabilities limits its UQ robustness and generalization, especially with noisy in-distribution data, long-tailed classes, and distribution shifts.
Approach
Predict the parameters (alpha, p, tau) of a flexible Dirichlet distribution, a generalization of the Dirichlet, via three neural heads; train with expected MSE under FD plus a Brier-score regularizer on p; derive closed-form label-wise variance-based TU/AU/EU measures.
Key results
- On CIFAR-10 classical setting, F-EDL reaches 91.19% test accuracy and 91.20 AUPR on SVHN/C-100 OOD detection, outperforming DAEDL (91.11 and 85.54).
- On CIFAR-10-LT heavy imbalance (rho=0.01), F-EDL attains 63.73% test accuracy and 85.99 misclassification AUPR, versus 63.36 and 82.15 for DAEDL.
- F-EDL adds only 1.8% parameter overhead on VGG-16 and runs 1.3% slower than EDL, over 50% faster than DAEDL on CIFAR-10.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the Dirichlet class-probability distribution with the flexible Dirichlet formulation | EDL · CIFAR-10 and CIFAR-100 UQ tasks | AUPR, OOD detection | Helped |
| Learn both allocation probabilities p and dispersion τ instead of fixing them (ablation) | F-EDL · DMNIST noisy ID | UQ performance | Helped |
| Fix allocation probabilities p to a uniform distribution (ablation) | F-EDL · DMNIST noisy ID | UQ performance | Hurt |
| Fix allocation probabilities p to normalized concentration parameters (ablation) | F-EDL · DMNIST noisy ID | UQ performance | Hurt |
| Fix dispersion τ=1 (ablation) | F-EDL · DMNIST noisy ID | UQ performance | Hurt |
| Fix both p and τ (ablation) | F-EDL · DMNIST noisy ID | UQ performance | Hurt |
| Use F-EDL rather than EDL | CIFAR-10 epistemic uncertainty estimation · CIFAR-10 with increasing training data | epistemic uncertainty trend | Helped |
Surprising findings
- On CIFAR-100 with ID SVHN/TIN OOD, F-EDL's test accuracy is higher but its confidence AUPR is 94.01 versus 86.00 for DAEDL, while in the classical CIFAR-100 Dropout and EDL baselines are competitive on some OOD metrics.
Limitations
- Currently limited to classification; extension to regression is future work.
- Does not fully disentangle aleatoric and epistemic uncertainty components.
- Still relies on external regularization (spectral normalization) to control epistemic uncertainty.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 CIFAR-10-LT Dirty-MNIST SVHN TinyImageNet FMNIST CIFAR-10-C
Benchmarks: CIFAR-10 CIFAR-100 CIFAR-10-LT Dirty-MNIST CIFAR-10-C
Metrics: test accuracy AUPR misclassification detection AUPR OOD detection AUPR distribution shift detection AUPR
Baselines: Dropout EDL I-EDL R-EDL DAEDL MSP DDU
Builds on: evidential deep learning flexible Dirichlet distribution prior networks deterministic uncertainty methods subjective logic
Closest papers by meaning
- Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage? (NeurIPS 2024 · similarity 0.94)
- Calibrating LLMs with Information-Theoretic Evidential Deep Learning (ICLR 2025 · similarity 0.91)
- Uncertainty Estimation by Density Aware Evidential Deep Learning (ICML 2024 · similarity 0.91)
- Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods? (ICML 2024 · similarity 0.90)
- ANEDL: Adaptive Negative Evidential Deep Learning for Open-Set Semi-supervised Learning (AAAI 2024 · similarity 0.88)
- Hyper-opinion Evidential Deep Learning for Out-of-Distribution Detection (NeurIPS 2024 · similarity 0.87)
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