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Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression
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Proposes a generalized auxiliary uncertainty estimator for vision regression that models aleatoric uncertainty with a Laplace likelihood and epistemic uncertainty via a Dirichlet posterior over discretized prediction errors (DIDO).
Problem
Robust aleatoric and epistemic uncertainty estimation for vision regression tasks using auxiliary uncertainty estimators that don't modify the main model, especially under noisy inputs and OOD data, where epistemic uncertainty and AuxUE robustness have been underexplored.
Approach
Discretize per-sample prediction errors into balanced bins (one-hot targets) and train a Dirichlet posterior over these classes with an evidential ELBO loss, measuring epistemic uncertainty as K/S; aleatoric uncertainty uses a Laplace NLL in a separate AuxUE head.
Key results
- On age-estimation OOD detection, DIDO reaches AUC 100 on CIFAR10, SVHN, MNIST and FashionMNIST, outperforming Deep Ensembles (99.2 on CIFAR10).
- On KITTI-C aleatoric estimation, the Laplace-based head gives the lowest AUSE-RMSE at the highest severities (e.g., 1.760 vs 2.202 for Gaussian at severity 5 with separate encoders).
- On KITTI vs NYU dataset change, shared-encoder DIDO achieves AUC 98.4 and AUPR 99.4, versus 78.4 AUC for the best training-free baseline (Grad.).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DIDO instead of Deep Ensembles for OOD detection | ResNet34 age estimation · AFAD test → CIFAR10 OOD | AUC: 99.2 -> 100 | Helped |
| Use DIDO instead of Deep Ensembles for OOD detection | ResNet34 age estimation · AFAD test → Oxford-Pets OOD | AUC: 56.1 -> 55.9 | No clear effect |
| Use DIDO instead of Deep Ensembles for OOD detection | ResNet34 age estimation · AFAD test → FakeData OOD | AUC: 33.2 -> 80.8 | Helped |
| Use Laplace rather than Gaussian noise modeling (ablation) | SLURP aleatoric AuxUE · KITTI Eigen-split validation, corruption severity 5 | AUSE-REL: 0.071 -> 0.059 | Helped |
| Share the aleatoric and epistemic encoders (ablation) | SLURP aleatoric AuxUE · KITTI Eigen-split validation, corruption severity 0 | AUSE-RMSE: 0.203 -> 0.205 | Hurt |
| Use DIDO rather than the strongest listed baseline | BTS monocular depth estimator · KITTI Eigen-split validation → NYU indoor OOD | AUC: 78.4 -> 98.4 | Helped |
| Use DIDO rather than LDU for OOD detection | BTS monocular depth estimator · KITTI Seg-Depth-C, corruption severity 5 | AUC: 96.5 -> 99.0 | Helped |
| Use DIDO rather than Deep Ensembles for tabular OOD detection | Red wine quality regression · Red wine quality OOD detection | AUC: 0.548 -> 0.936 | Helped |
| Replace the Generalized Gaussian noise assumption with Laplace (ablation) | BayesCap super-resolution AuxUE · Set5, corruption severity 5 | UCE: 0.0525 -> 0.0040 | Helped |
| Use the maximum Dirichlet output as aleatoric uncertainty instead of the Laplace head (ablation) | BTS monocular depth AuxUE · KITTI Eigen-split validation, S=0 | AUSE-RMSE: 0.203 -> 0.283 | Hurt |
| Modify the main-task BTS model with SinglePU rather than retaining the original | BTS monocular depth estimator · KITTI Eigen-split validation | absrel: 0.056 -> 0.065 | Hurt |
Surprising findings
- Evidential learning (Evi.) baseline scores AUC 50.0 on several age-estimation OOD datasets, near chance.
- The Oxford-Pets OOD case is a failure mode for DIDO (AUC 55.9 vs 82.9 for the aleatoric head), attributed to pet images resembling facial features.
Limitations
- On Oxford-Pets OOD detection, DIDO underperforms the aleatoric head and Deep Ensembles.
- On the sky OOD metric (Sky-All), DIDO is slightly worse than Deep Ensembles and gradient-based methods.
- Discretized Dirichlet outputs underperform as aleatoric estimators than direct distribution-based heads.
Experimental setup
Datasets: AFAD KITTI NYU ImageNet CIFAR10 SVHN MNIST FashionMNIST Oxford-Pets red wine quality Set5 Set14
Benchmarks: AFAD OOD detection (CIFAR10, SVHN, MNIST, FashionMNIST, Oxford-Pets, FakeData) KITTI-C aleatoric AUSE/AURG KITTI vs NYU dataset change KITTI Seg-Depth sky OOD Set5/Set14/BSDS100 UCE super-resolution toy 1D examples red wine OOD
Metrics: AUC AUPR AUSE-REL AUSE-RMSE AURG-REL AURG-RMSE UCE Sky-All MAE RMSE
Baselines: LDU Evidential learning Deep Ensembles Gradient-based uncertainty Dropout-injection variance Gaussian NLL NIG
Builds on: ConfidNet SLURP BayesCap Evidential deep learning Deep Ensembles
Closest papers by meaning
- Evaluating Robustness of Predictive Uncertainty Estimation: Are Dirichlet-based Models Reliable? (ICML 2021 · similarity 0.87)
- Deep Deterministic Uncertainty: A New Simple Baseline (CVPR 2023 · similarity 0.87)
- Training-Free Uncertainty Estimation for Dense Regression: Sensitivity as a Surrogate (AAAI 2022 · similarity 0.86)
- SURE: SUrvey REcipes for building reliable and robust deep networks (CVPR 2024 · similarity 0.85)
- Uncertainty Estimation by Flexible Evidential Deep Learning (NeurIPS 2025 · similarity 0.85)
- One Step Closer to Unbiased Aleatoric Uncertainty Estimation (AAAI 2024 · similarity 0.85)
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