Quantifying Ambiguity in Categorical Annotations: A Measure and Statistical Inference Framework
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916990937989120 |
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| author | Klugmann, Christopher Kondermann, Daniel |
| author_facet | Klugmann, Christopher Kondermann, Daniel |
| contents | Human-generated categorical annotations frequently produce empirical response distributions (soft labels) that reflect ambiguity rather than simple annotator error. We introduce an ambiguity measure that maps a discrete response distribution to a scalar in the unit interval, designed to quantify aleatoric uncertainty in categorical tasks. The measure bears a close relationship to quadratic entropy (Gini-style impurity) but departs from those indices by treating an explicit "can't solve" category asymmetrically, thereby separating uncertainty arising from class-level indistinguishability from uncertainty due to explicit unresolvability. We analyze the measure's formal properties and contrast its behavior with a representative ambiguity measure from the literature. Moving beyond description, we develop statistical tools for inference: we propose frequentist point estimators for population ambiguity and derive the Bayesian posterior over ambiguity induced by Dirichlet priors on the underlying probability vector, providing a principled account of epistemic uncertainty. Numerical examples illustrate estimation, calibration, and practical use for dataset-quality assessment and downstream machine-learning workflows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04366 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantifying Ambiguity in Categorical Annotations: A Measure and Statistical Inference Framework Klugmann, Christopher Kondermann, Daniel Machine Learning Human-generated categorical annotations frequently produce empirical response distributions (soft labels) that reflect ambiguity rather than simple annotator error. We introduce an ambiguity measure that maps a discrete response distribution to a scalar in the unit interval, designed to quantify aleatoric uncertainty in categorical tasks. The measure bears a close relationship to quadratic entropy (Gini-style impurity) but departs from those indices by treating an explicit "can't solve" category asymmetrically, thereby separating uncertainty arising from class-level indistinguishability from uncertainty due to explicit unresolvability. We analyze the measure's formal properties and contrast its behavior with a representative ambiguity measure from the literature. Moving beyond description, we develop statistical tools for inference: we propose frequentist point estimators for population ambiguity and derive the Bayesian posterior over ambiguity induced by Dirichlet priors on the underlying probability vector, providing a principled account of epistemic uncertainty. Numerical examples illustrate estimation, calibration, and practical use for dataset-quality assessment and downstream machine-learning workflows. |
| title | Quantifying Ambiguity in Categorical Annotations: A Measure and Statistical Inference Framework |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.04366 |