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Credal Prediction based on Relative Likelihood
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Proposes Credal Relative Likelihood (CreRL), an ensemble method that approximates credal sets from relative-likelihood alpha-cuts using staged early-stopped training and a ToBias bias initialization to encourage diversity.
Problem
Learning credal predictors that represent epistemic uncertainty as sets of distributions, with a principled criterion for which models are plausible and a controllable trade-off between coverage and efficiency.
Approach
Define the credal set as predictions of all models whose relative likelihood exceeds a threshold alpha, approximate this alpha-cut with an ensemble trained to staged relative-likelihood thresholds, and diversify members by initializing final-layer biases at large constants so that initial predictions sit at simplex vertices.
Key results
- On CIFAR-10 OoD detection (AUROC), CreRL with alpha=1.0 achieves the best or on-par results, e.g., 0.957 on FMNIST and 0.918 on Places, with CreWra best on SVHN (0.957 vs 0.948).
- CreRL covers a wide range of coverage values via alpha, whereas CreEns only reaches low coverage and CreNet collapses to near point predictions.
- Authors report that the method is only positioned in the high-coverage half of the Pareto front on QualityMRI.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CreRL₁.₀ instead of the strongest listed baseline | ResNet18 trained on CIFAR-10 · SVHN, Places, CIFAR-100, FMNIST, and ImageNet OoD detection | AUROC: SVHN: 0.957 ± 0.003 vs 0.948 ± 0.003; Places: 0.918 ± 0.000 vs 0.918 ± 0.002; CIFAR-100: 0.916 ± 0.000 vs 0.916 ± 0.001; | Mixed |
| Lower the CreRL relative-likelihood threshold α | CreRL on CIFAR-10 · SVHN, Places, CIFAR-100, FMNIST, and ImageNet OoD detection | AUROC: CreRL₁.₀: 0.948 ± 0.003, 0.918 ± 0.002, 0.916 ± 0.001, 0.957 ± 0.002, 0.889 ± 0.002; CreRL₀.₂: 0.582 ± 0.041, 0.736 ± 0. | Hurt |
Surprising findings
- CreEns with alpha=0.95 yields AUROC 0.500 on all OoD datasets, indicating a degenerate result.
- Lowering alpha for CreRL degrades OoD AUROC substantially (e.g., 0.582 on SVHN at alpha=0.2), contrary to the intuition that broader credal sets would help.
Limitations
- Evaluated only on neural networks; ToBias initialization is specific to neural networks.
- Convex credal sets are built from interval bounds, producing larger-than-necessary sets; convex hull alternative not evaluated.
- No theoretical approximation-quality guarantees on how many ensemble members are needed.
Experimental setup
Datasets: ChaosNLI CIFAR-10 CIFAR-10H QualityMRI SVHN Places365 CIFAR-100 FashionMNIST ImageNet
Benchmarks: ChaosNLI CIFAR-10 QualityMRI CIFAR-10H
Metrics: coverage efficiency AUROC
Baselines: CreWra CreEns CreBNN CreNet
Builds on: credal wrapper credal ensembling credal deep ensembles conformal credal sets
Closest papers by meaning
- Credal Learning Theory (NeurIPS 2024 · similarity 0.92)
- Conformalized Credal Set Predictors (NeurIPS 2024 · similarity 0.91)
- Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification (ICLR 2025 · similarity 0.90)
- Credal Deep Ensembles for Uncertainty Quantification (NeurIPS 2024 · similarity 0.88)
- Learning from Uncertain Data: From Possible Worlds to Possible Models (NeurIPS 2024 · similarity 0.83)
- Rethinking Aleatoric and Epistemic Uncertainty (ICML 2025 · similarity 0.83)
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