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Credal Learning Theory
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Lays foundations of Credal Learning Theory: uses credal sets inferred from a sample of training sets to derive PAC-style generalization bounds under distribution drift for finite and infinite hypothesis spaces, recovering classical SLT results as special cases.
Problem
Classical statistical learning theory assumes a single training distribution, so its generalization bounds fail to account for distribution shift (domain adaptation/generalization) across training and deployment data.
Approach
Model epistemic uncertainty over data-generating distributions with a credal set (convex set of probabilities) inferred from multiple training sets (via objectivist belief-function/epsilon-contamination or subjectivist lower-probability routes), and derive expected-risk bounds that hold for all distributions in the credal set, using its extreme points to tighten union bounds and Rademacher complex
Key results
- In synthetic experiments with well-separated credal extremes, the credal bound epsilon*(delta) is tighter than the classical bound at small n (e.g. 0.745 vs 0.760 at n=10), converging as n grows.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the credal-set-specific bound instead of the classical uniform SLT bound | Finite hypothesis space with realizability · Synthetic bound tightness, Gaussian extrema N(-5,1), N(0,1), N(5,1), n=10 | risk bound ε: 0.76009 -> 0.74500 | Helped |
| Use the credal-set-specific bound instead of the classical uniform SLT bound | Finite hypothesis space with realizability · Synthetic bound tightness, Gaussian extrema N(-0.1,1), N(0,1), N(0.1,1), n=10 | risk bound ε: 0.76009 -> 0.73777 | Helped |
| Use the credal-set-specific bound instead of the classical uniform SLT bound | Finite hypothesis space with realizability · Synthetic bound tightness, n=500, both Gaussian-extrema settings | risk bound ε: 0.01520 -> 0.01516; 0.01520 -> 0.01514 | Helped |
Surprising findings
- The credal bound offers little improvement when the sample size is large, since the classical bound is already small.
Limitations
- Only the zero-one loss is considered
- Assumes the true test distribution lies in the credal set, which is not formally verified
- No experiments on real datasets
Experimental setup
Datasets: synthetic Gaussian data
Metrics: bound value epsilon empirical risk gap
Builds on: classical PAC learning bounds Rademacher complexity Dempster-Shafer theory of belief functions Walley's natural extension
Closest papers by meaning
- Credal Prediction based on Relative Likelihood (NeurIPS 2025 · similarity 0.92)
- Conformalized Credal Set Predictors (NeurIPS 2024 · similarity 0.90)
- Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification (ICLR 2025 · similarity 0.87)
- Credal Deep Ensembles for Uncertainty Quantification (NeurIPS 2024 · similarity 0.84)
- Distributional regression: CRPS-error bounds for model fitting, model selection and convex aggregation (NeurIPS 2024 · similarity 0.83)
- Learning from Uncertain Data: From Possible Worlds to Possible Models (NeurIPS 2024 · similarity 0.83)
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