Provable Uncertainty Decomposition via Higher-Order Calibration

2024-12-25

AI Summary

This work addresses the lack of theoretical guarantees for decomposing model uncertainty into aleatoric and epistemic components. We propose a higher-order calibration framework that achieves, for the first time without distributional assumptions on the data, a semantically precise and verifiable decomposition of these two uncertainty types. Our method leverages *k*-snapshots—each sample associated with *k* independent conditional labels—to define an estimable higher-order calibration metric, enabling optimization and evaluation of Bayesian, ensemble, and other higher-order predictors. Theoretically, we (1) establish assumption-free calibration guarantees with respect to the true aleatoric uncertainty, and (2) introduce the first formal, testable criterion for uncertainty decomposition. Empirical validation on image classification demonstrates the decomposition’s reasonableness and interpretability, substantially enhancing the credibility and practical utility of uncertainty semantics.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have proposed such decompositions, they lack the type of formal guarantees we provide. Our method is based on the new notion of higher-order calibration, which generalizes ordinary calibration to the setting of higher-order predictors that predict mixtures over label distributions at every point. We show how to measure as well as achieve higher-order calibration using access to $k$-snapshots, namely examples where each point has $k$ independent conditional labels. Under higher-order calibration, the estimated aleatoric uncertainty at a point is guaranteed to match the real-world aleatoric uncertainty averaged over all points where the prediction is made. To our knowledge, this is the first formal guarantee of this type that places no assumptions whatsoever on the real-world data distribution. Importantly, higher-order calibration is also applicable to existing higher-order predictors such as Bayesian and ensemble models and provides a natural evaluation metric for such models. We demonstrate through experiments that our method produces meaningful uncertainty decompositions for image classification.

Problem

• Model Uncertainty
• Stochastic Uncertainty
• Epistemic Uncertainty Calibration

Innovation

• High-order Calibration
• Bayesian Models
• k-Snapshot Technique