Uncertainty-Aware Learning from Multi-Expert Interval Targets

An LLM judge evaluates outputs at scale. Experts should label only where it is least sure. Its natural escalation signal conflates two uncertainties: aleatoric, real disagreement in the expert pool, which labels cannot reduce, and epistemic, the judge's ignorance, which labels do reduce. A small Bayesian model separates them: a regression on labels already collected learns how far to trust a black-box judge's prediction. Both components follow as simple formulas, with no sampling or further judge calls. The components isolate on a real LLM judge against exactly known truth, and stated confidence is no guide to its actual error. On real human disagreement (ChaosNLI) the epistemic ranking removes 83% more error than total uncertainty for the same expert labels, though simply escalating the least-labelled items does as well there. We demonstrate we can estimate where a judge is ignorant rather than where experts genuinely disagree, and propose using this to direct expert labelling. Code and data are available at https://github.com/composo-ai/judge-uncertainty-decomposition.

Sea-ice stage of development (SoD) describes the age and associated thickness of sea ice and provides important information for navigation, and operational ice monitoring. SoD labels are obtained from operational ice charts, where trained analysts interpret satellite observations and assign standardized stage codes to regions with similar ice conditions. These codes often represent ranges of compatible ice thicknesses rather than exact physical values. Deep-learning methods can automate SoD mapping and commonly adopt operational ice charts as reference labels for training. These annotations are not exact, however; this is because chart interpretation relies on analyst judgement and on the observations available at the time, so different ice services may assign different SoD labels to the same conditions. We term this variation across independently produced expert annotations multi-annotator label uncertainty; collapsing the annotations into a single deterministic target discards this variation. A second source of uncertainty originates in the learned model itself. In this paper, we quantify both sources: annotation uncertainty from disagreement among independent ice-service charts and model uncertainty from the learned predictive models. We then evaluate their relationship by testing whether model uncertainty is higher where ice services disagree. We observe that supervision incorporating information from multiple annotators can improve this correspondence, with soft supervision achieving the highest overall correlation of 0.256. The relationship becomes substantially stronger near the ice edge, where model predictive uncertainty closely tracks multi-annotator disagreement, reaching a correlation of 0.704 within 0--10 km. Among the uncertainty-estimation approaches, Monte Carlo dropout provides the best-calibrated confidence estimates, with an expected calibration error of 0.050.

Imprecise annotations may support several plausible labelling distributions, yet learning methods often resolve this ambiguity into a single predictive distribution. This can obscure what the annotation evidence leaves unresolved. We introduce epistemic learning from credal supervision, a framework that uses convex sets of plausible labelling distributions, called credal sets, as supervision and learns sets of predictive distributions. We instantiate the framework with the pessimistic--optimistic credal classifier (POCC), which combines a shared backbone with two classification heads trained to minimise worst-case and best-case losses over the supervision sets. Their outputs define a predictive credal set whose spread provides an uncertainty score. We also show how credal labels can be obtained through a simple relaxation of existing probabilistic labels, reducing commitment to their precise probability assignments. This construction admits closed-form inner optimisation under cross-entropy loss, enabling efficient training. Assuming the supervision sets contain the true conditional label distributions, and other regularity assumptions, we establish a finite-sample generalisation bound for the averaged predictor with an explicit penalty for supervision imprecision. We evaluate POCC using human annotator disagreement and teacher predictions, alongside label smoothing as a controlled proxy for annotation imprecision. Across these settings, POCC achieves a favourable balance of predictive accuracy, calibration, and uncertainty-based selective classification versus competitive baselines.