Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Rethinking Aleatoric and Epistemic Uncertainty
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Proposes a decision-theoretic alternative to the aleatoric-epistemic view of uncertainty, deriving uncertainty, expected uncertainty reduction, and performance/dispersion decompositions from a loss function, and reinterpreting BALD as an imperfect estimator.
Problem
The aleatoric-epistemic view of uncertainty in machine learning is overloaded with multiple, incoherent mathematical definitions, conflating predictive uncertainty, predictive performance, and data dispersion.
Approach
Define predictive uncertainty as the expected loss of the Bayes-optimal action under beliefs, derive expected uncertainty reduction from a data-generating policy to get an irreducible-reducible decomposition, and separate model uncertainty from performance and dispersion; view BALD as an estimator of long-run predictive information gain and of one-step parameter information gain.
Key results
- In conjugate-model experiments, BALD (EIG_theta) is shown to be a coarse estimator of infinite-step predictive information gain, with errors that shrink as n increases.
- EIG_theta is a more accurate approximation of the one-step true parameter information gain than of the infinite-step predictive information gain, which the authors argue is consistent with BALD's utility in active learning.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BALD (EIGθ) instead of predictive entropy for active-learning data acquisition | Active learning · Active learning | predictive performance | Helped |
Surprising findings
- Under some settings, assuming infinite-step information gain equals current predictive entropy would be more accurate than estimating it with BALD (EIG_theta), per cited prior results.
Limitations
- Experiments use extremely simple setups (1D GP regression and conjugate models), so generality is limited.
- Proposed estimators are derived from subjective models and carry no general accuracy guarantee.
- Practical EUR estimation depends on approximations to the data-generating process and belief updating.
Experimental setup
Datasets: synthetic 1D regression data synthetic discrete and continuous conjugate model data
Metrics: estimation error of expected information gain expected uncertainty reduction expected score discrepancy
Baselines: BALD predictive entropy aleatoric-epistemic decomposition
Builds on: BALD Bayesian experimental design martingale posterior proper scoring rules
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