Conformalized Credal Regions for Classification with Ambiguous Ground Truth

2024-11-07

arXiv.org

AI Summary

In label-ambiguous classification—where ground-truth labels are intrinsically uncertain and prior knowledge is unavailable—existing methods lack rigorous uncertainty quantification. This paper pioneers the extension of conformal prediction to fuzzy truth settings, proposing a distribution-free framework for constructing credal regions: sets of probability distributions over classes that provably contain the true label distribution. Grounded in conformal inference, our method guarantees marginal coverage while rigorously disentangling epistemic uncertainty (arising from model or data limitations) from aleatoric uncertainty (inherent to label ambiguity). Unlike classical conformal predictors—which output singleton or set-valued class predictions—our approach yields compact, probabilistically calibrated credal regions. Empirical evaluation on synthetic and real-world benchmarks demonstrates substantial reductions in region size (improved tightness) without compromising coverage, alongside theoretically grounded robustness guarantees under distribution shift.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

An open question in emph{Imprecise Probabilistic Machine Learning} is how to empirically derive a credal region (i.e., a closed and convex family of probabilities on the output space) from the available data, without any prior knowledge or assumption. In classification problems, credal regions are a tool that is able to provide provable guarantees under realistic assumptions by characterizing the uncertainty about the distribution of the labels. Building on previous work, we show that credal regions can be directly constructed using conformal methods. This allows us to provide a novel extension of classical conformal prediction to problems with ambiguous ground truth, that is, when the exact labels for given inputs are not exactly known. The resulting construction enjoys desirable practical and theoretical properties: (i) conformal coverage guarantees, (ii) smaller prediction sets (compared to classical conformal prediction regions) and (iii) disentanglement of uncertainty sources (epistemic, aleatoric). We empirically verify our findings on both synthetic and real datasets.

Problem

• Fuzzy Probabilistic Machine Learning
• Confidence Region Determination
• Label Distribution Uncertainty

Innovation

• Fuzzy Probabilistic Machine Learning
• Confidence Region Identification
• Uncertainty Quantification